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Geometry/Parallelograms. Parallelograms. A parallelogram is a geometric figure with two pairs of parallel sides. Parallelograms are a special type of quadrilateral. The opposite sides are equal in length and the opposite angles are also equal. The area is equal to the product of any side and the distance between that side and the line containing the opposite side. Properties of Parallelograms. The following properties are common to all parallelograms (parallelogram, rhombus, rectangle, square)

Puzzles/Easy Sequence 1/Solution. < They are ascending powers of 2: 1 2 4 8 16 32 64 ... Note : 2 raise power 0 (i.e 2^0) equals 1

Puzzles/Easy Sequence 2/Solution. Add 1 2 3 4... OR x(x-1)/2+1 : 1 2 4 7 11 16 22 29 ... formula_1: 1 2 4 7 12 20 33 ... Add the three previous numbers: 1 2 4 7 13 24 44 ... The numbers with an odd number of ones in their binary representation: 1 2 4 7 8 11 13 ... or 1 10 100 111 1000 1011 1101 ... A formula for the formula_2th number is: formula_3, formula_4, formula_5.

Biochemistry/DNA and RNA. Deoxyribonucleic acid (DNA) and ribonucleic acid (RNA) are the information storage molecules and working templates for the construction of proteins. Every living cell and virus encodes its genetic information using either DNA or RNA. It is a true marvel of evolution that the vast amount of information needed to produce a human being can fit inside cells. Friedrich Miescher first isolated DNA and RNA from used surgical bandages in 1869. A series of experiments done by Oswald Avery, Colin MacLeod, and Maclyn McCarty in 1944 defined DNA as the genetic information. They injected virulent encapsulated bacteria into a mouse. As it a result, it died. On the contrary, nonvirulent nonencapsulated bacteria did not kill the mouse. Also, heating the virulent encapsulated bacteria and injecting did not kill the mouse either. The surprise lied in mixing the heat-killed virulent encapsulated bacteria with nonvirulent nonencapsulated bacteria did kill the mouse. Avery's group kept isolating factors until they discovered what killed the mouse, which was the DNA. In conclusion, the nonpathogenic bacteria was made pathogenic by DNA transfer from a pathogenic stain. A.D. Hershey and Martha Chase's work in 1952 reconfirmed that DNA is the carrier of genetic information. Hershey and Chase's group conducted an experiment involving two phages. One of the phages was radioactively labeled with heavy phosphorus to highlight the DNA and heavy sulfur to highlight the protein. The two phages inserted their "genetic material" into the bacterial cell. Afterwards, these cells were "blended" to remove the phage heads. The resulting radioactively-labeled heavy phosphorus was found in the cell. This experiment showed that DNA alone was sufficient to make new viruses, and therefore, defined as the genetic information. Rosalind Franklin, Chargaff, and other chemists provided information that led to the discovery of DNA as well. Franklin provided crystallographic data that implied a helical structure. Chargaff's rule said that the adenine content was equal to the thymine content and cytosine was equal to guanine. Also the aromaticity of the electron-rich purine and pyrimidine rings allowed for tautomer shifts between the keto and enol form. The keto tautomer (lactam) dominated at physiological pH. Garnering all this information, James Watson and Francis Crick discovered the structure of DNA (double-helix) in 1953. Structure of DNA and RNA. DNA is a polymer of nucleotides. Nucleotides consist of a pentose sugar (2-deoxyribose for DNA and ribose for RNA), a phosphate group (formula_1), and a nitrogen-containing base. There are five nitrogen bases - adenine, guanine, thymine, cytosine and uracil. Individual nucleotides are connected by phosphodiester bonds to form polynucleotides. DNA exists as a double helix of two (2) strands of polynucleotides. According to the principle of complementarity nucleotides A (adenine) bases are bound with a hydrogen bridge to the T (thymine) or U (uracil in case of RNA) on the other thread and similarly C (cytosine) bind themselves to G (guanine). This principle allows for DNA and RNA replication and for limited possibilities of repairing the genetic information when one of the threads gets damaged. Difference between DNA and RNA. DNA is the permanent genetic information storage medium, found in the nucleus of most cells of most living organisms. RNA is, in the case of eukaryotes, the medium that transfers the genetic information from the nucleus to the cytoplasm where proteins are synthesized. The most basic structural difference between a DNA molecule and an RNA molecule is that DNA lacks an hydroxyl group at its 2' carbon while RNA has an hydroxyl group at its 2' carbon. There are three major types of RNA: Each tRNA contains an "anticodon" which is a series of 3 bases that complements 3 bases on mRNA. Additionally, by 2005, other types of RNA, such as siRNA (small, interfering RNA) and miRNA have been characterized. DNA structure is typically a double stranded molecule with long chain of nucleotides, while RNA is a single stranded molecule " in most biological roles" and it has shorter chain of nucleotide. Deoxyribose sugar in DNA is less reactive because of the carbon- hydrogen bonds. DNA has small grooves to prevent the enzymes to attack DNA. on the other hand, RNA contain ribose sugar which is more reactive because of the carbon-hydroxyl bonds. RNA not stable in its alkaline conditions.RNA has larger grooves than that of DNA, which makes RNA easier to be attacked by enzymes. DNA has a unique features because of its helix geometry which is in B-form. DNA is protected completely by the body in which the body destroys any enzymes that cleave DNA. In contrast the helix geometry of RNA is in the A- form; RNA can be broken down and reused. RNA is more resistance to be damage by Ultra- violet rays, while DNA can be damaged if exposed to Ultra-violet rays. DNA can be found in nucleus, while RNA can be found in nucleus and cytoplasm. The bases of DNA are A,T,C,and G, DNA is a long polymer with phosphate and deoxyribose backbone. In contrast, RNA bases are A,U, C,and G, RNA backbone contain ribose and phosphate. The job of DNA on the cell is to store and transmit genetic information. RNA job is to transfer the genetic codes that are needed for the creation of proteins from the nucleus to the ribosome, this process prevents the DNA from leaving the nucleus, so DNA stays safe. Plasmid. Plasmids are small, circular DNA molecules that replicate separately from the much larger bacterial chromosome can be use in laboratory to manipulate genes. Plasmids can carry almost any gene and they can passed it on from one generation of bacteria to the next generation, therefore plasmids are key tools for “gene cloning” which is the production of multiple identical copies of a gene carrying piece of DNA =DNA Replication ;Semi-conservative replication= In the process of DNA replication, as cells divide, copies of DNA must be produced in order to transfer the genetic information. In DNA replication, the strands in the original DNA separate, and then each of the parent strands make copies by synthesizing complementary strands. Enzyme called helicase will start The process of replication by catalyzing the unwinding of protein of the double helix. This enzyme can break the H bonds between the complementary bases. These single strands now act as templates for the synthesis of new complementary strands. The energy for the reaction can be provided when a nucleoside triphosphate bonds to a sugar (at the end of a growing strand), and 2 phosphate group are cleaved. Then a T in the template forms H bond with an A in ATP, and a G on the template forms H bond with CTP. After the entire double helix of the parent DNA is copied, the new DNA molecule will form . The new DNA molecule is consist of one strand from the parent (original) DNA and one strand from the daughter strand( newly synthesized strand). This process is called "semi-conservative replication". Recombination. Recombination refers to ways in which DNA modification leads to distinct gene expressions and functions. Deletions, insertions and substitutions are the most useful changes implemented for the synthesis of new genes. Recombination techniques and recombinant DNA technologies has made possible the modification and creation of new genes for specific proposes. These techniques helps clone, amplified and introduce new DNA into suitable cells for replication. Restriction enzymes and DNA ligase play a vital role in the production of recombinant DNA. Vectors are useful for cloning. Plasmids or viral DNA (lambda Phage) used to introduced a DNA sequence into a cell is refer as vector. The semi-conservative hypothesis was confirmed by both Matthew Meselson and Franklin Stahl in 1958. The parent DNA was labeled with "heavy nitrogen," the radioisotope of fifteen. This radioactive nitrogen was made through growing E. coli with ammonium chloride (also with "heavy nitrogen") environment. Directly after the labeling of "heavy nitrogen" to the parent DNA strand, it was transferred to a medium with only regular nitrogen (isotope of fourteen). The proposed question was "What is the distribution between the two nitrogens in the DNA molecules after successive rounds of replication?" Using density-gradient equilibrium sedimentation, this question was answered. In this centrifugation, similar densities were grouped together in the tube. Afterwards, an absorbance was applied with ultra-violet light to determine the density bands of all the different kinds of DNA in the solution. After one generation, a unique single density band was shown. It was not exactly the band of heavy nitrogen nor the regular band of regular nitrogen, but rather halfway between the two. This proved that DNA was not conservative but semi-conservative due to this nitrogen hybrid. One generation after this one, there were two nitrogen-14 molecules and two hybrid nitrogen molecules. The probability and statistics of this second generation reassures the semi-conservative hypothesis. As DNA strands can combine and form molecules, it can also be melted, resulting in separation or denaturation. It is important to note that the heat from the melting process does not disrupt the DNA structure, but rather DNA helicase takes energy from the heat, separating the DNA strands. The denaturation process occurs at about ninety-four degrees Fahrenheit where the double strands are converted to single stands. Absorbance readings were taken to reconfirm the denaturation process. When the DNA molecule is in its double-stranded form, it absorbs less UV light. In its single-stranded form, it absorbs more UV light because the single strand is more exposed than its double-strand counterpart. This is known as the hypochromic effect. In a PCR, polymerase chain reaction, it utilizes this denaturation capability in its primary step. Afterwards, it is then annealed at fifty to sixty degrees Fahrenheit. In this step, this is where the primers bind to their corresponding flanking DNA base sequence. In the last step, DNA polymerization, it requires a few ingredients: heat-resistant DNA polymerase, magnesium ion, buffer, and corresponding nucleotides. The DNA polymerase requires heat resistance because throughout the entire process, it undergoes a constant temperatures changes. The magnesium stabilizes the phosphate backbone. The buffer prevents drastic changes in pH, because if the pH lies near the extremes on the scale, it may denature the DNA so drastically that it will not recombine. This final step of DNA polymerization happens at the "melting temperature." The melting temperature is the temperature at which half of the DNA is single-stranded and the other half is double-stranded. At this optimal temperature of seventy-two degrees Fahrenheit, the DNA is amplified with its respective primers, replicating at an exponential rate. =DNA manipulation: human's effort to desire DNA and "read" DNA= Restriction endonucleases. What's endonuclease?--Endonucleases are enzymes that can recognize specific base sequences in double-helical DNA and cleave, at specific places, both strands of that duplex. Many prokaryotes contain restriction enzymes. Biologically, they cleave foreign DNA molecules. Because the sites recognized by its own restriction enzymes are metylated, the cells' own DNA are not cleaved. One striking properties of endonucleases is that they recognize DNA cleavage sites by "two-fold symmetry". In another word, within the cleavage site domain (usually 4 to 8 base pair), there exists a center, around which the cleavage site rotate 180 degree, the whole cleavage site would be indistinguishable. The following graph shows an example of how endonuclease recognize cleavage site by symmetry..After cleavage from several different endonulcease, a DNA sample would be sliced into many different duplex fragments, which are then separated by electrophoresis. The restriction fragments are then denatured to form single stranded DNA, which are then transferred to a nitrocellulose sheet, where they are exposed to a 32P-labeled single-stranded DNA probe. The single-stranded DNA are then hybridized by the radio active complementary strand. These duplex are then examined by autoradiography, which reveals the sequence of the DNA. This technique is named Southern plot, after Edwin South, who invented the technique. The following image shows the steps for creating a southern plot. DNA sequencing. DNA subunits are dGMP, dAMP, dCMP and dTMP. In a DNA molecule, these subunits are connected in a way that their phosphate on 5 prime carbon are bonded to another subunit's hydroxy group on 3 prime carbon. If there is no hydroxy group on 3 prime carbon, then the DNA polymeration will be terminated. Utilizing this idea, subunit analogies were invented, ddGMP, ddAMP, ddCMP and ddTMP. These analogies have the same structure as their parent molecule except that they have hydrogen on 3 prime carbon instead of hydroxyl group. In practice, target DNA template is put into four polymeration environments, dNTP+ddGMP or ddAMP or ddCMP or ddTMP, respectively.. Statically, fragments with different length terminated at base, G, A, C, T will be formed, respectively. Then these fragments will be separated by electrophoresis, which will tell the sequence of the target DNA. DNA synthesis. Although nature synthesize DNA from 5 prime carbon to 3 prime carbon, human synthesize DNA from 3 prime carbon to 5 prime carbon. The following monomer is commercially available for each of the base and is used as basic building block for DNA synthesis. It starts with the subunit with the first base bonded to resin by the 3 prime hydroxyl group. The second monomer with its own 5 hydroxyl protected by DMT (protecting group) was activated on its 3 prime phosphate, which is attached to the 5 prime hydroxyl group by nucleophilic substitution. Then the phosphite is oxidized by iodine to yield phosphate. Then DMT is removed to make the 5 prime hydroxyl available for the incoming of the third monomer. The graphical representation is shown below. Polymerase Chain Reaction (PCR). It is used for amplification of DNA. It includes three stages: DNA denaturation, oligonucleotide annealing, and DNA polymerization. In each cycle, the DNA duplex is denatured at first, then the primers for both strands (forward and reverse) bind to the desired sites and at last both strands polymerize to form the desired sequence. What needed in PCR are the DNA containing the desired sequence, primers for both strands, heat resistant DNA polymerase, dNTP and constantly changing temperature. The following image shows the detailed steps in PCR. =RNA Editing= Introduction. Adenosine deaminases (ADAR) are mRNA editing enzymes that alternate a double stranded RNA sequence by tuning it. When tuning the mRNA, ADARs retype the nucleotides of the mRNA at certain, specific points they wish to change. Because ADARs can change the sequence of mRNA, they can create or remove a splice site, delete or alter the meaning of a codon, and finally change the sequence of the RNA altogether. ADAR plays a vital part in editing mRNA and modulating the mRNA translational activity and is mainly found in the nervous system and is important in regulating the nervous systems. Lacking the ADAR gene is very detrimental to health. Function. <br> RNA splicing and RNA editing are very similar to one another. RNA splicing is more of a cut, copy, and past process while RNA editing is an alteration of one or more nucleotides. There are mainly two types of ADAR that alternate the sequence of a single nucleotide. The first type of ADAR retypes cytidine nucleotides into uridine nucleotides while a second type of ADAR retypes adenosine into inosine. <br><br> mRNA consisting of many inosine nucleotides in its sequence is known to be very abundant in the nucleus and only mRNAs that leave the nucleus can be translated. In this case, ADAR is modulating the translational activities of mRNAs. In modulating the translational activities of the specified mRNA, it is also modulating the abundance of the certain proteins that are expressed in the edited mRNA. Also, increasing inosine can stabilize the structure of mRNA. Hence, ADAR can function as an mRNA stabilizer too. <br><br>ADARs target the coding sequence, introns, and 5’ and 3’ untranslated reigions (UTR). ADAR targets the coding sequence by changing the nucleotide which then changes the geometry of the protein. Change in the geometry of the protein may yield to higher protein-protein affinity interaction. This high protein-protein affinity can improve biological reactions by facilitating those reactions. Alternation of the non-coding sites such as introns, 5’, and 3’ UTR is still unknown. The only thing that is known is that alternating the sequence within these sites can create new splice sites. Importance of ADAR. <br>Adar is mainly found in the nervous system because it plays a very important role in regulating the nervous system. One of Adars’ primary functions is its regulation of the nervous system. Adar regulates the nervous system by editing the glutamate receptors’ mRNA. These glutamate receptors construct the glutamate-gated ion channels which are important in transferring electrical signals between neurons. When ADARs edit gluR mRNA, they change the calcium permeability of these glutamate channels. They can either lower the calcium permeability for certain glutamate channel or increase calcium permeability for other glutamate channels. Regulation of calcium permeability is important to proper neurotransmission between neurons. Disease connecting to ADAR. <br>Adenosine deaminase Deficiency (ADD) is caused by the lack of ADAR gene. Hence ADARs editing is important for survival especially for human. Without ADAR, the body can not break down the toxin deoxyadenosine. The accumulation of this toxin destroys the immune cells making its host vulnerable to infection from bacteria and viruses. Seizures can also be caused by ADAR. Unedited version of gluR mRNA strongly causes seizures. When a seizure happens, the body mechanism increases the level of ADAR activity to edit gluR mRNA to prevent future seizures. DNA Replication:Initiation. <br>There are multiple mechanisms that have been proposed for the melting of the DNA strand and the subsequent unwinding of the double helix during the initiation process of DNA replication. Two recently proposed models are E1 and LTag. These two models function differently to attain the same overall goal of melting the DNA double helix due to differences in their overall structure. E1 model: In the E1 hexamer, there are six ß-hairpins in the central channel of the protein. They are arranged in a staircase-like structure. Two adjacent E1 trimers assemble at the origin point to melt the double-stranded DNA. A ring shaped E1 hexamer is then formed around the melted single-stranded DNA and the DNA is then pumped through the ring hexamer to from a fork that allows for the replication of the DNA. Ltag: The channel diameters of these hexamers vary between 13-17 angstroms. The hexamer responsible for melting has an assortment of planar ß-hairpins in the narrow channel. Two of these hexamers surround the origin point of the double-stranded DNA and squeeze the area together. This causes the melting of the dsDNA by forcing the breakage of base pairing. The two single-stranded DNA strands are then pumped into a larger channeland finally out through two separate Zn-domains. This allows for the replication of the DNA. The two mechanisms here are built solely on the structural knowledge of the proteins involved in the process and as such more experimental support is needed to confirm. There are not an excessive amount of helicases. Currently, work is being done in discerning the more simple helicases, and trying to find the different mechanisms that they may have. While there are some similarities, for example helicases all seem to have a hexameric structure, there are also differences as well in their structures that contribute greatly to the differences in their mechanisms. -This article refers to a recently published article in Curr Opin Struct Biol. published 2010, Sep. 24.: "Origin DNA melting and unwinding in DNA replication" by Gai "et al."

High School Mathematics Extensions/Logic. Introduction. Logic is the study of the way we reason. In this chapter, we focus on the "methods" of logical reasoning, i.e. digital logic, predicate calculus, application to proofs and the (insanely) fun logical puzzles. Boolean algebra. In the black and white world of ideals, there is absolute truth. That is to say "everything" is either true or false. With this philosophical backdrop, we consider the following examples: <br> That is (without a doubt) true! That is also true. But what about: It is true! Although 1 + 1 = 3 is not true, the OR in the statement made the whole statement to be true if "at least one" of the statements is true. Now let's consider a more puzzling example The truth or falsity of the statements depends on the "order" in which you evaluate the statement. If you evaluate "2 + 2 = 4 OR 1 + 1 = 3" first, the statement is false, and otherwise true. As in ordinary algebra, it is necessary that we define some rules to govern the order of evaluation, so we don't have to deal with ambiguity. Before we decide which order to evaluate the statements in, we do what most mathematician love to do -- replace sentences with symbols.<br> Let "x" represent the truth or falsity of the statement 2 + 2 = 4.<br> Let "y" represent the truth or falsity of the statement 1 + 1 = 3.<br> Let "z" represent the truth or falsity of the statement 1 - 3 = -1.<br> Then the above example can be rewritten in a more compact way:<br> To go one step further, mathematicians also replace OR by + and AND by ×, the statement becomes: Now that the order of precedence is clear. We evaluate (y AND z) first and then OR it with x. The statement "x + yz" is true, or symbolically where the number 1 represents "true". There is a good reason why we choose the multiplicative sign for the AND operation. As we shall see later, we can draw some parallels between the AND operation and multiplication. The Boolean algebra we are about to investigate is named after the British mathematician George Boole. Boolean algebra is about two things -- "true" or "false" which are often represented by the numbers 1 and 0 respectively. Alternative, T and F are also used. Boolean algebra has operations (AND and OR) analogous to the ordinary algebra that we know and love. Basic Truth tables. We have all had to memorize the 9 by 9 multiplication table and now we know it all by heart. In Boolean algebra, the idea of a truth table is somewhat similar. Let's consider the AND operation which is analogous to the multiplication. We want to consider: where and "x" and "y" each represent a true or false statement (e.g. It is raining today). It is true if and only if both "x" and "y" are true, in table form: We shall use 1 instead of T and 0 instead of F from now on. Now you should be able to see why we say AND is analogous to multiplication, we shall replace the AND by ×, so x AND y becomes x×y (or just "xy"). From the AND truth table, we have: To the OR operation. "x" OR "y" is FALSE if and only if "both" "x" and "y" are false. In table form: We say OR is almost analogous to addition. We shall illustrate this by replacing OR with +: The NOT operation is not a "binary operation" like AND and OR, but a "unary operation", meaning it works with one argument. NOT "x" is true if "x" is false and "false" if "x" is true. In table form: In symbolic form, NOT x is denoted x' or ~x (or by a bar over the top of x). Alternative notations: and Compound truth tables. The three truth tables presented above are the most basic of truth tables and they serve as the building blocks for more complex ones. Suppose we want to construct a truth table for xy + z (i.e. x AND y OR z). Notice this table involves three variables (x, y and z), so we would expect it to be bigger than the previous ones. To construct a truth table, firstly we write down all the possible combinations of the three variables: There is a pattern to the way the combinations are written down. We always start with 000 and end with 111. As to the middle part, it is up to the reader to figure out. We then complete the table by hand computing what value each combination is going to produce using the expression xy + z. For example: We continue in this way until we fill up the whole table The procedure we follow to produce truth tables are now clear. Here are a few more examples of truth tables. Example 1 -- x + y + z Example 2 -- (x + yz)' When an expression is hard to compute, we can first compute intermediate results and then the final result. Example 3 -- (x + yz')w Exercise. Produce the truth tables for the following operations: Produce truth tables for: Laws of Boolean algebra. In ordinary algebra, two expressions may be equivalent to each other, e.g. xz + yz = (x + y)z. The same can be said of Boolean algebra. Let's construct truth tables for: xz + yz (x + y)z By comparing the two tables, you will have noticed that the outputs (i.e. the last column) of the two tables are the same! Definition We list a few expressions that are equivalent to each other "Take a few moments to think about why each of those laws might be true." The last law is not obvious but we can prove that it's true using the other laws: It has been said: "the only thing to remember in mathematics is that there is nothing to remember. Remember that!". You should not try to commit to memory the laws as they are stated, because some of them are so deadly obvious once you are familiar with the AND, OR and NOT operations. You should only try to remember those things that are most basic, once a high level of familiarity is developed, you will agree there really isn't anything to remember. Simplification. Once we have those laws, we will want to simplify Boolean expressions just like we do in ordinary algebra. We can all simplify the following example with ease: the same can be said about: From those two examples we can see that complex-looking expressions can be reduced very significantly. Of particular interest are expressions of the form of a "sum-of-product", for example: We can factorise and simplify the expression as follows It is only hard to go any further, although we can. We use the identity: "If the next step is unclear, try constructing truth tables as an aid to understanding." And this is as far as we can go using the algebraic approach (or any other approach). The algebraic approach to simplification relies on the principle of elimination. Consider, in ordinary algebra: We simplify by rearranging the expression as follows Although we only go through the process in our head, the idea is clear: we "bring" together terms that cancel themselves out and so the expression is simplified. De Morgan's theorems. So far we have only dealt with expressions in the form of a "sum of products" e.g. xyz + x'z + y'z'. De Morgan's theorems help us to deal with another type of Boolean expressions. We revisit the AND and OR truth tables: You would be correct to suspect that the two operations are connected somehow due to the similarities between the two tables. In fact, if you invert the AND operation, i.e. you perform the NOT operations on x AND y. The outputs of the two operations are almost the same: The connection between AND, OR and NOT is revealed by "reversing" the output of x + y by replacing it with x' + y'. Now the two outputs match and so we can equate them: this is one of de Morgan's laws. The other which can be derived using a similar process is: We can apply those two laws to simplify equations: Example 1<br> Express "x" in "sum of product" form Example 2<br> Express "x" in "sum of product" form Example 3<br> Express "x" in "sum of product" form Example 4<br> Express "x" in "sum of product" form Another thing of interest we learnt is that we can "reverse" the truth table of any expression by replacing each of its variables by their opposites, i.e. replace x by x' and y' by y etc. This result shouldn't have been a surprise at all, try a few examples yourself. De Morgan's laws Propositions. We have been dealing with propositions since the start of this chapter, although we are not told they are propositions. A proposition is simply a statement (or sentence) that is either TRUE or FALSE. Hence, we can use Boolean algebra to handle propositions. There are two special types of propositions -- tautology and contradiction. A tautology is a proposition that is always TRUE, e.g. "1 + 1 = 2". A contradiction is the opposite of a tautology, it is a proposition that is always FALSE, e.g. 1 + 1 = 3. As usual, we use 1 to represent TRUE and 0 to represent FALSE. Please note that opinions are not propositions, e.g. "42 is an awesome number" is just an opinion, its truth or falsity is not universal, meaning some think it's true, some do not. Examples. Since each proposition can only take two values (TRUE or FALSE), we can represent each by a "variable" and decide whether compound propositions are true by using Boolean algebra, just like we have been doing. For example "It is always hot in Antarctica OR 1 + 1 = 2" will be evaluated as true. Implications. Propositions of the type if "something" "something" then "something" "something" are called implications. The logic of implications are widely applicable in mathematics, computer science and general everyday common sense reasoning! Let's start with a simple example is an example of implication, it simply says that 2 - 1 = 1 is a consequence of 1 + 1 = 2. It's like a cause and effect relationship. Consider this example: There are four situations: In which of the four situations did John NOT fulfill his promise? Clearly, if and only if the second situation occurred. So, we say the proposition is FALSE if and only if John becomes a millionaire and does not donate. If John did not become a millionaire then he can't break his promise, because his promise is now claiming nothing, therefore it must be evaluated TRUE. If "x" and "y" are two propositions, "x" implies "y" (if "x" then "y"), or symbolically has the following truth table: For emphasis, formula_19 is FALSE if and only if "x" is true and "y" false. If "x" is FALSE, it does not matter what value "y" takes, the proposition is automatically TRUE. On a side note, the two propositions "x" and "y" need not have anything to do with each other, e.g. "1 + 1 = 2 implies Australia is in the southern hemisphere" evaluates to TRUE! If then we express it symbolically as It is a two way implication which translates to "x" is TRUE if and only if "y" is true. The "if and only if" operation has the following truth table: The two new operations we have introduced are not really new, they are just combinations of AND, OR and NOT. For example: "Check it with a truth table". Because we can express the "implication" operations in terms of AND, OR and NOT, we have open them to manipulation by Boolean algebra and de Morgan's laws. Example 1<br> Is the following proposition a tautology (a proposition that's always true) Solution 1<br> Therefore it's a tautology. Solution 2<br> A somewhat easier solution is to draw up a truth table of the proposition, and note that the output column are all 1s. Therefore the proposition is a tautology, because the output is 1 regardless of the "inputs" (i.e. x, y and z). Example 2<br> Show that the proposition z is a contradiction (a proposition that is always false): Solution Therefore it's a contradiction. Back to Example 1, :formula_24. This isn't just a slab of symbols, you should be able translate it into everyday language and understand intuitively why it's true. Logic Puzzles. Puzzle is an all-encompassing word, it refers to anything trivial that requires solving. Here is a collection of logic puzzles that we can solve using Boolean algebra. Example 1 We have two type of people -- knights or knaves. A knight always tell the truth but the knaves always lie. Two people, Alex and Barbara, are chatting. Alex says :"We are both knaves" Who is who? We can probably work out that "Alex" is a knave in our heads, but the algebraic approach to determine "Alex" 's identity is as follows: we simplify: Therefore "A" is FALSE and "B" is TRUE. Therefore Alex is a knave and Barbara a knight. Example 2 There are three businessmen, conveniently named Archie, Billy and Charley, who order martinis together every weekend according to the following rules: Putting all these into one formula and simplifying: formula_43 Exercises. Please go to Puzzles/Logic puzzles. Problem Set. 1. Decide whether the following propositions are equivalent: 2. Express in simplest sum-of-product form the following proposition: 3. Translate the following sentences into symbolic form and decide if it's true: 4. NAND is a binary operation: Find a proposition that consists of only NAND operators, equivalent to: 5. Do the same with NOR operators. Recall that x NOR y = (x + y)'

Puzzles/Logic puzzles/10 Hats. Puzzles | Logic puzzles | 10 Hats Ten students are caught cheating on a math exam and the teacher wants to give them a final chance. He makes them sit on separate rows, each one behind the other, facing the board. Each one sees all others at the front (i.e. 10th row student sees 9 students, 9th sees 8 students, ..., 1st one sees no one). He puts a hat on each student's head randomly, white or red. If at least 9 of them guess what color hat is on his or her head, the teacher will release them without punishment. Each student is allowed to talk once and may only say one word, which is his or her guess. They may decide on a strategy before starting to talk. Once they begin, they are not allowed to say or do anything else but guessing a color. Only one student is allowed to make a mistake. "What kind of a strategy should they follow?" See also Infinite Hats. Solution

Puzzles/Logic puzzles/10 Hats/Solution. Puzzles | Logic puzzles | 10 Hats | Solution = Solution 1 = The 10th student says "white" if she sees an even number of white hats and "red" if she sees an odd number of white hats (she will be the only one that could make a mistake). The 9th student now sees 8 hats in front of her. Say X of them are white. Now there are four possibilities: The 9th student can figure out which case occurs and tell her correct hat color. From then on the students have to subtract the correctly guessed hats from the total and apply the even/odd reasoning again (using what the 10th student has said and counting the number of white hats in front of them). = Solution 2 = There is a slight variation on this solution by transformation: instead of wearing red and white hats, the students wear hats labeled 0 or 1. Let x1...,x10 be the numbers on the students' hats. Let a1...,a10 be the students' answers. The students answer in decreasing order as in the first solution. The answers are defined recursively as These equations can be succinctly described as follows: each student sums up the numbers they see and the numbers they've heard. The student says one if the grand total is odd and zero otherwise. To prove that ai === xi mod 2, let si = x1+...+xi and use induction. Base case: a9 === x9 mod 2 "Proof:" Inductive step: Assume ai === xi mod 2 for i = n+1..., 9 Then Thus ai === xi mod 2 for i = n, n+1..., 9 Therefore ai === xi mod 2 for i = 1...,9 and at most one answer (a10) is incorrect. = Solution 3 = The 10th student will see 9 hats with only one or two colours. One of those colours has to have an odd number showing. The initial setup might be easier for the students if the 10th student just said which colour has an odd number showing. The rest of the students will be correct through the same logical reasoning as in Solution 1.

French/Lessons/Weather. The preposition means "at" or "in": The contraction is used in place of "à le" (singular): Likewise, the contraction is used in place of "à les" (plural). Mireille: Monique: Mireille: Monique: Marcelle: Similar to English, "pleuvoir" is an : it has only a third-person singular conjugation: In order to say that one did "not" do something, the construction must be used. The is placed before the verb, while the is placed after. Formation and rules. Simple negation is done by wrapping around the verb: In a past tense, surrounds the auxiliary verb, not the participle: When an infinitive and conjugated verb are together, usually surrounds the conjugated verb: can also precede the infinitive for a different meaning: precedes any pronoun relating to the verb it affects: In spoken French, the can be omitted, leaving simply after the verb in context: Negation of indefinite articles. The indefinite articles "un", "une", and "des" change to "de" (or "d’") when negating a sentence. Note that means both "the weather" and "the time". The verb is translated to "to go". It is irregularly conjugated (it does not count as a regular verb). Usage. There is no present progressive tense in French, so "aller" in the present indicative is used to express both "I go" and "I am going": "Aller" must be used with a place and cannot stand alone. In addition to meaning "at" or "in", the preposition means "to" when used with : An infinitive preceded by is used to say that something is going to happen in the near future: Recall that the negative goes around the conjugated verb. In place of a preposition and place, the pronoun , meaning "there", can be used; "y" comes before the verb: Remember that "aller" must be used with a place ("there" or a name) when indicating that you are going somewhere, even if a place wouldn't normally be given in English. The negative form of "aller" with the "y" pronoun has both the verb and pronoun enclosed between "ne" and "pas":

C++ Programming. __NOEDITSECTION__ This book covers the C++ programming language, its interactions with software design and real life use of the language. It is presented in a series of chapters as an introductory prior to advance courses but can also be used as a reference book. This is an open work; if you find any problems with terms or concepts "you can help by contributing to it"; "your participation is needed and welcomed!" You are also welcomed to state any preference, shortcomings, vision for the actual book content, structure or other conceptual matters; see . Appendix A: References Tables. • Keywords • Preprocessors Directives • Standard Headers • Data Types • Operators • Standard C Library Functions • ASCII chart Appendix B: External References. • Weblinks • Books

Algebra/Factoring Polynomials. =Formulas= Computing factors of polynomials requires knowledge of different formulas and some experience to find out which formula to be applied. Below, we give some important formulas: formula_1 formula_2 formula_3 formula_4 formula_5 formula_6 Examples. :formula_7 :formula_8 formula_9<br> formula_10<br> formula_11<br> formula_12 :formula_13 :formula_14 :formula_15 :formula_16 formula_17<br> formula_18<br> formula_19<br> formula_20<br> formula_21 :formula_22 :formula_23 :formula_24 :formula_25 :formula_26 :formula_27 :formula_28 :formula_29 formula_30<br> formula_31<br> formula_32<br> formula_33 :formula_34 :formula_35 :formula_36 :formula_37 write out the coefficients and if the end is equal to zero, than it is a root example: formula_38 formula_39 = Possible Factors = To factor we must first look for possible factors. Possible factors are any number that might be a factor. Once we have a possible factor then we divide that number into the number we are factoring. If they divide evenly then we have a factor! The factor is the possible factor we found and the result of the division problem. Here is an example. Let's say the number we are factoring is 20. 2 is the possible factor. 20 / 2 = 10. They divide evenly which means we have a factor. The factors are 2 (the possible factor), and 10 (the result of the division problem). Now that we have a factor we start over with a new possible factor and find all of the factors. Examples. Factor 12 First find all the possible factors The possible factors are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 Next we will try them one by one 12/1 = 12 (1 and 12 are factors) 12/2 = 6 (2 and 6 are factors) 12/3 = 4 (3 and 4 are factors) 12/4 = 3 (we already have the factors 3 and 4) Once we get a factor we already have then we know we have all the factors. So the factors for 12 are 1, 2, 3, 4, 6, and 12. Factor 54 First find all the possible factors Do not worry this is not as much work as it seems! 54/1 = 54 (1 and 54 are factors) 54/2 = 27 (2 and 27 are factors) 54/3 = 18 (3 and 18 are factors) 54/4 = 13r2 (4 is not a factor) 54/5 = 10r4 (5 is not a factor) 54/6 = 9 (6 and 9 are factors) 54/7 = 7r5 (7 is not a factor) 54/8 = 6r6 (8 is not a factor) 54/9 = 6 (we already have the factors 9 and 6) So the factors for 54 are 1, 2, 3, 6, 9, 18, 27, and 54 Factor 180 First find all the possible factors Do not worry this is not as much work as it seems! 180/1 = 180 (1 and 180 are factors) 180/2 = 90 (2 and 90 are factors) 180/3 = 60 (3 and 60 are factors) 180/4 = 45 (4 and 45 are factors) 180/5 = 36 (5 and 36 are factors) 180/6 = 30 (6 and 30 are factors) 180/7 = 25r5 (7 is not a factor) 180/8 = 22r4 (8 is not a factor) 180/9 = 20 (9 and 20 are factors) 180/10 = 18 (10 and 18 are factors) 180/11 = 16r4 (11 is not a factor) 180/12 = 15 (12 and 15 are factors) 180/13 = 13r11 (13 is not a factor) 180/14 = 12r12 (14 is not a factor) 180/15 = 12 (we already have the factors 15 and 12) So the factors for 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180. = Dividing polynomials = The process of factoring will require dividing polynomials. This form of division is not too different from long division method, and is known as "synthetic division". Consider the polynomial x3 - 21x2 + 143x - 315. In this case, determining factors may require trial and error (until you learn of alternate techniques), and when you do, you will need to divide the polynomial with the discovered factor. In this example, we will divide by (x-5). The full division starts like this: 1x -5 | 1x^3 -21x^2 +143x - 315 As with long division, you need to find the number used for subtraction and place it on top - in this case, you need to make sure the left-most term becomes zero. Next, multiply the newly added top-most term with the left hand side to get the amount to subtract, and perform the subtraction. 1x^2 1x -5 | 1x^3 -21x^2 +143x - 315 1x^3 -5x^2 -16x^2 +143x - 315 Repeat until the division is complete: 1x^2 -16x + 63 1x -5 | 1x^3 -21x^2 +143x - 315 1x^3 -5x^2 -16x^2 +143x - 315 -16x^2 + 80x 63x - 315 63x - 315 0 Some people may find writing the x3 and other variables to be bulky - if writing on pen and paper, they can be omitted as part of shorthand. 1 -16 + 63 1 -5 | 1 -21 +143 - 315 1 -5 -16 +143 - 315 -16 + 80 63 - 315 63 - 315 0 In this case, factoring is straight forward since you can easily determine the number to use for the next step in division. =See also=

German/Grammar/Alphabet and Pronunciation. The Alphabet. Like English, the German alphabet consists of 26 basic letters. However, there are also combined letters and three umlauted forms. An "umlaut" is the pair of dots placed over certain vowels; in German, "Umlaut" describes the dotted letter, not just the dots. As in English, letters may be pronounced differently depending on word and location. The first column is the German letter, the second describes the IPA pronunciation and rough English approximation of the letter name. The third gives an English word that matches or approximates the German letter sound. Reading down this column and pronouncing the "English" words will recite the alphabet "auf Deutsch" ("in German"). Note that letter order is exactly the same as in English, but pronunciation is not for many of the letters. In the list of pronunciation notes, no entry means essentially "pronounced as in English". Unique German Letters. Combined Letters. Notes: •There is no uppercase ß. •All vowels (withot umlauts) are pronounced like those in Spanish, but in Spanish the long ones are pronounced much shorter in Spanish. •In German you capitalize these: •Modern German, Luxembourgish, and Bavarian are the only languages in the world that capitalizes every noun. •Also, the only English word that is always capitalized whose German translation (unless it starts a sentence) is not capitalized is the pronoun "I". •in a title, like in Spanish only the first word and other "always" capitalized words are capitalized The silent letters in German appear in five situations: • H after a vowel or T • First letter of double consonants, ck, and tz* • E after I, in which I is always long • Final W. • D before the T Vowels are long with one consonant after it, and short with two. But… A is always short Diphthongs are long Compound words are broken up: Weg|weiser Borrowed and short words may break this rule. Any following H's: Tuch, John, Sohn, Joshua, Buch have a long vowel sound. In French loanwords, if a vowel is followed by a nasal consonant in the same syllable, then the nasal consonant will be silent and the vowel will be nasal. A nasal vowel produces air through your mouth and your nose. A double vowel is long, except for AA (see above) Konsonanten ~ Consonants. Most German consonants are pronounced similarly to the way they are pronounced in English, with exceptions noted in column 3 above. Details of certain consonant sounds and uses are discussed further here. Note that as above, L only uses the front of your tongue, just like in Spanish or French, which is similar to the L in Laugh. German Sounds not found in English. There are sounds in the German language that have no real equivalent in the English language. These are discussed here. •It always sounds like an S. •It can't be the first letter of a word. •It always follows a vowel. •It doesn't have an uppercase version. •It looks like a Greek letter, the formula_1, but never replace it with the Greek letter formula_1. Audio: ~ ach | ~ ich auch | ~ richtig Syllable Stress. The general rule in German is that words are stressed on the first syllable. However, there are exceptions. Almost all exceptions are of Spanish or French origin. For those borrowed from French it will generally stressed on the last syllable, for example, Vokal, Konsonant, and Lektion (vowel, consonant, lesson). In loanwords from Spanish, however, the stress is generally on the next-to-last syllable if it ends in N, S, or a vowel and the last one otherwise. These words (not stressed on the first syllable) appear in the (Level II and III) lesson vocabularies as "Vokal", "Lektion" (in some regions: "Lektion"), etc. Words starting in common prefixes (ge-, be-, ver-, etc.) stress the syllable following said prefix. Examples are Gemüse, Beamte, and Vereinigung. Also, the German word "Ski" means "ski" and is spelled "ski" but it is actually pronounced like the pronoun "She" in English. Notice that we have genders in German, masculine, feminine, neutral. English doesn't have genders. Also as mentioned above, all nouns are capitalized in German, Bavarian and Luxembourgish. And finally, we saw that in words of French origin the letter J, as well as the letter G (before E or I) makes the sound of S as in vi"s"ion, which is the English J sound without the initial D, and the IPA is this: /ʒ/, a very rare sound in both German and English. Example: In Garage the first G is pronounced the same as how it is pronounced in English, while the second one is pronounced /ʒ/ because it comes before an E, and the word has a French origin. Again, remember that this sound is very rare in both of these languages. Don't forget the formula_3, which will go on back vowels only and move the sound from the back to the front, except for AU. The AU sounds like ow as in cow, while the ÄU sounds like the oy in boy. The formula_4 may not appear on the A in the AI or AY diphthongs. Last the A, which is always short, except in a diphthong and as formula_5, as well as long vowels without double-dots on top, are pronounced like those in Spanish, but the Spanish vowel sounds are pronounced short, while in German, all of them except for the A are longer. Again A is always short, never long.

Indonesian/Tenses. Tenses. As we learned from Lesson 4, Indonesian has no tenses. In order to express idea in different time frame, we need to attach time signals, such as "yesterday", "tomorrow", "this morning", etc. These time signals are very easy to learn. When you say a sentence without any time signal, we can never be sure what time frame it is assumed to be, if it is taken out of context. For example: Saya makan apel. The general translation would be in present tense: "I eat apple". However, it depends on the speaker on what it means. It may also mean progressive tense. The speaker may be eating an apple as he/she speaks. Also, you can incorporate as many time signals as you want to express more specific ideas, as long as the addition doesn't contradict the existing ones and follows the "general rule of thumb". This is especially useful since Indonesian has no notion of complex grammar such as future perfect. Present Tense. To express habitual activity, we use present tense. In English, we use the form of "infinitive + (-s/-es)". In Indonesian, we use the time signal "setiap X", where X can be subtituted with "hari", "pagi", "siang", "malam", "minggu", etc to denote that the activity is recurrent. Remember that when you mention a noun, it is uncertain whether it is singular or plural, as discussed here. The assumption is always singular, but it can still mean plurals. Here's a helpful word signals appropriate for present tenses: Note: The word setiap may be shortened as tiap. Both are acceptable in formal written/spoken Indonesian. To indicate that the action is a habit, you can put the word biasa right before the verb: Progressive Tense. To express a currently ongoing activity, we use progressive tense. In English, we use the form of to be + infinitive + -ing. In Indonesian, we use the time signal sedang. The word other than sedang that can be used is lagi. Be careful with the word placement. The word "sedang" or "lagi" are used right before the verb in order to form progressive tense. Be extra careful in the word "lagi", because if the placement is wrong, then it will mean "again" instead of to mean a progressive tense. You can also attach time signals to further reinforce your idea; such as: "sekarang" = now. Past Tense. Indonesian only has one notion of past tense, which is simple past. It has no notion of past progressive or past perfect tenses. (See below for further clarification) As always, to form the tenses, we just need to attach time signals. To express undefinite past, Indonesian has these phrases: Both the words sudah and telah literally means already. It explains that the action has already happened. It is uncertain whether it's in the recent or distant past. Note that due to English influence, sudah or telah are often used to express past perfect tenses due to the closeness of their meaning. See below for more. When people are talking about distant past, the assumption is that the activity discussed is recurrent (unless the context dictates otherwise), especially if we attach habitual time signal. For example: The notion of recent past is roughly limited to about last night. So, "tadi malam" means last night. Baru saja is roughly equivalent to "just now". However, it can also means within an hour or so. To express definite past, we can use the phrase "lalu", which roughly means ago. For example: Note that sometimes the phrase "yang lalu" is used instead of "lalu". They are equivalent. Literally, the word lalu means pass and yang means that or which. So, "dua jam yang lalu" literally means "[at] two hours that pass". Other words that may be useful to express ideas in the past: Future Tense. The same goes with future tense: We need to attach time signals. For example: To express undefinite future, Indonesian has these phrases: Note that the word akan must be placed right before the verb, just like sedang. See the example above. The difference between kelak and nanti is on the distance to the future they are. Their usage can be combined with the word akan. The first two sentences are equivalent, as are the last two. The difference is that the first two implies more distant future than the last two. How distant? It depends on the context. The good rule of thumb is kelak usually refers to a time frame of months or years in the future, whereas nanti refers to a much shorter time in the future than that (i.e. days). To specify definite future, the word akan can also be combined with other future time signals, such as besok ( = tomorrow). The word kelak or nanti can be combined with future time signals too in order to specify a definite future: Note that when specifying definite future, the word kelak and nanti is equivalent. So, "dua jam nanti" is equivalent as "dua jam kelak". Usually people still follow the "rule of thumb" above. So, "dua jam nanti" is used more often than "dua jam kelak"; and "dua tahun kelak" is used more often than "dua tahun nanti". However, people usually use "dua bulan nanti" and "dua bulan kelak" interchangeably. Example: Note that the word akan can also be combined with kelak or nanti. But kelak and nanti cannot be used together. For example: The two examples are equivalent. Another good time signal to use for future tense is "depan", which means next (in next week, etc.): Tense Combinations. As stated above, Indonesian has no complex tenses such as future perfect (i.e. "will have + infinitive"). The way Indonesian gets around with it is to throw in the appropriate time signals. This practice is influenced by Romance languages and sounds inherently unnatural to Indonesian people. However, you may do that and people may still be able to understand it, may be just a bit strange. Present Perfect. Due to English language influence, people began using the words sudah or telah to express present perfect. This is because Indonesian actually doesn't have present perfect. So: It's a bit weird, but it works. So you can use it if you want to. Future Perfect. We use the phrase "akan telah" or "akan sudah" to indicate future perfect. Conditional Perfect. Conditional perfect is expressed using "would have". Unfortunately, Indonesian has no way to express this. The usual translation is using "mungkin telah", but that would actually mean "may have". This is very awkward situation. It sounds very unnatural. The best way translating it is to translate the sentence in its entirety in a different way.

Botany/Plant reproduction laboratory flower. Chapter 5. Plant Reproduction Laboratory ~ Flowers. <br> An orchid flower. This first laboratory exercise for Chapter 4 deals with the flowers of a ground orchid from Southeast Asia. The photograph on the right demonstrates the descriptive terminology that can be applied to this species. You may wish to read about to place this plant taxonomically and better understand unusual aspects of the structure of this flower. In reading the description below, be sure you understand how or why each bolded word applies to this specimen. Also, observe that the flowering-through-fruiting sequence is well demonstrated in the photograph because each flower is in a slightly different phase of its life cycle from bud to fruit. 4-1. Review the photograph of the inflorescence of the orchid. "Which one of these statements is true": <br> Following are a series of photographs of flowers from various plants. "Note that by clicking on the word" "Examine" "in each title, you can enlarge the particular photograph for closer examination". Read each question and the offered answers carefully. All parts of answer choice must be correct for that choice to be correct. 4-2. "The structure at B is": <br> 4-3. "Although the flowers in these three photographs appear very different, the following parts or floral structures are essentially the same": 4-4. "Which statement of the following applies to the structure indicated at E ": <br> « Return to Chapter 5 Answers to Chapter 4 Laboratory Questions:

Latin/Lesson 3-Present Verbs. = Grammatical Introduction to Verbs = This introductory section may be a bit overwhelming, but is an overall look at verbs. The majority of this section will be covered in later chapters. Nevertheless, looking over this chapter may help you to familiarize yourself with verbs. Verbs are parts of speech which denote action. There are two main forms of verbs in Latin: • Principal Verbs (the main verb which is found in every sentence. e.g.,: vir ambulat = the man is walking) • Adjectival Verbs (also known as participles, gerunds and gerundives which describe the state of the described noun. e.g.,: vir ambulans = the walking man. The verb behaves as an adjective) Every sentence must have a verb. In a sense, the principal verb is the sentence and all the nouns, adverbs and participles are only describing the scenario of the verb. Thus in Latin this constitutes a sentence: est. If you want to explain 'who' is or exists, you add a nominative substantive: Cornēlia est. We now know Cornelia 'is'. But what is she? So we add an adjective. Cornēlia est bona. Now we can see that Cornelia is good, but to elaborate further we can add an adverb: Cornēlia vix est bona. Now we know that Cornelia is 'hardly' ("vix": hardly, scarcely, barely) good. Thus, in English, the shortest Latin sentence is: You are. in Latin: es Examples. These two examples will demonstrate the difference between an adjectival verb and a principal verb. Personal Endings. Verbs in Latin are inflected to reflect the person who performs the action. English does the same to some extent in the verb to be: Latin, however, inflects all verbs, and is much more extensive than English, allowing writers and speakers of Latin to often drop the personal pronoun, as the performer of the action is understood by the formation of the verb. The Personal pronoun is only usually added for emphasis. In a way, the ending on Latin verbs are a type of pronoun. Moods. There are several moods. Each has its own uses to convey certain ideas. The most commons moods are: • Indicative • Subjunctive or Conjunctive • Imperative The two moods we will first learn are the imperative (commands and orders) and the indicative (declarative statements and factual questions). Voice. There are two constructions verbs can have regarding voice. Verbs can have either an active or passive voice. E.g. 'I smash the car.' 'smash' is an active verb construct. The passive is used when the nominative is affected by the verb. E.g. 'The car is smashed by me.' 'is smashed' is a passive construct. Tense. Tense in Latin comprises two parts: TIME and ASPECT. Time reflects when the action is occurring or did occur: past, present, or future. Aspect refers to the nature of the action: simple, completed, or repeated. The "completed" aspect is generally termed "perfective" and repeated aspect "imperfective." Theoretically, a verb could have nine tenses (combinations of time and aspect). However, Latin only has six, since some possible combinations are expressed by the same verb forms. Latin tenses do not correspond exactly to English ones. Below is a rough guide to tense in Latin. As is evident, some Latin tenses do "double duty." The Latin Present and Future Tenses can either express simple or progressive aspect. Particularly difficult to grasp is the Latin Perfect tense, which can either express an action completed from the point of view of the present ("I have just now finished walking"), or a simple action in past time (its "aorist" sense, from the old Indo European aorist tense, which Latin lost but is still present in Greek). Infinitive. The infinitive (impersonal) is the form of the verb which simply means 'to (verb)' e.g. 'to do', or 'to be', or 'to love', or 'to hate' etc. All forms which are not in the infinitive are in the finite (personalised) form. The infinitive has a -re at the end of the stem of the verb. The infinitive of 'to be' is an exception and is 'esse'. dēbeō currere nunc = I ought to run now. esse, aut nōn esse = To be, or not to be? Exercises. Answer these two questions about the infinitive and finite. Irregularities. Verbs which use the passive formation in an active sense are known as deponent. Verbs which don't have a form for every tense and mood are known as defective. You will meet a few words like this soon. Personal Pronouns. In case you do ever use a personal pronoun to emphasise the SUBJECT of the verb, you must remember that the personal pronoun must be in the nominative case and the number and person of the verb must match that of the subject. (Review Lesson 7 if unfamiliar with the terms person and subject). Principal Parts. When one looks up a verb in the dictionary, the principal parts are given. From these principal parts you can find the correct form of the verb for every circumstance. Exercises. Answer this question about principal parts. Using the Dictionary. All nouns are given in the nominative, as well as the declension and gender of the noun. Verbs are alphabetized using the 1st person singular (the first principal part) and the infinitive is given. Supplementary principal parts are given if the various other principal parts do not follow the standard pattern of formation from the infinitive and 1st person singular. =Verbs: Conjugation in the Present Imperfect = The present imperfect is the simplest tense. To form the present imperfect all that is required is to place the personal endings at the end of the verb stem. Thus, if you have the stem 'ama' (love), to make it 'I love' you place an ō at the end. I love = amō (amaō*) we love = amāmus Latin could add personal pronouns, however only for added emphasis and in conjunction with the corresponding person ending on the verb. Otherwise the sentence will not make sense. For example: ego amō = I (not you) love nōs amāmus = We (not you) love but that would be for special emphasis: It's I, not you, who loves. Here are the forms of the verb 'porta', carry, in the present imperfect tense: portō I carry first person singular portās thou carriest, you carry second person singular portat he, she, it carries third person singular portāmus we carry first person plural portātis you (all) carry second person plural portant they carry third person plural 'porto' can also be translated 'I am carrying' (present imperfect), 'I do carry' (present emphatic). 'I carry' is known as the 'present simple' tense in English. Again the 'a' gets dropped when the 'ō' is placed on porta. Porta, and ama are known as 1st conjugation verbs; in other words, verbs which have a stem ending in 'a'. There are three other conjugations, and below are some examples of verbs from each of the four conjugations (present imperfect tense): Each verb uses the same final letter or letters to indicate the 'subject' - I, thou, he/she/it, we, you, they. Before these final letters, the first conjugation has an 'a' (although when an 'o' is placed, the 'a' is often dropped), the second an 'e', and the third and fourth usually an 'i'. The third person plural forms in the third and fourth conjugations have a 'u'. These verb forms really should be learned by heart. The most common verb of all is irregular (see next lesson). Here is a table of the verb 'to be' in Latin, English, and four Romantic languages (French, Spanish, Italian and Portuguese) The personal endings are the same as in the four regular conjugations. Exercises. <br> Imperative Mood. The imperative mood conveys an order (e.g. Go!, Run!, Away Now!). The imperative mood is formed by simply using the stem of the verb. If the order is to a large group of people, or you are trying to show respect, you must use the -te suffix. amō eum = I love him. amā eum = Love him! amāte eum = Love (respectful, or plural) him! currō casam = I run home. curre casam = Run home! currite casam = Run (respectful, or plural) home! regō prudente = I rule wisely. rege prudente = Rule wisely! regite prudente = Rule (respectful order) wisely!

Latin/Appendix H. External Links. This textbook can be heard read out aloud here:

Linear Algebra/Eigenvalues and eigenvectors. Eigenvalues and eigenvectors are related to fundamental properties of matrices. Motivations. Large matrices can be costly, in terms of computational time, to use, and may have to be iterated hundreds or thousands of times for a calculation. Additionally, the behavior of matrices would be hard to explore without important mathematical tools. One mathematical tool, which has applications not only for Linear Algebra but for differential equations, calculus, and many other areas, is the concept of "eigenvalues" and "eigenvectors". Eigenvalues and eigenvectors are based upon a common behavior in linear systems. Let's look at an example. Let and What happens with x and y if they are transformed by "A"? Well, But what is remarkable is that So when we operate on the vector x with the matrix "A", instead of getting a different vector (as we would normally do), we get the "same" vector x multiplied by some constant. And the same goes for vector y. We call the values 1 and -2 the "eigenvalues" of the matrix "A", and the vectors x and y are called "eigenvectors" for the matrix "A". Definitions. We now generalize this concept of when a matrix/vector product is the same as a product by a scalar as above: essentially if we have a "n"×"n" matrix A, we seek solutions in v to find the eigenvectors, and solutions in λ to find the eigenvalues for the equation How are we to do this? Let us rearrange the equation But (A-λI) is a matrix, so we are trying to solve Bv=0 where B=(A-λI), and this solution is merely the kernel of B, ker B. So the eigenvectors are in ker (A-λI), where λ is an eigenvalue. But how do we find the eigenvalues? Bv=0 has nonzero solution if |B| = det(B) is zero. So to find the eigenvalues, we let |A-λI|=0 and then solve for λ. We will thus obtain a polynomial equation over the complex numbers (eigenvalues can be complex), known as the "characteristic equation". The roots of the characteristic equation are the eigenvalues. Note that we exclude 0 as an eigenvector, because it is trivially a solution to Av=λv and is not really interesting to consider. Additionally, if the zero vector were to be included, it would allow for an infinite number of eigenvalues, since any value of λ satisfies A0=λ0. If we have an eigenvalue λ of a matrix A, together with a corresponding eigenvector, x, then any multiple of x is also an eigenvector for the same eigenvalue. To see that kx is also an eigenvector, follow this argument: If Ax=λx, then A(kx)=kAx=kλx=λ(kx). (Here k may be any scalar.) Thus, every multiple of an eigenvector is also an eigenvector. Note the asymmetry here: eigenvalues are unique, while an eigenvalue has many eigenvectors. </gallery> </gallery> </gallery> Bold textÆə=== Finding eigenvalues and eigenvectors === Here are some examples of finding eigenvalues and eigenvectors using our definitions. Let Firstly, we expand |A-λI|=0 to find the eigenvalues: Now, elementary algebra tells us the roots of this equation are 3 and 2, and thus these are our eigenvalues. Now we can find our eigenvectors. Consider the first eigenvalue λ=3. To find our first eigenvector At this point we can row-reduce and back-substitute, but usually it suffices to guess the kernel since our matrix is small and we have linearly dependent columns. Now, observe: So, for any scalar a, the vector As noted above the eigenvalues of a matrix are uniquely determined, but for each eigenvalue there are many eigenvectors. We usually choose an eigenvector for some convenience such as "most whole number entries", "first entry is 1", or "length of the eigenvector is 1". Most Computer Algebra Systems choose unit vectors for eigenvectors. So here we may take formula_16 to be the eigenvector, for example. Similarly for our second eigenvalue λ=2, to find our second eigenvector: And so, our second eigenvector is chosen as Our eigenvalues then are λ=2,3, with eigenvectors formula_19, as may be checked by multiplying each by the given matrix. Problem set. Given the above, find the eigenvalues and eigenvectors of the following matrices (Answers follow to even-numbered questions): Applications. Eigenvalues and eigenvectors are not mere pretty facts about these vectors; they have relevant and important applications. Matrix powers. Let us first examine a certain class of matrices known as "diagonal" matrices: these are matrices in the form Now, observe that This is a useful property! However, the number of matrices to which we can apply this fact is clearly limited, so we ask ourselves whether we can transform a given matrix into a diagonal matrix. The answer to this question is "sometimes", but for the moment, we will only look at matrices for which this answer is "yes". What we seek is a matrix P such that where D is diagonal. If such a matrix P exists, we say that A is "diagonalizable". (Note that "xyx"-1 is often called a "similarity transformation"). Then by multiplying throughout forward by P-1, then by multiplying backward by P. Now, we have The PP-1 terms cancel to give We can calculate Dk easily, so we need to find P. It turns out (the entire proof is quite difficult) that we simply create a matrix from concatenating the linearly independent eigenvectors to create P. D, then, is the diagonal matrix containing the eigenvalues on the main diagonal corresponding to the associated eigenvectors (the eigenvalue in the first place corresponds to the eigenvector it is created from, in the first column). Example. Let's work through an example to show these ideas. So what do we do if we want to find A14? Let's use the method we've just described. Find the eigenvalues: Find the eigenvectors: The eigenvectors are then so put the eigenvectors together to form the matrix P Now -1 generated the eigenvector in the "first" column, and 4 generated the eigenvector in the "second" column, so form D in this way: We can easily calculate (-1)14=1, so we get and we have the fast method for creating inverses of 2×2 matrices: So now we can now directly multiply out Simplifying we get Problem set. Given the above, find the following matrix powers (Answers follow to even-numbered questions): Coupled ordinary differential equations. We can use the method of diagonalisation to solve coupled ordinary differential equations. For example, let x(t) and y(t) be differentiable functions and x' and y' their derivatives. The differential equations are relatively difficult to solve: but it has solution remembering this fact, we translate the ODEs into matrix form Diagonalise the square matrix, we get: we put then it follows that thus as discussed above the solutions are easy. We have for some constants C and D. Now that we get and so This method generalises well into higher dimensions. Coupled differential equations. Matrices, strangely enough, have a great use in relation to "calculus" in the calculation of solutions to coupled differential equations, where one differential equation has some function that depends on another differential equation. For example: Without going any further, the solution to these differential equations looks very difficult! However if we formulate this in terms of matrices, it becomes a little bit easier to analyze. Example. Let's take the above example, so Now form a vector: Then Now the problem becomes This is reminiscent of the differential equation we have already encountered in calculus, that of in which the solution is y = "c"ekt. We can make a wild guess then the solution to the above matrix equation will have a solution in a similar form. So let's try a solution v = weλt. Then D v = λweλt. Let us then try and substitute this guess solution into our equation: If we let we see that the equation above becomes, on dividing through by formula_61 (since it is never zero) But wait - this is the equation before to find the eigenvalues - and we have that the solution v = weλt is a solution if and only if λ is an eigenvalue of A and w is its corresponding eigenvector. The eigenvalues are 4, 2, with eigenvectors respectively. So we have two solutions and Note that if we have two solutions to the differential equation D v = Av, linear combinations of the two solutions will give the same solution. So then we have then the general solution: Separating into the first and second components we get our two solutions Problem set. Given the above solve the following problems (answers to even-numbered questions follow) Answers. Form the matrix The eigenvalues of this matrix are and the eigenvectors are So now and y("t") and x("t") can be read off by inspection.

Linear Algebra/OLD/Vector Spaces. A vector space is a way of generalizing the concept of a set of vectors. For example, the complex number 2+3i can be considered a vector, since in some way it is the vector formula_1. The vector space is a "space" of such abstract objects, which we term "vectors". Some familiar friends. Currently in our study of vectors we have looked at vectors with real entries: formula_2, and so on. These are all vector spaces. The advantage we gain in abstracting to vector spaces is a way of talking about a space without any particular choice of objects (which define our vectors), operations (which act on our vectors), or coordinates (which identify our vectors in the space). Further results may be applied to more general spaces which may have infinite dimension, such as in Functional Analysis. Notations and concepts. We write a vector, like we have before, bold, but you should write these on paper underlined or with an arrow on top. So we write formula_3 for that vector. When we multiply a vector by a scalar number, we usually ascribe it a Greek letter, writing λv for the multiplication of v by a scalar λ. We write addition and subtraction of vectors as we have been doing before, x+y for the sum of vectors x and y. With scalar multiplication and adding vectors, we can move to our definition of a vector space. When we refer to an operation being 'closed' in a definition, we are saying that the result of the operation does not violate our definition. For example, if we are looking at the set of all integers, we can say that it is closed under addition, because adding any integers results in something inside the set of integers. However the set of integers is not closed under division, because dividing 3 by 2 (for example) doesn't result in a member of the set of integers. Definition. A "vector space" is a nonempty set V of objects, called "vectors", on which are defined two operations, called "vector addition" and "scalar multiplication", respectively, such that, for formula_4 and αformula_5, where F is a field x+y and αx are well-defined elements of V with the following properties: Alternative Definition. People who are familiar with group theory and field theory may find the following alternative definition more compact: Linear Spaces. The linear space is a very important vector space. Let n1, n2, n3, ..., nk be k elements of a field F. Then the ordered k-tuples (n1, n2, n3, ..., nk) form a vector space with addition being the sum of the corresponding numbers, and scalar multiplication by an element of F being the result of multiplying each one in the k-tuple. This would then be the k dimensional linear space. Subspaces. A "subspace" is a vector space inside a vector space. When we look at various vector spaces, it is often useful to examine their subspaces. The subspace S of a vector space V means that S is a sub"set" of V and that it has the following key characteristics Any subset with these characteristics is a vector space. The trivial subspace. The singleton set with the zero vector ({0}) is a subspace of every vector space. Scalar multiplication closure: "a" 0=0 for all "a" in R Addition closure: 0+0=0. Since 0 is the only member of the set we need to check only 0 Zero vector: 0 is the only member of the set and it is the zero vector. Examples. Let us examine some subspaces of some familiar vector spaces, and see how we can prove that a certain subset of a vector space is in fact a subspace. A slightly less trivial subspace. In R2, the set V of all vectors from R2 of the form (0,α) where α is in R is a subspace Scalar multiplication closure: "a" (0,α) = (0,a α) and a α is in R Addition closure: (0,α) +(0,β) =(0, α + β) and α + β is in R Zero vector: taking α to be zero in our definition of (0, α) in V we get the zero vector (0,0) A whole family of subspaces. Pick any number from R, say ρ. Then the set V of all vectors of the form (α, ρα) is a subspace of R2 Scalar multiplication closure: "a" (α, ρα) = (aα, ρaα) which is in V. Addition closure: (α, ρα) +(β, ρβ) =(α + β, ρα + ρβ) = (α+β, ρ(α+β)) which is in V Zero vector: taking α to be zero in our definition we get (0, ρ0) = (0,0) in V. That means V2 = the set of all vectors of the form (α,2α) is a subspace of R2 and V3 = the set of all vectors of the form (α,3α) is a subspace of R2 and V4 = the set of all vectors of the form (α,4α) is a subspace of R2 and V5 = the set of all vectors of the form (α,5α) is a subspace of R2 and Vπ = the set of all vectors of the form (α,πα) is a subspace of R2 and V√2 = the set of all vectors of the form formula_11 is a subspace of R2 As you can see, even a simple vector space like R2 can have many different subspaces. Linear Combinations, Spans and Spanning Sets, Linear Dependence, and Linear Independence. Linear Combinations. Definition: Assume formula_12 is a "vector space" over a field formula_13 and formula_14 is a nonempty subset of formula_12. Then a vector formula_16 is said to be a linear combination of elements of formula_14 if there exists a finite number of elements formula_18 and formula_19 such that formula_20. Spans. Definition: Assume formula_12 is a "vector space" over a field formula_13. The set of all linear combinations of formula_23 is called the span of formula_24. This is sometimes denoted by formula_25. Note that formula_26 is a subspace of formula_12. Proof: Consider closure under addition and scalar multiplication for two vectors, x and y, in the span of the vectors formula_28 formula_29 formula_30 formula_31, which is also contained in the set. formula_32, which is also contained in the set. Spanning Sets. Definition: Assume formula_12 is a "vector space" over a field formula_13 and formula_24 are vectors in such a vector space. The set formula_36 is a spanning set for the vector space formula_12 if and only if every vector in formula_12 is a linear combination of formula_24. Alternately, formula_40 Linear Independence. Definition: Assume formula_12 is a "vector space" over a field formula_13 and formula_43 is a finite subset of formula_12. Then we say formula_14 is linearly independent if formula_46 implies formula_47. Linear independence is a very important topic in Linear Algebra. The definition implies that linearly dependent vectors may form the nulvector as a non-trivial combination, from which we may conclude that one of the vectors can be expressed as a linear combination of the others. If we have a vector space V spanned by 3 vectors formula_48 we say that v1, v2, and v3 are linearly dependent if there is a combination of one or two of them that can produce a third. For instance, if one of the following equations: can be satisfied, then the vectors in V are said to be linearly dependant. How can we test for linear independence? The definition sets it out to us: If V is a vector space spanned by 3 vectors of length N: and we try to test whether these 3 vectors are linearly independent, we form the equations: and solve them. If the only solution is then the 3 vectors are linearly independent. If there is another solution they are linearly dependent. ?????? We can say that for V to be linearly independent it must satisfy this condition: Where we are using 0 to denote the null vector in V. If formula_56 is square and invertable, we can solve this equation directly: And if we know that formula_59 is zero, then we know that the system is linearly independent. If, however, formula_56 is not square, or if it is not invertable, we can try the following technique: Multiply through by the transpose matrix: Find the inverse of formula_62, and multiply through by the inverse: Cancel the terms: And our conclusion: This again means that V is linearly independent. Span. A span is the set of all possible vectors that are in a given vector space. Basis. A basis for a vector space is the least amount of linearly independent vectors that can be used to describe the vector space completely. The most common basis vectors are the kronecker vectors, also called canonical basis: In the cartesian graphing space, we say an ordered triple of coordinates is defined as: And we can make any point (x, y, z) by combining the kronecker basis vectors: Some theorems: Bases and Dimension. If a vector space V is such that:<br> it contains a linearly independent set B of N vectors, and</br><br> any set of N + 1 or more vectors in V is linearly dependent,</br> then V is said to have dimension N, and B is said to be a basis of V. TODO. Tell about what is a "basis" in a vector space and about coordinate transformations. (this article contains an abstract definition of a "basis" which is a generalization of a basis in vector space and can be used as the foundation to explain about bases and coordinate transformations.) Discuss the geometry of subspaces (points, lines, planes, hypersurfaces) and connect them to the geometry of solutions of linear systems. Connect the algebra of subspaces and linear combinations of vectors to the algebra of linear systems.

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Physics Study Guide/Linear motion. Kinematics is the description of motion. The motion of a point particle is fully described using three terms - position, velocity, and acceleration. For real objects (which are not mathematical points), "translational kinematics" describes the motion of an object's center of mass through space, while "angular kinematics" describes how an object rotates about its centre of mass. In this section, we focus only on translational kinematics. Position, displacement, velocity, and acceleration are defined as follows. Position. "Position" is a relative term that describes the location of an object RELATIVE to some chosen stationary point that is usually described as the "origin". A vector is a quantity that has both magnitude and direction, typically written as a column of scalars. That is, a number that has a direction assigned to it. In physics, a vector often describes the motion of an object. For example, Warty the Woodchuck goes 10 meters towards a hole in the ground. We can divide vectors into parts called "components", of which the vector is a sum. For example, a two-dimensional vector is divided into x and y components. Displacement. Displacement answers the question, "Has the object moved?" Note the formula_1 symbol. This symbol is a sort of "super equals" symbol, indicating that not only does formula_2 EQUAL the displacement formula_3, but more importantly displacement is operationally defined by formula_2. We say that formula_2 operationally defines displacement, because formula_2 gives a step by step procedure for determining displacement. Namely: Be sure to note that displacement is not the same as distance travelled. For example, imagine travelling one time along the circumference of a circle. If you end where you started, your displacement is zero, even though you have clearly travelled some distance. In fact, displacement is an average distance travelled. On your trip along the circle, your north and south motion averaged out, as did your east and west motion. Clearly we are losing some important information. The key to regaining this information is to use smaller displacement intervals. For example, instead of calculating your displacement for your trip along the circle in one large step, consider dividing the circle into 16 equal segments. Calculate the distance you travelled along each of these segments, and then add all your results together. Now your total travelled distance is not zero, but something approximating the circumference of the circle. Is your approximation good enough? Ultimately, that depends on the level of accuracy you need in a particular application, but luckily you can always use finer resolution. For example, we could break your trip into 32 equal segments for a better approximation. Returning to your trip around the circle, you know the true distance is simply the circumference of the circle. The problem is that we often face a practical limitation for determining the true distance travelled. (The travelled path may have too many twists and turns, for example.) Luckily, we can always determine displacement, and by carefully choosing small enough displacement steps, we can use displacement to obtain a pretty good approximation for the true distance travelled. (The mathematics of calculus provides a formal methodology for estimating a "true value" through the use of successively better approximations.) In the rest of this discussion, I will replace formula_7 with formula_8 to indicate that small enough displacement steps have been used to provide a good enough approximation for the true distance travelled. Velocity. [Δ, "delta", upper-case Greek D, is a "prefix" conventionally used to denote a "difference".] Velocity answers the question "Is the object moving now, and if so - how quickly?" Once again we have an "operational" definition: we are told what steps to follow to calculate velocity. Note that this is a definition for average velocity. The displacement Δ"x" is the vector sum of the smaller displacements which it contains, and some of these may subtract out. By contrast, the distance travelled is the scalar sum of the smaller distances, all of which are non-negative (they are the "magnitudes" of the displacements). Thus the distance travelled can be larger than the magnitude of the displacement, as in the example of travel on a circle, above. Consequently, the average velocity may be small (or zero, or negative) while the speed is positive. If we are careful to use very small displacement steps, so that they come pretty close to approximating the true distance travelled, then we can write the definition for instantaneous velocity as [δ is the lower-case "delta".] Or with the idea of limits from calculus, we have: [d, like Δ and δ, is merely a "prefix"; however, its use definitely specifies that this is a sufficiently small difference so that the error--due to stepping (instead of smoothly changing) the quantity--becomes negligible.] Acceleration. Acceleration answers the question "Is the object's velocity changing, and if so - how quickly?" Once again we have an operational definition. We are told what steps to follow to calculate acceleration. Again, also note that technically we have a definition for average acceleration. As for displacement, if we are careful to use a series of small velocity changes, then we can write the definition for instantaneous acceleration as: Or with the help of calculus, we have: Vectors. Notice that the definitions given above for displacement, velocity and acceleration included little arrows over many of the terms. The little arrow reminds us that direction is an important part of displacement, velocity, and acceleration. These quantities are vectors. By convention, the little arrow always points right when placed over a letter. So for example, formula_9 just reminds us that velocity is a vector, and does not imply that this particular velocity is rightward. Why do we need vectors? As a simple example, consider velocity. It is not enough to know how fast one is moving. We also need to know which direction we are moving. Less trivially, consider how many different ways an object could be experiencing an acceleration (a change in its velocity). Ultimately, there are three distinct ways an object could accelerate: More general accelerations are simply combinations of 1 and 3 or 2 and 3. Importantly, a change in the direction of motion is just as much an acceleration as is speeding up or slowing down. In classical mechanics, no direction is associated with time (you cannot point to next Tuesday). So the definition of formula_10 tells us that acceleration will point wherever the change in velocity formula_11 points. Understanding that the direction of formula_12 determines the direction of formula_13 leads to three non-mathematical but very powerful rules of thumb: Again, more general motion is simply a combination of 1 and 3 or 2 and 3. Using these three simple rules will dramatically help your intuition of what is happening in a particular problem. In fact, much of the first semester of college physics is simply the application of these three rules in different formats. = Equations of motion (constant acceleration) = A particle is said to move with constant acceleration if its velocity changes by equal amounts in equal intervals of time, no matter how small the intervals may be Since acceleration is a vector, constant acceleration means that both direction and magnitude of this vector don't change during the motion. This means that average and instantaneous acceleration are equal. We can use that to derive an equation for velocity as a function of time by integrating the constant acceleration. Giving the following equation for velocity as a function of time. To derive the equation for position we simply integrate the equation for velocity. Integrating again gives the equation for position. The following are the equations of motion: The following equations can be derived from the two equations above by combining them and eliminating variables. What does force in motion mean? Force means strength and power. Motion means movement. That’s why we need forces and motions in our life. We need calculation when we want to know how fast things go, travel and other things which have force and motion. How do we calculate the speed? If you want to calculate the average speed, distance travelled or time taken you need to use this formula and remember it: formula_14 This is an easy formula to use, you can find the distance travelled, time taken or average speed, you need at least 2 values to find the whole answer. Is velocity the same thing as speed? Velocity is a vector quantity that refers to "the rate at which an object changes its position", whereas speed is a scalar quantity, which cannot be negative. Imagine a kid moving rapidly, one step forward and one step back, always returning to the original starting position. While this might result in a frenzy activity, it would result in a zero velocity, because the kid always returns to the original position, the motion would never result in a change in position, in other words formula_15 would be zero. Speed is measured in the same physical units of measurement as velocity, but does not contain an element of direction. Speed is thus the magnitude component of velocity. Velocity contains both the magnitude and direction components. You can think of velocity as the displacement/duration, whereas speed can be though as distance/duration. Acceleration. When a car is speeding up we say that it is accelerating, when it slows down we say it is decelerating. How do we calculate it? When we want to calculate it, the method goes like that: A lorry driver brakes hard, and slows from 25 m/s to 5 m/s in 5 seconds. What was the vehicle's acceleration? formula_16 What is initial velocity and final velocity? Initial velocity is the beginning before motion starts or in the middle of the motion, final velocity is when the motion stops. There is another way to calculate it and it is like that This equations which are written is the primary ones, which means that when you don’t have lets say final velocity, how will you calculate the equation? This is the way you are going to calculate. Observing motion. When you want to know how fast an athletic person is running, what you need is a stopwatch in your hand, then when the person starts to run, you start the stopwatch and when the person who is sprinting stops at the end point, you stop the watch and see how fast he ran, and if you want to see if the athlete is wasting his energy, while he is running look at his movement, and you will know by that if he is wasting his energy or not. This athletic person is running, and while he is running the scientist could know if he was wasting his energy if they want by the stop watch and looking at his momentum. Measuring acceleration. Take a slope, a trolley, some tapes and a stop watch, then put the tapes on the slope and take the trolley on the slope, and the stopwatch in your hand, as soon as you release the trolley, start timing the trolley at how fast it will move, when the trolley stops at the end then stop the timing. After wards, after seeing the timing , record it, then you let the slope a little bit high, and you will see, how little by little it will decelerate. = Newton = Isaac Newton was an English physicist, mathematician (described in his own day as a "natural philosopher") , astronomer and alchemist. Newton is one of the most influential scientists of all time, and he is known, among other things, for contributing to development of classical mechanics and for inventing, independently from "Gottfried Leibniz", calculus. Newton's laws of motion. Newton is also known by his three laws of motion, which describe the relationship between a "body" and the "forces acting upon it", and "its motion in response to said forces". =Symbols= Some useful symbols seen and that we will see: Force. A force is any interaction that tends to change the motion of an object. In other words, a force can cause an object with mass to change its velocity. Force can also be described by intuitive concepts such as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of "newtons" and represented by the symbol formula_17. How to calculate the force? When we want to calculate the force, and we have the "mass" and "acceleration", we can simply use the simple formula stated in the Newton's second law above, that is formula_20, where formula_18 is the mass (or the amount of matter in a body), and formula_19 is the acceleration. Note that the Newton’s second law is defined as a numerical measure of inertia. What is inertia? Inertia is the tendency of a body to maintain its state of rest or uniform motion, unless acted upon by an external force. Robert Hooke. Robert Hooke was an English polymath who played an important role in the scientific revolution, through both experimental and theoretical work. Hooke's law. Hooke's law is a principle of physics that states that the force formula_17 needed to extend or compress a spring by some distance formula_26 is proportional to that distance, or algebraically formula_27, where formula_28 is a constant factor characteristic of the spring, its stiffness.

German/Lesson 4. Lektion 4 Lesestück 4-1 ~ Eine Geschichte über Zürich. Although this short story contains quite a number of impressive German nouns and adjectives, with the aid of "Vokabeln 4-1" following you should have no trouble reading and understanding it. The passage makes considerable use of the German genitive case (English possessive case), which you have not yet learned. However, a clue applicable here: translate "des" as "of the" or "of" and note there are other "der"-words that also mean "of the". Vokabeln 4-1. die Alpen Alps der Ausfluss outlet, effluence (of a lake) die Bankinstitute banking institutes die Bankenwirtschaft banking business das Ende end die Großbanken major banks die Hauptstadt capital city das Haus house der Kanton canton (Swiss state) das Lesestück reading passage die Schweiz Switzerland die Sicht view der Sitz office das Wetter weather das Zentrum center (centre) das Zürich Zurich (city and canton in Switzerland) der Zürichsee Lake Zurich d.h. (das heißt) i.e. ("that is" in Latin) Glarner Alpen Glarner Alps man hat... one has... nach Hause (toward) home (compare: "zu Hause" = "at home") anrufen call, telephone geben (gab, gegeben) give kommen (kam, gekommen) come liegen (lag, gelegen) lie (lay, lain) am (an dem) at the ausgesprochen markedly bei in beiden two etliche a number of, quite a few, several gleichnamig same named größte largest klar clear klein small neben besides nördlich northern schweizer of or pertaining to Swiss Grammatik 4-1 ~ Introduction to adjectives. An is a part of speech which can be thought of as a "describing word"—typically, an adjective modifies a noun. In both English and German, adjectives come before the noun they describe or modify. In many other languages (such as French) they usually come after the noun. Here are some examples of adjectives (underlined) you have already encountered: Because nouns are capitalized in German, it is fairly obvious in these sentences where the adjectives occur: just before the nouns they modify. Note how the endings on German adjectives can change, depending upon the noun ("keinen Käse"; "klarem Wetter"; "gute Sicht")—specifically, the gender and case of the noun they are modifying. Before explaining the basic rules governing adjective endings, you need to have a better understanding of person, gender, and case in German nouns—concepts that will be explored in the next few lessons. Finally, realize that the ordinal numbers you learned in Lektion 3 are, in fact, adjectives—subject to the same rules governing word endings for adjectives. Gespräch 4-1 ~ Das neue Mädchen. This short conversational passage contains more examples of adjectives. Vokabeln 4-2. die Brünette brunette die Haare hair(s) das Mädchen girl das Ferkel piglet gefallen appeal to glauben believe heißen name, call mag like, desire, wish dort there (dort) drüben over there dunkel dark ihr her hübsch cute klein short lang long neue new wenn if wer? who? Grammatik 4-2 ~ Nouns and pronouns in the accusative and dative. As was noted previously when the concept of case was introduced for pronouns (Grammatik 2-2), there are four cases used in German. Recall that the nominative case in German corresponds to the "subjective case" in English and applies to nouns and pronouns used in a sentence as the subject of a verb. Nouns (and pronouns) that are used as objects of transitive (action) verbs are in the English objective case. If these are direct objects (recipients of the action of a verb), then these nouns are in the accusative case in German. If indirect objects, then these nouns are in the dative case in German. Essentially, the English "objective case" is divided, in German, into an accusative case used for direct objects and a dative case used for indirect objects. Pronouns. For comparison with English, recall that the singular personal pronouns ("nominative case") are "I", "you", and "he/she/it" (1st, 2nd, and 3rd persons). The "objective case", personal pronouns in English are "me", "you", and "him/her/it"—and are used for both direct and indirect objects of verbs. For example: The German accusative case, personal pronouns (singular) are: "mich, dich, ihn/sie/es". The German dative case, personal pronouns (singular) are: "mir", "dir", "ihm/ihr/ihm". Thus, the above English example sentence becomes, in German: Because "mir" is a dative pronoun, there is no need in German to use a modifier as in English, where "to" is used as a signal of an indirect object. The following table summarizes the German pronouns in three cases for both singular and plural number: Recall from Gespräch 2-1 the "incomplete" sentence "Und Ihnen?" ('And you?'). Note that the pronoun agrees in case (here, dative) with the implied sentence — "Und wie geht es Ihnen?" The same rule is evident in Gespräch 1-1 ("Und dir?"). Such agreement is important to convey the correct meaning. Tables giving the German personal pronouns in all cases can be found in an appendix: Pronoun Tables. Nouns. Nouns do not change their form (spelling) relative to case in German; instead, a preceding article indicates case. You have learned the nominative case definite and indefinite articles (Grammatik 3-3: "der", "die", "das" and "ein", "eine". "ein") for each of the three noun genders. Now we will learn the "accusative" (used to signal a direct object) and "dative" (used to signal an indirect object) articles. First, the definite articles: This table might seem a bit overwhelming (and there is yet one more case in German: the genitive!), but some points to note can make memorizing much easier. First, as you can see from the table, "gender" does not really exist for plural nouns. No matter what the noun gender in its singular number, its plural always has the same set of definite articles: "die", "die", "den" for nominative, accusative, and dative cases. The plural "der"-words are similar to the feminine singular "der"-words, differing only in the dative case. Another point: the dative for both masculine and neuter nouns is the same: "dem". Finally, for feminine, neuter, and plural nouns, there is no change between nominative and accusative cases. Thus, only for masculine nouns is there a definite article change in the accusative compared with the nominative. The following examples demonstrate the use of the definite article in various parts of speech: In the last example, you need to know that in both English and German, the noun (or pronoun) that follows the verb 'to be' is a predicate noun, for which the correct case is the nominative. That is why, in English, 'It is I' is grammatically correct and 'It is me' is simply incorrect. The indefinite articles are as follows: Of course, there are no plural indefinite articles in German or English ("ein" means "a". "an", or "one"). It is important to see that there is a pattern in the case endings added to "ein" related to the "der"-words in the definite articles table above. For example, the dative definite article for masculine nouns is "dem"—the indefinite article is formed by adding "-em" onto "ein" to get "einem". The dative definite article for feminine nouns is "der"—the indefinite is "ein" plus "-er" or "einer". These ending changes will be covered in greater detail in a future lesson. You will see that there are a number of words (adjectives, for example) whose form relative changes by addition of these endings to signal the case of the noun they modify. Finally, we can see a pattern relationship between these "endings" and the 3rd person pronouns as well: We could construct a similar table to compare the definite articles to the 3rd person pronouns. And in that case, we would also see how the plural definite articles ("die", "die", "den") compare with the third person plural pronouns ("sie", "sie", "ihnen"). Grammatik 4-3 ~ Interrogatives. You have encountered nearly all of the interrogatives commonly used in German (review Grammatik 1-2): "wann" when "warum" why "Warum sind Sie müde?" "was" what "Was ist das?" "wer" who "Wer ist das Mädchen?" "wie" how "Wie geht es dir?" "wieviel" how much "Wieviel Uhr ist es?" "wo" where "Wo ist das Buch?" "wohin" where (to) "Wohin gehst du?" In a question, interrogatives replace the unknown object and establish the class of answer expected. Note that the English construction for some of the questions differs from the German in that the former uses the progressive form of "do". Übersetzung 4-1. Translate the following sentences into German:

Physics Study Guide/Greek alphabet. =About the "Common uses in Physics"= While these are indeed common usages, it should be pointed out that there are many other usages and that other letters are used for the same purpose. The reason is quite simple: there are only so many symbols in the Greek and Latin alphabets, and scientists and mathematicians generally do not use symbols from other languages. It is a common trap to associate a symbol exclusively with some particular meaning, rather than learning and understanding the physics and relations behind it. =See Also= Greek alphabet on Wikipedia

Cascading Style Sheets. This book is a guide to Cascading Style Sheets (CSS), a technique widely used in web pages including Wikipedia to describe their visual style and appearance. CSS can take HTML to new places creatively and functionally. Once you learn how to style mark-up, you can additionally learn JavaScript functions that make dynamic web pages.

German/Level III/Der Engländer in Österreich. Lektion Fünf <br> Gespräch 5-2 ~ Der Engländer in Österreich. <br> Wenn er auf den Kontinent fährt, wandert Herr Standish gern. Heute früh fährt er in die Stadt St. Pölten in Niederösterreich. Er spricht mit einer fremden Frau: Vokabeln 5A. das Abendessen supper (evening meal) [das] Österreich Austria die Ecke corner das Frühstück breakfast das Hotel hotel der Kilometer kilometer die Küche cooking, cuisine der Kontinent continent (Europe) [das] Niederösterreich (federal state of) Lower Austria das Rathaus city hall das Restaurant restaurant die Stadt city Bitte sehr You're welcome Entschuldigen Sie Pardon me, excuse me Es gibt dort... There is there... Gibt es...? Is there..? Guten Tag good day (parting) immer geradeaus straight on ahead können Sie could you (polite form) Wie bitte? Pardon me? (polite "come again?") empfehlen recommend fahren travel kommen come, go, get wandern wander sagen say, tell sprechen speak anderer, andere, anderes other besonders especially bitte please das that dann then darin therein ein a (indefinite article) eins one (cardinal number) fremd unknown gern gladly gleich just, right (correct), right here, same heute früh this morning hier here (in this place) ich I (personal pronoun) links left (direction) neben next to rechts right (direction) ungefähr approximately von of ("Rathaus von St. Pölten" = St. Polten City Hall) wie how (interrogative) wo where (interrogative) zu to ("zum" = contraction of "zu dem") Andere Wörter 4A. der Bahnhof train station der Flughafen airport die Polizeiwache police station die Post post office genau exact(ly) heute today Lesestück 5-1 ~ Eine Geschichte über St. Pölten. Niederösterreich ist sowohl flächenmäßig als auch nach Einwohnern das größte der neun österreichischen Bundesländer. Sankt Pölten ist die Landeshauptstadt von Niederösterreich. Der Name St. Pölten geht auf den heiligen Hippolytos zurück, nach dem die Stadt benannt wurde. Die Altstadt befindet sich dort, wo vom 2. bis zum 4. Jahrhundert die Römerstadt "Aelium Cetium" stand. 799 wurde der Ort als "Treisma" erwähnt. Das Marktrecht erhielt St. Pölten um 1050, zur Stadt erhoben wurde es 1159. Bis 1494 stand St. Pölten im Besitz des Bistums Passau, dann wurde es landesfürstliches Eigentum. Bereits 771 findet sich ein Benediktinerkloster, ab 1081 gab es Augustiner-Chorherren, 1784 wurde deren Kollegiatsstift aufgehoben, das Gebäude dient seit 1785 als Bischofssitz. Zur Landeshauptstadt von Niederösterreich wurde St. Pölten mit Landtagsbeschluss vom 10. Juli 1986, seit 1997 ist es Sitz der Niederösterreichischen Landesregierung. <br> Vokabeln 5B. Die Altstadt old town Der Augustiner Augustinian Der Besitz possession, holding Das Bistum diocese Der Bischofssitz bishop's see (a seat of a bishop's authority) Die Bundesländer federal states Die Chorherren men's choir Das Eigentum proprietorship Die Einwohner inhabitants Das Gebäude premises Die Geschichte history Das Jahrhundert century Das Kloster monastery, friary Das Kollegiatsstift monastery college Die Landeshauptstadt regional or state capital city Die Landesregierung provincial (state) government Der Landtagsbeschluss day of jurisdictional reorganization Das Marktrecht right to hold markets Der Name name Der Ort place, spot, city Die Römerstadt Roman town Der Sitz official place Bistum Passau a dioecian region in Bavaria sowohl... als auch both... and zurück auf goes back to aufheben (hob auf, aufgehoben) merged in (or turned into?) befinden sich situated, located (befand sich, haben sich befunden) finden sich* found (located) benennen (benannte, benannt) call (as to label) erhalten (erhielt, erhalten) receive erheben (erhob, erhoben) arise, raise erwähnen (erwähnte, erwähnt) mention stehen (stand, gestanden) stand (stood, stood) werden (wurde, [ist]geworden) become ab from auf up bereits already bis until, by, up to flächenmäßig (no direct translation) ~ when measured in surface heilig holy landesfürstlich baronial or princely (holdings) nach in terms of um around

High School Mathematics Extensions/Mathematical Proofs. Introduction. Mathematicians have been, for the past five hundred years or so, obsessed with proofs. They want to prove everything, and in the process proved that they can't prove everything (see this). This chapter will introduce the axiomatic approach to mathematics, and several types of proofs. Direct proof. The direct proof is relatively simple — by logically applying previous knowledge, we "directly prove" what is required. Example 1 Prove that the sum of any two even integers formula_1 and formula_2 is even. Solution 1 We know that since formula_1 and formula_2 are even, they must have 2 as a factor. Then, we can write the following: Then: by the distributive property of integers The number formula_9 clearly has 2 as a factor, which implies it is even. Therefore, formula_10 is even. Example 2 Prove the following statement for non-zero integers formula_11: If formula_12 divides formula_13 and formula_13 divides formula_15 , then formula_12 divides formula_15 . Solution 2 If an integer formula_1 divides an integer formula_2 , then we can write formula_20 , for some non-zero integer formula_21 . So let's say that formula_22 and formula_23 , for some non-zero integers formula_21 and formula_25 . Then: by the associative property of integer multiplication. But since formula_21 and formula_25 are integers, their product formula_29 must also be an integer. Therefore, formula_15 is the product of some integer multiplied by formula_12 , so we get that formula_12 divides formula_15 . Mathematical induction. Deductive reasoning is the process of reaching a conclusion that is guaranteed to follow. For example, if we know then we can conclude: Induction is the opposite of deduction. To induce, we observe how things behave in specific cases and from that we draw conclusions as to how things behave in the general case. Suppose we want to show that a statement (let us call it formula_34 for easier notation) is true for all natural numbers. This is how induction a proof by induction works: To understand how the last step works, notice the following Example 1 Show that the identity holds for all positive integers. Solution Firstly, we show that it holds for 1 Suppose the identity holds for some natural number "k": This supposition is known as the induction hypothesis. We assume it is true, and aim to show that, is also true. We proceed which is what we have set out to show. Since the identity holds for 3, it also holds for 4, and since it holds for 4 it also holds for 5, and 6, and 7, and so on. There are two types of mathematical induction: strong and weak. In weak induction, you assume the identity holds for certain value k, and prove it for k+1. In strong induction, the identity must be true for any value lesser or equal to k, and then prove it for k+1. Example 2 Show that n! > 2n for n ≥ 4. Solution The claim is true for n = 4. As 4! > 24, i.e. 24 > 16. Now suppose it's true for n = k, k ≥ 4, i.e. it follows that We have shown that if for n = k then it's also true for n = k + 1. Since it's true for n = 4, it's true for n = 5, 6, 7, 8 and so on for all n. Example 3 Show that Solution Suppose it's true for n = k, i.e. it follows that We have shown that if it's true for n = k then it's also true for n = k + 1. Now it's true for n = 1 (clear). Therefore it's true for all integers. Exercises. 1. Prove that formula_53 2. Prove that for n ≥ 1, where xn and yn are integers. 3. Note that Prove that there exists an explicit formula for formula_57 4. The sum of all of the interior angles of a triangle is formula_58; the sum of all the angles of a rectangle is formula_59. Prove that the sum of all the angles of a polygon with "n" sides, is formula_60. Proof by contradiction. The idea of a proof by contradiction is to: √2 is irrational. As an example, we shall prove that formula_61 is not a rational number. Recall that a rational number is a number which can be expressed in the form of p/q, where p and q are integers and q does not equal 0 (see the 'categorizing numbers' section here). First, assume that formula_61 is "rational":<br> where "a" and "b" are coprime (i.e. integers with no common factors, with greatest common divisor 1). If "a" and "b" are not coprime, we remove all common factors. In other words, "a/b" is in simplest form. Now, continuing: We have now found that "a2" is some integer multiplied by 2. Therefore, "a2" must be divisible by two. If "a2" is even, then "a" must also be even, for an odd number squared yields an odd number. Therefore we can write "a = 2c", where "c" is another integer. We have discovered that "b2" is also an integer multiplied by two. It follows that "b" must be even. We have a contradiction! Both "a" and "b" are even integers. In other words, both have the common factor of 2. But we already said that "a/b" is in simplest form, with no common factors. Since such a contradiction has been established, we must conclude that our original assumption was false. Therefore, √2 is irrational. Contrapositive. Some propositions that take the form of "if xxx then yyy" can be hard to prove. It is sometimes useful to consider the "contrapositive" of the statement. Before I explain what contrapositive is let us see an example is harder to prove than although they mean the same thing. So instead of proving the first proposition directly, we prove the second proposition instead. If "A" and "B" are two propositions, and we aim to prove we may prove the equivalent statement instead. This technique is called proof by contrapositive. To see why those two statements are equivalent, we show the following boolean algebra expressions is true (see Logic) (to be done by the reader). Exercises. 1. Prove that there is no perfect square number for 11,111,1111,11111... 2. Prove that there are infinitely number of "k"'s such that, 4"k" + 3, is prime. (Hint: consider N = p1p2...pm + 3) Reading higher mathematics. This is some basic information to help with reading other higher mathematical literature. "... to be expanded" Quantifiers. Sometimes we need propositions that involve some description of rough quantity, e.g. "For "all" odd integers x, x2 is also odd". The word "all" is a description of quantity. The word "some" is also used to describe quantity. Two special symbols are used to describe the quanties "all" and "some" Example 1<br> The proposition: can be expressed symbolically as: Example 2<br> The proposition: can be expressed symbolically as: This proposition is false. Example 3<br> Consider the proposition concerning (z = x'y' + xy): can be expressed symbolically as: This proposition is true. Note that the order of the quantifiers is important. While the above statement is true, the statement is false. It asserts that there is one value of y which is the same for all x for which z=1. The first statement only asserts that there is a y for each x, but different values of x may have different values of y. Negation. Negation is just a fancy word for the opposite, e.g. The "negation" of "All named Britney can sing" is "Some named Britney can't sing". What this says is that to disprove that all people named Britney can sing, we only need to find one named Britney who can't sing. To express symbolically: Similarly, to disprove we only need to find one odd number that doesn't satisfy the condition. Three is odd, but 3×3 = 9 is also odd, therefore the proposition is FALSE and is TRUE In summary, to obtain the "negation" of a proposition involving a quantifier, you replace the quantifier by its opposite (e.g. formula_67 with formula_77) and the "quantified proposition" (e.g. "x is even") by its negation (e.g. "x is odd"). Example 1 is a true statement. Its negation is Axioms and Inference. If today's mathematicians were to describe the greatest achievement in mathematics in the 20th century in one word, that word will be abstraction. True to its name, abstraction is a very abstract concept (see Abstraction). In this chapter we shall discuss the "essence" of some of the number systems we are familiar with. For example, the real numbers and the rational numbers. We look at the most fundamental properties that, in some sense, "define" those number systems. We begin our discussion by looking at some of the more obscure results we were told to be true Most people simply accept that they are true (and they are), but the two results above are simple consequences of what we believe to be true in a number system like the real numbers! To understand this we introduce the idea of axiomatic mathematics (mathematics with simple assumptions). An axiom is a statement about a number system that we assume to be true. Each number system has a few axioms, from these axioms we can draw conclusions (inferences). Let's consider the Real numbers, it has axioms Let "a", "b" and "c" be real numbers These are the "minimums" we assume to be true in this system. These are "minimum" in the sense that everything else that is true about this number system can be derived from those axioms! Let's consider the following true identity which is not included in the axioms, but we can prove it using the axioms. We proceed: Before we proceed any further, you will have notice that the real numbers are not the only numbers that satisfies those axioms! For example the rational numbers also satisfy all the axioms. This leads to the abstract concept of a "field". In simple terms, a "field" is a number system that satisfies all those axiom. Let's define a "field" more carefully: A number system, "F", is a "field" if it supports + and × operations such that: Now, for M3, we do not let "b" be zero, since 1/0 has no meaning. However for the "M" axioms, we have excluded zero anyway. For interested students, the requirements of "closure", "identity", having "inverses" and "associativity" on an operation and a set are known as a . If "F" is a group with addition and "F"* is a group with multiplication, plus the distributivity requirement, "F" is a field. The above axioms merely state this fact in full. Note that the natural numbers are not a field, as M3 is generally not satisfied, i.e. not every natural number has an inverse that is also a natural number. Please note also that (-"a") denotes the additive inverse of "a", it doesn't say that (-a) = (-1)(a), although we can prove that they are equivalent. Example 1 Prove using only the axioms that 0 = -0, where -0 is the additive inverse of 0. Solution 1 Example 2 Let F be a field and "a" an element of F. Prove using nothing more than the axioms that 0"a" = 0 for all "a". Solution Example 3 Prove that (-"a") = (-1)"a". Solution 3 One wonders why we need to prove such obvious things (obvious since primary school). But the idea is not to prove that they are true, but to practise inferencing, how to logically join up arguments to prove a point. That is a vital skill in mathematics. Exercises. 1. Describe a field in which 1 = 0 2. Prove using only the axioms if u + v = u + w then v = w (subtracting u from both sides is not accepted as a solution) 3. Prove that if xy = 0 then either x = 0 or y = 0 4. In F-, the operation + is defined to be the difference of two numbers and the × operation is defined to be the ratio of two numbers. E.g. 1 + 2 = -1, 5 + 3 = 2 and 9×3 = 3, 5×2; = 2.5. Is F- a field? 5. Explain why Z6 (modular arithmetic modular 6) is not a field. Problem Set. 1. Prove for formula_82 2. Prove by induction that formula_83 3. Prove by induction where 4. Prove by induction formula_87 5. Prove that if x and y are integers and n an odd integer then formula_88 is an integer. 6. Prove that (n~m) = n!/((n-m)!m!) is an integer. Where n! = n(n-1)(n-2)...1. E.g. 3! = 3×2×1 = 6, and (5~3) = (5!/3!)/2! = 10. "Many questions in other chapters require you to prove things. Be sure to try the techniques discussed in this chapter."

German/Appendices/Grammar II. Conjugating 'to be'. In these cases, we use the correct form of "sein" for each situation. Please notice the final two sentences both use 'Sie', and we must look at the verb to determine the difference between 'she' and 'they'. In German, the English infinitive 'to be' is translated as "sein". This is the table of the forms of 'sein', with rough English translations. Note that in English, there are only three forms (am, is, are) while German has five (bin, bist, ist, sind, seid). Also, the verb conjugation of the two you-formals are always the exact same. German sein English to be Conjugating Normal Verbs. In these sentences, different verbs and endings are used. Note that the verb is always in second position. When conjugating normal verbs, use the endings shown below (a memory hook is the "best ten" endings). Note that in normal verbs, such as spielen and machen, ihr-form and er/sie/es-form are the same and the wir-form, sie (pl)-form and the formal are all the same as the infinitive. -en spielen - to play machen - to make/do Conjugating Irregular Verbs. In each of these sentences, we use an irregular verb. Irregularity occurs in the ich-form or the du-form and er/sie/es-forms. There are three types of irregularity. E in the first syllable. One form of irregularity occurs "sometimes" when the verb contains an 'e' in the first syllable. The change is simple: the du-form and er/sie/es forms both change the 'e' to an 'i.e.' or an 'i'. Two common examples are shown. Note that the er/sie/es-form and ihr-form are no longer the same. sehen - to see geben - to give Haben. A similar, yet different, change occurs in the verb "haben". As in the irregularity above, the du-form and er/sie/es-form change. haben - to have Verbs ending in Consonant-N. Some verbs change the ich-form for obvious reasons. "Wandern" and "basteln" are two examples. Both drop the first e in the ich-form. wandern - to hike basteln - to build Conjugating Modals. Modals are a new kind of verb. They are the equivalent to helping verbs in English. There are seven basic modals: können (can), mögen (like), dürfen (may), wollen (want), sollen (should), müssen (must), and möchten (would like). Möchten isn't technically a modal, but it acts like one in most aspects. Modals are conjugated very differently. The ich-form and er/sie/es-form are always alike and singular has a different verb in the first syllable (except in sollen and möchten). Below are the conjugations of the six basic modals and möchten. können - can mögen - like dürfen - may wollen - want sollen - should müssen - must möchten - would like Separable Verbs. Some verbs in German are separable: they have a prefix that can be separated from the base. When the verb is used with a modal, it regains the prefix at the end of the sentence. When it is the main verb of the sentence, the prefix is moved to the end of the sentence. An "example" in English would be the word "intake". When it is used as a verb, it becomes "take ... in". When it is used as an adjective or a noun, it becomes "intake" again. Two easy examples of separable verbs are "aussehen" and "mitkommen". Note that aussehen is also irregular. aussehen - to appear mitkommen - to come along/with

Physics Study Guide/Force. =Force= A net force on a body causes a body to accelerate. The amount of that acceleration depends on the body's inertia (or its tendency to resist changes in motion), which is measured as its mass. When Isaac Newton formulated Newtonian mechanics, he discovered three fundamental laws of motion. Later, Albert Einstein proved that these laws are just a convenient approximation. These laws, however, greatly simplify calculations and are used when studying objects at velocities that are small compared with the speed of light. Friction. It is the force that opposes relative motion or tendency of relative motion between two surfaces in contact represented by f. When two surfaces move relative to each other or they have a tendency to move relative to each other, at the point (or surface) of contact, there appears a force which opposes this relative motion or tendency of relative motion between two surfaces in contact. It acts on both the surfaces in contact with equal magnitude and opposite directions (Newton's 3rd law). Friction force tries to stop relative motion between two surfaces in contact, if it is there, and when two surfaces in contact are at rest relative to each other, the friction force tries to maintain this relative rest. Friction force can assume the magnitude (below a certain maximum magnitude called limiting static friction) required to maintain relative rest between two surfaces in contact. Because of this friction force is called a self adjusting force. Earlier, it was believed that friction was caused due to the roughness of the two surfaces in contact with each other. However, modern theory stipulates that the cause of friction is the Coulombic force between the atoms present in the surface of the regions in contact with each other. Formula: Limiting Friction = (Friction Coefficient)(Normal reaction) Static Friction = the friction force that keeps an object at relative rest. Kinetic Friction = sliding friction Newton's First Law of Motion. This means, essentially, that acceleration does not occur without the presence of a force. The object tends to maintain its state of motion. If it is at rest, it remains at rest and if it is moving with a velocity then it keeps moving with the same velocity. This tendency of the object to maintain its state of motion is greater for larger mass. The "mass" is, therefore, a measure of the inertia of the object. In a state of equilibrium, where the object is at rest or proceeding at a constant velocity, the net force in every direction must be equal to 0. At a constant velocity (including zero velocity), the sum of forces is 0. If the sum of forces does not equal zero, the object will accelerate (change velocity over time). It is important to note, that this law is applicable only in non-accelerated coordinate systems. It is so, because the perception of force in accelerated systems are different. A body under balanced force system in one frame of reference, for example a person standing in an accelerating lift, is acted upon by a net force in the earth's frame of reference. Inertia is the tendency of an object to maintain its velocity i.e. to resist acceleration. Newton's Second Law of Motion. These two statements mean the same thing, and is represented in the following basic form (the system of measurement is chosen such that constant of proportionality is 1) : The product of mass and velocity i.e. "m"v is called the momentum. The net force on a particle is thus equal to rate change of momentum of the particle with time. Generally mass of the object under consideration is constant and thus can be taken out of the derivative. Force is equal to mass times acceleration. This version of Newton's Second Law of Motion assumes that the mass of the body does not change with time, and as such, does not represent a general mathematical form of the Law. Consequently, this equation cannot, for example, be applied to the motion of a rocket, which loses its mass (the lost mass is ejected at the rear of the rocket) with the passage of time. An example: If we want to find out the downward force of gravity on an object on Earth, we can use the following formula: Hence, if we replace m with whatever mass is appropriate, and multiply it by 9.806 65 m/s2, it will give the force in newtons that the earth's gravity has on the object in question (in other words, the body's weight). Newton's Third Law of Motion. This means that for every force applied on a body A by a body B, body B receives an equal force in the exact opposite direction. This is because forces can only be applied by a body on another body. It is important to note here that the pair of forces act on two different bodies, affecting their state of motion. This is to emphasize that pair of equal forces do not cancel out. There are no spontaneous forces. It is very important to note that the forces in a "Newton 3 pair", described above, can never act on the same body. One acts on A, the other on B. A common error is to imagine that the force of gravity on a stationary object and the "contact force" upwards of the table supporting the object are equal by Newton's third law. This is not true. They may be equal - but because of the second law (their sum must be zero because the object is not accelerating), not because of the third. The "Newton 3 pair" of the force of gravity (= earth's pull) on the object is the force of the object attracting the earth, pulling it upwards. The "Newton 3 pair" of the table pushing it up is that it, in its turn, pushes the table down. Equations. "To find Displacement" "To find Final Velocity" "To find Final Velocity" "To find Force when mass is changing" "To find Force when mass is a constant"

Physics Study Guide/Gravity. Newtonian Gravity. Newtonian Gravity (simplified gravitation) is an "apparent" force (a.k.a. "pseudoforce") that simulates the attraction of one mass to another mass. Unlike the three fundamental (real) forces of electromagnetism and the strong and weak nuclear forces, gravity is purely attractive. As a force it is measured in newtons. The distance between two objects is measured between their centers of mass. Gravitational force is equal to the product of the universal gravitational constant and the masses of the two objects, divided by the square of the distance between their centers of mass. The value of the gravitational field which is equivalent to the acceleration due to gravity caused by an object at a point in space is equal to the first equation about gravitational force, with the effect of the second mass taken out. Gravitational potential energy of a body to infinity is equal to the universal gravitational constant times the mass of a body from which the gravitational field is being created times the mass of the body whose potential energy is being measured over the distance between the two centers of mass. Therefore, the difference in potential energy between two points is the difference of the potential energy from the position of the center of mass to infinity at both points. Near the earth's surface, this approximates: Potential energy due to gravity near the earth's surface is equal to the product of mass, acceleration due to gravity, and height (elevation) of the object. If the potential energy from the body's center of mass to infinity is known, however, it is possible to calculate the escape velocity, or the velocity necessary to escape the gravitational field of an object. This can be derived based on utilizing the law of conservation of energy and the equation to calculate kinetic energy as follows: Variables<br> Definition of terms A black hole is a geometrically defined region of space time exhibiting such large centripetal gravitational effects that nothing such as particles and electromagnetic radiation such as light may escape from inside of it. That is the escape velocity upon the event horizon is equivalent to the speed of light. General relativity is a metric theory of gravitation generalizing space time and Newton's law of universal gravitational attraction as a geometric property of space time.

Physics Study Guide/Work. =Work = Work is equal to the scalar product of force and displacement. The scalar product of two vectors is defined as the product of their lengths with the cosine of the angle between them. Work is equal to force times displacement times the cosine of the angle between the directions of force and displacement. Work is equal to change in kinetic energy plus change in potential energy for example the potential energy due to gravity. Work is equal to average power times time. The Work done by a force taking something from point 1 to point 2 is Work is in fact just a transfer of energy. When we 'do work' on an object, we transfer some of our energy to it. This means that the work done on an object is its increase in energy. Actually, the kinetic energy and potential energy is measured by calculating the amount of work done on an object. The gravitational potential energy (there are many types of potential energies) is measured as 'mgh'. mg is the weight/force and h is the distance. The product is nothing but the work done. Even kinetic energy is a simple deduction from the laws of linear motion. Try substituting for v^2 in the formula for kinetic energy. Variables<br> Definition of terms When work is applied to an object or a system it adds or removes kinetic energy to or from that object or system. More precisely, a net force in one direction, when applied to an object moving opposite or in the same direction as the force, kinetic energy will be added or removed to or from that object. Note that work and energy are measured in the same unit, the joule (J). Advanced work topics

Physics Study Guide/Energy. =Energy= Kinetic energy is simply the capacity to do work by virtue of motion. (Translational) kinetic energy is equal to one-half of mass times the square of velocity. (Rotational) kinetic energy is equal to one-half of moment of inertia times the square of angular velocity. Total kinetic energy is simply the sum of the translational and rotational kinetic energies. In most cases, these energies are separately dealt with. It is easy to remember the rotational kinetic energy if you think of the moment of inertia I as the "rotational mass". However, you should note that this substitution is not universal but rather a rule of thumb. Potential energy is simply the capacity to do work by virtue of position (or arrangement) relative to some zero-energy reference position (or arrangement). Potential energy due to gravity is equal to the product of mass, acceleration due to gravity, and height (elevation) of the object. Note that this is simply the vertical displacement multiplied by the weight of the object. The reference position is usually the level ground but the initial position like the rooftop or treetop can also be used. Potential energy due to spring deformation is equal to one-half the product of the spring constant times the square of the change in length of the spring. The reference point of spring deformation is normally when the spring is "relaxed," i.e. the net force exerted by the spring is zero. It will be easy to remember that the one-half factor is inserted to compensate for finite '"change in length" since one would want to think of the product of force and change in length formula_1 directly. Since the force actually varies with formula_2, it is instructive to need a "correction factor" during integration. Variables<br> Definition of terms

Physics Study Guide/Momentum. =Momentum= Linear momentum. Momentum is equal to mass times velocity. Angular momentum. Angular momentum of an object revolving around an external axis formula_1 is equal to the cross-product of the position vector with respect to formula_1 and its linear momentum. Angular momentum of a rotating object is equal to the moment of inertia times angular velocity. Force and linear momentum, torque and angular momentum. Net force is equal to the change in linear momentum over the change in time. Net torque is equal to the change in angular momentum over the change in time. Conservation of momentum. Let us prove this law. We'll take two particles formula_3 . Their momentums are formula_4 . They are moving opposite to each other along the formula_5-axis and they collide. Now force is given by: According to Newton's third law, the forces on each particle are equal and opposite.So, Rearranging, This means that the sum of the momentums does not change with time. Therefore, the law is proved. Variables<br> Calculus-based Momentum. Force is equal to the derivative of linear momentum with respect to time. Torque is equal to the derivative of angular momentum with respect to time.

German/Level III/Die Geschäftsleute. Vokabeln 4-3. der Ärmelkanaltunnel Chunnel (England-France channel tunnel) die Arbeit work die Bibliothek library die Buchhaltung accounting office das Büro office der Donnerstag Thursday die Geschäftsbibliothek company (business) library der Montag Monday der Name name der Schnellzug express train das Sehen vision die Versammlung meeting das Wien Vienna (Austria) das Wiedersehen reunion die Woche week das Zürich Zurich alles klar all right, everything clear am Montag on Monday dann wenn at such time when Darf ich... ? May I... ? Es freut mich sehr It gives me pleasure Guten Morgen! Good morning! ("greeting") Ja, gewiss certainly, of course vor Ende der Woche before the end of the week Wiener Büro Vienna branch office abhalten hold abschließen complete ankommen (kam an, angekommen) arrive fahren ride geben give kennen lernen meet, make acquaintance müssen must ("aux.") reisen travel sehen see, look tun do, accomplish sich vorstellen introduce werden will würde would bitte please da there durch through, by means of endlich finally gestern yesterday nach to, towards natürlich of course mich myself ("reflexive") mit with schnell fast, quick, rapid sofort directly, forthwith wieder again, once again Grammatik 4-4 ~ Personal Pronouns: Accusative Case. Here are the personal pronouns in the accusative case: * The accusative case is that of the object of a verb. Only transitive verbs take direct objects. The pronoun (and noun in two cases) object in each of these sentences is underlined in the German and the English: "Können Sie mich verstehen?" Can you understand me? "Ich kann Sie verstehen." I can understand you. "Ich kann sie verstehen" I can understand (her or them). "Ich kann ihn dir zurück kicken!" I can kick it back to you! Note the order of the pronouns in this last sentence. If the direct object (here: "ihn") is a personal pronoun, it precedes the dative ("dir"); if it were a noun, the dative would precede it, as in these sentences: "Hier, ich kicke dir den Ball zu." Here, I kick the ball to you. "Darf ich Ihnen meine Freundin vorstellen?" May I introduce my friend to you? Other uses of the accusative case in German will be explored in future lessons. Tables of the personal pronouns in all cases are summarized in Pronoun Tables. Grammatik 4-5 ~ Personal Pronouns in the Dative Case. Here are the personal pronouns in the dative case: The dative case is that of the indirect object of a verb. The pronoun indirect object of these sentences is underlined in the German and the English: "Es geht mir gut" It goes (for) me well "Wie geht es dir?" How goes it (for or with) you "Und können Sie mir sagen...?" And can you tell me...? "Karl gibt ihm den Ball" Karl gave him the ball. "Wie geht es Ihnen?" How goes it (with) you? (How are you?) This last sentence is an example from Gespräch 1-2 using the polite form of 'you'. Whether singular or plural must be established by context. This next sentence translates with "ihnen" as 'them': "Wie geht es ihnen?" How goes it with them? (How are they?) The meaning of "ihnen" (or "Ihnen") would have to come from context in a conversation. Another use of the dative case in German is after these prepositions: aus, bei, mit, nach, seit, von, zu. You will be introduced to the meanings of these prepositions over many future lessons rather than all at once, because some have many meanings in English. Indeed, because each language associates specific prepositions with many common sayings (and these often do not correspond in German and English), these "little" words can be troublesome for students. Nonetheless, you should memorize now the list of prepositions above to always remember their association with the dative case. Tables of the pronouns in all cases are summarized in Appendix 2. Word order in a German sentence with an indirect object depends upon whether that direct object is a pronoun or a noun. If the direct object is a noun, the dative precedes the accusative; if the direct object is a personal pronoun, the accusative precedes the dative: English sentence structure is similar.

History of Islam. "This wikibook concerns about the history and development of thoughts, theology, and philosophy stemming from the Islamic faith throughout the centuries. For the political history of Islamic civilization, see History of Islamic Civilization." The history of Islam begins in the 7th century AD. (Muslims believe that God sent messages on different time period, through different messengers, from Adam to Muhammad).

Spanish/Lesson 9. Grammar - Past Participle (el participio). Spanish uses the past participle primarily for present perfect, past perfect, and other similar times. For -ar verbs form the past participle by adding -ado to the stem. For -er and -ir verbs add -ido: If the stem of an -er or -ir verb ends in one of the vowels -a, -e, or -o, the i of -ido gets an accent mark: There are a few verbs with an irregular past participle: As in English, the past participle can also be used as an adjective for a noun. In that case the ending has to match gender and number of the noun. Example: Finally, there are a few verbs with "both" a regular and an irregular past participle. In this case, the irregular past participle is used as an adjective, while the regular form is used for the verb tenses. Grammar - Present Perfect (el pretérito perfecto). The Spanish present perfect is formed by conjugating the auxiliary verb haber (= "to have") and adding the past participle of the verb. Here are a few examples of the Spanish Present perfect. Note that in Spanish the auxiliary verb haber and the past participle are never separated: Grammar - Pluperfect (el pretérito pluscuamperfecto). The Spanish pluperfect is formed by conjugating imperfect of haber (= "to have") and adding the past participle of the verb. Here are a few examples of the Spanish pluperfect. It is used to refer to an event that happened before another event in the past. As in the present perfect, the auxiliary verb haber and the past participle are never separated:

German/Lesson 2. Lektion 2 "Fremde und Freunde" ~ Strangers and Friends Grammatik 2-1 ~ Introduction to Verbs. A is that part of speech that describes an action. Verbs come in an almost bewildering array of tenses, aspects, and types. For now, we will limit our discussion to verbs used in the present tense — i.e., describing an action occurring in the present. You should start to recognize that the form a verb takes is related to the subject of that verb: the verb form must match the person of the subject. This requirement is sometimes evident in English, but always so in German. Consider the following English and German sentences (the verb is "studieren" in every case): Several things are illustrated by these sentence pairs. First, all verbs in German follow the rule just stated that a verb form must agree with its subject. Starting in "Lektion 6" we will learn the verb forms associated with each person in German. Second, this rule in English applies mostly to the verb 'to be' (e.g., I am, you are, he is, etc.). In some English verbs, the 3rd person singular form is unique, often taking an 's' or 'es' ending: "I give at the office", but "He gives at the office" (and "She studies..." above). Finally, some German verbs are best translated with an English 'to be' verb form added. This is called the "progressive" form in English ('What are you studying?'), but it does not exist in German. Thus, a verb like "nennen" can best be translated as "to name" or "to call". The following example may make this clearer. In the present tense, the following statements in English: are all expressed in German in only one way: "Sie nennen die Firma, "Trans-Global"". And the question statement: 'Do they call the corporation, "Trans-Global"?' becomes, in German: "Nennen sie die Firma, "Trans-Global"?" Grammatik 2-2 ~ Pronouns in the Nominative Case. Most of the personal pronouns introduced in Lektion 1 are used as subjects of their verbs. These represent the nominative case in German (as in English). We will shortly learn three other cases in German: the accusative for direct objects, the dative for indirect objects, and the genitive for expressing possession. For now, remember that the singular personal pronouns in English (nominative case) are "I", "you", and "he/she/it" (1st, 2nd, and 3rd persons) and the nominative case is used as the subject of a verb. In German, these pronouns are rendered as "ich", "du", and "er/sie/es". In these example sentences, the subject of the verb is underlined: There are, of course, plural personal pronouns in the English nominative case: "we", "you", and "they"; and in German, these nominative case pronouns are "wir", "ihr", and "sie". These appear in the following examples (again, subject underlined): In both English and German, the 3rd person singular also has gender. As you will next learn, the 2nd person (person being addressed) in German has both familiar and polite (formal) forms. Further, it is worth repeating here — although introduced in "Grammatik 2-1" above and to be covered in detail in future lessons — that the verb form changes when the subject changes. That is, in German the verb form must match the subject of a sentence. Here are some examples; compare with the previous three example sentences above and note how the verb form changed to match the sentence subject (subject and verb underlined): In the last example, the English verb form ('have') also changed based upon the subject of the sentence. Gespräch 2-1 ~ "Die Geschäftsleute". In this conversation, although the subject matter is basically casual, a more formal form of German is being used intoning respect between coworkers in an office setting. The polite form is expressed by the pronouns as explained below (Grammatik 2-3). Vokabeln 2-1. die Anleitungen instructions das Deutsch German (language) (more common is "die deutsche Sprache") der Fremde foreigner, stranger die Firma company, firm, business concern die Frage question die Geschäftsleute business people ("die Leute" = people) der Hauptsitz head office ("das Haupt" = head or chief) der Tag day, daytime aus England from England Das ist richtig! That is right! Frau Baumann Ms. Baumann Herr Schmidt Mr. Schmidt zu Besuch visiting arbeiten work getroffen (have) met (past participle of "treffen") nennen name, call alle all an at Ihnen (with "or" to) you (polite form) heute today ihr you (plural), you all ja yes nein no richtig correct sie they (note: also "she") Sie you (polite form) wir we Grammatik 2-3 ~ Familiar and Polite Pronoun Forms. Many pronouns were introduced in Lesson 1. In "Grammatik 2-1" and "Gespräch 2-1" we have been presented with the following additional pronouns: "Ihnen" – (to) you (2nd person singular, dative case) "ihr" – you (2nd person, plural, nominative case) "sie" – they (3rd person, plural, nominative case) "Sie" – you (2nd person, singular, nominative case) "wir" – we (1st person, plural, nominative case) In the conversations between friends presented in "Gespräche 1-1" and "1-2" (Lektion 1) the familiar form of the personal pronouns (e.g., "du", "dir") was used. However, German also has a polite or formal form of some of these personal pronouns. The polite form is used in conversations between strangers and more formal situations, as illustrated in the "Gespräch 2-1": greetings between business associates. The polite form is always first-letter capitalized in German, which can be helpful in differentiating "Sie" (you) from "sie" (she and they); "Ihnen" (you) from "ihnen" (them). However, you will soon learn that the form of the verb (see "Grammatik 2-3" below) is most telling, as shown by these example pairs using the verb, "haben" (have): Because the first letter in a sentence is always capitalized, we cannot determine (without the verb form) whether the second and third examples begin with "sie" ('she' or 'they') or with "Sie" (polite 'you'); a problem that would also exist in conversation. The fourth example, where subject and verb are reversed in a question, demonstrates the pronoun 'they'; compare it with the polite 'you' in the first example. It is relatively easy for an English speaker to appreciate how context, especially in conversation, overcomes confusion considering that English has fewer forms for these pronouns than German. However, this fact does present some difficulty when learning German, since improper use of a pronoun may just create confusion in speaking or writing German. Gespräch 2-2 ~ "Die Geschäftsmänner". <br> <br> <br> Vokabeln 2-2. die Bundesrepublik Deutschland Federal Republic of Germany die Geschäftsmänner businessmen ("die Geschäftsleute" is preferred) Großbritannien Great Britain (technically "Vereinigtes Königreich" "von Großbritannien und Nordirland") der Morgen morning die Übersetzung translation bis morgen until tomorrow Guten Morgen! Good morning (greeting) nicht so gut not so well so viel so much Wie bitte? How is that? zu viel too much bis until kein no (in the sense on "none") müde tired nicht not sich each other warum ? why ? Grammatik 2-4 ~ Personal pronoun gender. In both English and German the 3rd person personal pronouns have gender (Grammatik 1-3). However, in English, the pronoun "it" is used for most inanimate or non-living things. There are a few exceptions: a ship might be referred to as "she". However, in German, the 3rd person personal pronoun reflects the gender of the noun (antecedent) referred to by the pronoun. For examples: The following table summarizes these gender relationships: Übersetzung 2-1. You may, at this point, try the flash cards developed for Level I German. This set has a few words and concepts not yet presented in Level II, but for the most part can be very helpful in enhancing your vocabulary. Go to FlashcardExchange.com. Translate the following sentences into German. Pay attention to whether familiar or polite form of the pronoun is requested:

The Once and Future King/Minor Characters. "The Once and Future King" - Minor Characters See also Major Characters. As many characters have only a given name, or take "of Somewhere" as their last name, the characters are listed alphabetically by first name. Note that characters in "The Once and Future King" may not exactly match with traditional Arthurian legend. Sir Ector - Owns the Castle of the Forest Sauvage. He adopts and cares for the Wart . He is the father of Kay. Sir Kay - Son of Sir Ector and friend of the Wart. He tries to act superior over the Wart. He follows Arthur on one adventure: the rescue mission at Morgan le Fay's castle (see "../The Sword in the Stone/"). When Arthur brings Kay the Sword in the Stone, Kay falsely claims to have drawn the sword himself, but soon gives the credit to Arthur. He later becomes a knight of the Round Table. Morgan le Fay - The most evil of the Cornwalls, and the strongest in magic. "Le Fay" means "the Fairy". She is the antagonist in the major adventure in "../The Sword in the Stone/". Her sisters are Elaine (not mentioned) and Morgause.

German/Level III/Mach Dir Keine Sorgen!. Lektion Drei für Fortgeschrittene Gespräch 3-3 ~ "Mach dir keine Sorgen!". Beim Ballspielen macht Karl sich Sorgen um die Uhrzeit. Vokabeln 3-3. das Ballspiel ball game die Minute minute das Motorrad motorcycle die Sorge, die Sorgen problem(s), worry(-ies) das Viertel quarter, one-fourth die Woche week die Wohnung apartment mach dir keine Sorgen! do not worry! nach Hause gehen go home kicken kick zurückkicken kick back, return kick beim when, while (usually, "at the") danach after that dein your erst only halb half jetzt now komisch comical, funny mein my schon already zurück back warum why (interrogative) Grammatik 3-5 ~ Numbers. Gender of Ordinals. Ordinal numbers are adjectives, and therefore have forms for each of the three genders in German. The forms are derived from the feminine form (as introduced in the beginning of Lesson 3) by adding an 'r' (masculine) or an 's' (neuter). Thus: "erste" (feminine), "erster (masculine), and "erstes (neuter). Examples: Grammatik 3-6 ~ Expressions of Time. Idioms used in Telling Time. As in English, there are a number of idiomatic phrases associated with giving or telling time. For example, note that the half hour is given as approaching the next hour. The German preposition, "um", is used to mean "at" a given time. Periods of the Day. There are a number of adverbial phrases used in German to denote time periods during the day. Common ones are listed here: Additional Notes. The first sentence in Gespräch 3-3 uses "Beim Ballspielen" in the sense of "during the ball game" or "while playing ball". "Beim" is a contraction of "bei dem" or "at the". However, "das Ballspiel" is a noun that represents an action ("playing with a ball"), so it is correct to use "beim" in the sense intended here. It is not the most beautiful way of saying this—but is correct. With the infinitive of a verb you can use "beim" too: "Beim Spielen" means "while playing". This form is more common in modern German language. Vokabeln 3-4. der Abend evening der Himmel heaven der Mittag noon, noontime der Morgen, die Morgen morning(s) der Nachmittag afternoon die Nacht night der Tag, die Tage day(s) abreisen depart (from a trip) auf for (duration), after gegen towards, about, approximately letzt(er) last ungefähr (at) about, approximately Note that "morgen" does not change in plural; thus, "Die Morgen" = "the mornings". It is uncommon to use it in plural, unless as a measure of land "Vier Morgen Land" = "four 'morgens of land". For a plural use of "mornings", it is better to substitute "die Vormittage". Andere Wörter 3A. Using these additional vocabulary words, you may be able to restate Gespräch 3-3 above, altering the meaning (or time of day) of the conversation. die Hälfte half die Viertelstunde quarter of an hour Übersetzung 3-2. Translate the following sentences into German:

Organic Chemistry/Introduction to reactions/Oxymercuration/demercuration. Oxymercuration is a process by which water is added to an alkene through treatment of the alkene with mercury(II) acetate [Hg(O2CCH3)2, usually abbreviated Hg(OAc)2] in an aqueous tetrahydrofuran (THF) solvent. Rarely this reaction is referred to as Oxymercuration/reduction. This reaction looks just like Markovnikov. addition of water across a double bond, however there is no carbocation intermediate, so there is no rearrangement. You will learn that NaBH4 is a common reducing agent.

Puzzles/Easy Sequence 6/Solution. They are powers of 3: 3 9 27 81 243 729 2,187 ...

HyperText Markup Language/Text Formatting. The Text Formatting elements give logical structure to phrases in your HTML document. This structure is normally presented to the user by changing the appearance of the text. We have seen in the Introduction to this book how we can "emphasize" text by using codice_1 tags. Graphical browsers normally present emphasized text in italics. Some Screen readers, utilities which read the page to the user, may speak emphasized words with a different inflection. A common mistake is to tag an element to get a certain "appearance" instead of tagging its "meaning". This issue becomes clearer when testing in multiple browsers, especially with graphical and text-only browsers as well as screen readers. You can change the default presentation for any element using Cascading Style Sheets. For example, if you wanted all emphasized text to appear in red normal text you would use the following CSS rule: In this section, we will explore a few basic ways in which you can markup the logical structure of your document. Emphasis. HTML has elements for two degrees of emphasis: An example of emphasized text: It is essential not only to guess but actually <em>observe</em> the results. An example rendering: An example of strongly emphasized text: Let us now focus on <strong>structural markup</strong>. An example rendering: Preformatted text. Preformatted text is rendered using fixed-width font, and without condensing multiple spaces into one, which results in preserved spacing. Newlines are rendered as newlines, unlike outside preformatted text. HTML markup in the preformatted text is still interpreted by browsers though, meaning that "a" will still be rendered as "a". To create preformatted text, start it with <pre> and end it with </pre>. An example: <pre> </pre> The resulting rendering: Omitting the preformatting tags will cause the same text to appear all in one line: Special Characters. To insert non-standard characters or characters that hold special meaning in HTML, a character reference is required. For example, to input the ampersand, "&", "&" must be typed. Characters can also be inserted by their ASCII or Unicode number code. Abbreviations. Another useful element is codice_4. This can be used to provide a definition for an abbreviation, e.g. <abbr title="HyperText Markup Language">HTML</abbr> Graphical browsers often show abbreviations with a dotted underline. The codice_5 appears as a tooltip. Screen readers may read the codice_5 at the user's request. Note: very old browsers (Internet Explorer version 6 and lower) do not support codice_4. Because they support the related element codice_8, that element has been commonly used for all abbreviations. An acronym is a special abbreviation in which letters from several words are pronounced to form a new word (e.g. radar - Radio Detection And Ranging). The letters in HTML are pronounced separately, technically making it a different sort of abbreviation known as an initialism. Discouraged Formatting. HTML supports various formatting elements whose use is discouraged in favor of the use of cascading style sheets (CSS). Here's a short overview of the discouraged formatting, so that you know what it is when you see it in some web page, and know how to replace it with CSS formatting. Some of the discouraged elements are merely discouraged, others are deprecated in addition. Cascading Style Sheets. The use of style elements such as <b> for bold or <i> for "italic" is straight-forward, but it couples the presentation layer with the content layer. By using Cascading Style Sheets, the HTML author can decouple these two distinctly different parts so that a properly marked-up document may be rendered in various ways while the document itself remains unchanged. For example, if the publisher would like to change cited references in a document to appear as bold text as they were previously "italic", they simply need to update the style sheet and not go through each document changing <b> to <i> and vice-versa. Cascading Style Sheets also allow the reader to make these choices, overriding those of the publisher. Continuing with the above example, let's say that the publisher has correctly marked up all their documents by surround references to cited material (such as the name of a book) in the documents with the <cite> tag: <cite>The Great Gatsby</cite> Then to make all cited references bold, one would put something like the following in the style sheet: Later someone tells you that references really need to be italic. Before CSS, you would have to hunt through all your documents, changing the <b> and </b> to <i> and </i> (but being careful *not* to change words that are in bold that are not cited references). But with CSS, it's as simple as changing one line in the style sheet to

GCSE Science/The motor effect. GCSE Science/Electricity The motor effect is the term used when a current-carrying wire in the presence of a magnetic field experiences a force. A simple experimental demonstration will show you that this is true. Place a wire that is connected to a power pack in between the poles of a horseshoe magnet. Turn on the power and the wire moves. Often the movement is only very slight because a typical horseshoe magnet is not very strong. The force depends on a number of things: The force obeys the formula: formula_1 The first two points are pretty much obvious, so let's look at the third point in a little more detail. The magnetic field of a horseshoe magnet points pretty much in a straight line from the north pole to the south pole. If the wire cuts this field at right angles the resulting force will be a maximum. If the wire runs parallel to the field, from the north the south pole or vice versa, the wire will still experience the motor effect. However, the net result of this force is along the wire, not perpendicular to it, thus the wire does not turn. Having said that, at GCSE you only really need to think about situations where the field and the wire cut each other at right angles. The force is always at right angles to both the field and the current flowing in the wire. This means that if you draw the direction of the magnetic field and the wire on a piece of paper the force will be out of the plane of the paper pointing straight up or down {More about how you work out which way later). Look at the diagram above. For simplicity, only the two ends of the horseshoe magnet have been drawn. Also the power pack and connecting wires are not shown either. The magnetic field is going into the screen. The current is traveling from right to left. The black line represents the force, and therefore the direction that the wire moves. Fleming's Left Hand Rule. This rule allows you to work out which direction the force will point in. Arrange your left hand with your thumb, first finger, and second fingers all pointing at right angles to one another. Remember you have to use your left hand for this! Although you may use your right hand so long as you swap the direction of current with the force Q4) A student uses her right hand instead of her left. What effect will that have on the force she works out? You will recall that a current carrying wire is surrounded by its own magnetic field. The diagram below shows the wire end on in a magnetic field of two magnets that are NS facing. The field due to the magnets is shown in blue, and the field due to the current in the wire is shown in black. Notice the direction of the two fields as shown by the arrows. On top of the wire the fields are both going in the same direction. They add up making an overall strong field. Underneath the wire, they go in opposite directions. They cancel each other out to some extent making an overall weaker field. The new field is shown in the diagram below. See how the field above the wire is stronger. The lines are closer together. Below the wire the field is weaker (due to partial canceling out) the field lines are further apart. The force pushes the wire downwards, away from the strong field into the weak field. It's as if the field lines try to repel each other. They don't like being squashed together and try to straighten out. They also act as if they are made of elastic bands, they don't like being stretched out of shape. (This is just a model of what's going on. The lines aren't real, they don't actually try to push each other away, but I find it a way of helping me understand what's going on. If it doesn't help you, don't use it) A simple electric motor. Ok, so far we have been looking at the force that results when we put a current carrying wire in a magnetic field. In this section we will look at a practical use for this force.As you have probably already guessed from the name of this page, the practical use is going to be an electric motor. Look at the diagram above. A rectangular loop of wire is sitting inside a magnetic field. We can consider the current in the four sections of the loop and work out which way the force acts. The net result of these different forces is that there will be a turning moment that makes the coil rotate by 90°. At that point the upwards and downwards forces will be acting along the same line and the coil will stop turning. Another way to think about it is to consider the loop as a tiny little one turn solenoid. The solenoid will have a little north pole and a little south pole and will therefore move until its north pole lines up with the south pole of the magnet on the right, and its south pole lines up with the north pole of magnet on the left. This is all very interesting but not much use as a motor. We want something that keeps turning all the time the current flows. They way this is achieved is by the use of the commutator – a circular metal ring that is split into two halves. The ends of the wire loop turn around inside the commutator. They are in electrical contact with it. One side of the commutator is connected to the positive output of a power pack or battery . the other half of the commutator is connected to the negative. Let's look at what happens as the coil turns inside the commutator: Q7)A student sets up an electric motor and turns it on. The coil turns clockwise. List two ways she could reverse the direction. «Uses of electromagnets | Induction»

C Programming/Advanced data types. In the chapter Variables we looked at the primitive data types. However "advanced" data types allow us greater flexibility in managing data in our program. Structs. Structs are data types made of variables of other data types (possibly including other structs). They are used to group pieces of information into meaningful units, and also permit some constructs not possible otherwise. The variables declared in a struct are called "members". One defines a struct using the codice_1 keyword. For example: struct mystruct { int int_member; double double_member; char string_member[25]; } struct_var; codice_2 is a variable of type codice_3, which we declared along with the definition of the new codice_3 data type. More commonly, struct variables are declared after the definition of the struct, using the form: struct mystruct struct_var; It is often common practice to make a "type synonym" so we don't have to type "struct mystruct" all the time. C allows us the possibility to do so using a codice_5 statement, which aliases a type: typedef struct { } Mystruct; The codice_1 itself is an "incomplete" type (by the absence of a name on the first line), but it is aliased as codice_7. Then the following may be used: Mystruct struct_var; The members of a struct variable may be accessed using the member access operator codice_8 (a dot) or the indirect member access operator codice_9 (an arrow) if the struct variable is a pointer: struct_var.int_member = 0; struct_var->int_number = 0; // this statement is equivalent to: (*struct_var).int_number = 0; Structs may contain not only their own variables but may also contain variables pointing to other structs. This allows a recursive definition, which is very powerful when used with pointers: struct restaurant_order { char description[100]; double price; struct restaurant_order *next_order; This is an implementation of the linked list data structure. Each node (a restaurant order) is pointing to one other node. The linked list is terminated on the last node (in our example, this would be the last order) whose codice_10 variable would be assigned to codice_11. A recursive struct definition can be tricky when used with codice_5. It is not possible to declare a struct variable inside its own type by using its aliased definition, since the aliased definition by codice_5 does not exist before the codice_5 statement is evaluated: typedef struct Mystruct { struct Mystruct *pointer; // Mystruct *pointer; would cause a compile-time error } Mystruct; The size of a struct type is at least the sum of the sizes of all its members. But a compiler is free to insert padding bytes between the struct members to align the members to certain constraints. For example, a struct containing of a char and a float will occupy 8 bytes on many 32bit architectures. Unions. The definition of a union is similar to that of a struct. The difference between the two is that in a struct, the members occupy different areas of memory, but in a union, the members occupy the same area of memory. Thus, in the following type, for example: union { int i; double d; } u; The programmer can access either codice_15 or codice_16, but not both at the same time. Since codice_15 and codice_16 occupy the same area of memory, modifying one modifies the value of the other, sometimes in unpredictable ways. This is also the main reason that unions are rarely seen in practice. The size of a union is the size of its largest member. Enumerations. Enumerations are artificial data types representing associations between labels and integers. Unlike structs or unions, they are not composed of other data types. An example declaration: enum color { red, orange, yellow, green, cyan, blue, purple, } crayon_color; In the example above, red equals 0, orange equals 1, ... and so on. It is possible to assign values to labels within the integer range, but they must be a literal. Similar declaration syntax that applies for structs and unions also applies for enums. Also, one "normally" doesn't need to be concerned with the integers that labels represent: enum weather weather_outside = rain; This peculiar property makes enums especially convenient in switch-case statements: enum weather { sunny, windy, cloudy, rain, } weather_outside; switch (weather_outside) { case sunny: wear_sunglasses(); break; case windy: wear_windbreaker(); break; case cloudy: get_umbrella(); break; case rain: get_umbrella(); wear_raincoat(); break; Enums are a simplified way to emulate associative arrays in C.

Physics Study Guide/Logs. =Review of logs= Been a while since you used logs? Here is a quick refresher for you. The log (short for logarithm) of a number N is the exponent used to raise a certain "base" number B to get N. In short, formula_1 means that formula_2. Typically, logs use base 10. An increase of "1" in a base 10 log is equivalent to an increase by a power of 10 in normal notation. In logs, "3" is 100 times the size of "1". If the log is written without an explicit base, 10 is (usually) implied. Another common base for logs is the trancendental number formula_3, which is approximately 2.7182818... Since formula_4, these can be more convenient than formula_5. Often, the notation formula_6 is used instead of formula_7. The following properties of logs are true regardless of whether the base is 10, formula_3, or some other number. <br> Adding the log of A to the log of B will give the same result as taking the log of the product A times B. <br><br> Subtracting the log of B from the log of A will give the same result as taking the log of the quotient A divided by B. <br><br> The log of (A to the Bth power) is equal to the product (B times the log of A). <br><br> A few examples: <br> log(2) + log(3) = log(6) <br> log(30) – log(2) = log(15) <br> log(8) = log(23) = 3log(2)

Physics Study Guide/Electricity. =Electricity= The force resulting from two nearby charges is equal to k times charge one times charge two divided by the square of the distance between the charges. This what force of attraction between to charged particle says, according to coulomb's law. The electric field created by a charge is equal to the force generated divided by the charge. Electric field is equal to a constant, “k”, times the charge divided by the square of the distance between the charge and the point in question. Electric potential energy is equal to a constant, “k” multiplied by the two charges and divided by the distance between the charges. Variables<br> Electricity acts as if all matter were divided into four categories: Charges are positive (+) or negative (-). Any two like charges repel each other, and opposite charges attract each other. Electric fields. A charge in an electrical field feels a force. The charge is not a vector, but force is a vector, and so is the electric field. If a charge is positive, then force and the electric field point in the same direction. If the charge is negative, then the electric field and force vectors point in opposite directions. A point charge in space causes an electric field. The field is stronger closer to the point and weaker farther away. Electricity is made of subatomic particles called Electrons and so are Electric Fields and Magnetic Fields. One must also note that electrical fields come under the category of spherical fields as the inverse square law may be applied to the electrical field. This means that the electrical force, exhibited by the electrical field emitted by the subatomic electron charge (-), acting upon a body is inversely proportional to the distance between the center point of the electric field (subatomic electron) and the body on which the electric force is acting upon. An electric circuit is composed of conducting wires (through which an electric current flows through), a key or switch which is utilized to open and close the circuit, components which transfer electrical energy to a form of energy required by the component and an electromotive source (such as a voltaic cell). A voltaic cell is an electromotive source in which are present two plates, zinc and copper, placed in dilute sulphuric acid. Whence the circuit is closed the zinc reacts with the sulphuric acid to produce zinc sulphate. The electromotive force which discharges the electrical energy in the electric current is considered to be originated on the surface of the zinc plate in the voltaic cell. However, depending upon the cell, closing the circuit gives rise to polarization, accumulation of hydrogen bubbles on the surface of the copper plate which seriously interferes with the movement of electricity and reduces the magnitude of the electromotive force. For this reason Leclanché cells are utilized. Consisting of similar characteristics as that of the voltaic cell however a Mage difference is present. Instead of the use of copper plates, a carbon plate is used. For this reason, magneze dioxide may be placed on the carbon to react to form a compound which whence in contact with hydrogen bubbles will turn the hydrogen into water, hence increasing the size of the electromotive force produced by the cell. The resistance encountered in conducting wires: Inversely proportional to the diameter of the conducting wire. Directly proportional to the length of the conducting wire. Varies with different substances. Varies with temperature of the conducting wire. In order to maintain a constant flow of an electric current a constant expenditure of chemical or mechanical energy is required. An electric current is accompanied by an electric field and a magnetic field. A device employed into determining the presence of an electric current is known as a galvanoscope. The conducting wire through which the electric current flows through is he led over and parallel to the galvanoscope the magnetoscope preset inside of the galvanoscope being deflected in the opposite direction to which the electric current flows in. So with the aid of a galvanoscope one may not only deduce the magnetic properties of an electric current, the exhibition of a magnetic field, but the direction in which the current flows through. An electromotive force may also be generators by a dynamo. A rotating magnet present inside of a helix. The magnetic properties of electric currents may be used to construct magnets. An electromagnet is commonly described as a mass of iron on which is placed a helix/solenoid through which flows an electric current. The magnetic field emitted by the electric current is increased if the solenoid is placed around a magnetic mass of iron or any other substance possessing magnetic properties, that is the magnetic field of the iron is added to that of the electric current producing a more powerful magnetic field. Conductors may be arranged in two variants. Series and parallel circuits. In series, the current passes through each conductor in turn, where Ohm's law changes to I = nE/(nr + R), where I is the current intensity, n is the number of cells arranged in series in the circuit, E is the electromotive force applied to the circuit, r is the internal resistance ( the resistance the current that is produced in the cell experiences whence passing from the zinc plate to the copper or carbon plate through the sulphuric acid ) and R is the external resistance.

Lojban/Vocabulary 1. cmavo. doi DOI vocative marker generic vocative marker; identifies intended listener; elidable after COI coi COI greetings vocative: greetings/hello be'e COI request to send vocative: request to send/speak je'e COI roger vocative: roger (ack) - negative acknowledge; used to acknowledge offers and thanks je'enai COI* negative acknowledge vocative: roger (ack) - negative acknowledge; I didn't hear you co'o COI partings vocative: partings/good-bye re'i COI ready to receive vocative: ready to receive - not ready to receive re'inai COI* not ready to receive vocative: ready to receive - not ready to receive zo ZO 1-word quote quote next word only; quotes a single Lojban word (not a cmavo compound or tanru) ma KOhA7 sumti ? pro-sumti: sumti question (what/who/how/why/etc.); appropriately fill in sumti blank la LA that named name descriptor: the one(s) called ... ; takes name or selbri description mi KOhA3 me pro-sumti: me/we the speaker(s)/author(s); identified by self-vocative doi. In English poetry sometimes people say O before names, but usually people just put the name at the beginning or the end of a sentence separated from the rest by a comma or as a sentence of its own. In English, people also say "Hey" before names. This carries the added effect of getting someone's attention. If I felt like saying something completely useless, I would say {doi do}, identifying the listener as the person listening. "Can someone say {doi} by itself (without a name following like I can with the rest of the vocatives)?" coi. Near the beginning of a conversation or upon noticing another Lojban speaker to talk to, a Lojban speaker will often say {coi}. The listener usually replies {coi}. This has about the same meaning as the English words "Hi", "Hello", "Howdy", and "Greetings". As with most of the vocatives, I can follow it with a name. It must either have la or a mandatory pause between {coi} and the name. A common Lojban phrase {coi ro do} means "Hi, all.". be'e. A Lojban speaker not speaking, wanting to speak, and not sure if other speakers will allow him/her to speak will sometimes say {be'e} to ask permission. In English, people usually only ask to speak on formal occasions like the courtroom and in large meetings. In school students raise their hands for a turn to speak. When people say "Excuse me.", they don't expect someone to deny them from speaking. They also ask "May I have a word with you?" Like most vocatives, I can follow {be'e} with the listener. While I see {be'enai} as correct grammar, I can't figure out a meaning for it beyond "Ha ha, I know a cmavo you don't!" "To me, {be'enai} seems fairly obvious: "Permission not to speak?" which could be used in a fairly similar way to "No comment!" but asking permission not to comment rather than refusing." je'e. In English, people acknowledge "Thank you.", with "Welcome.". They say "I heard." to acknowledge they heard the last utterance. They say "I understand." To point out they understand the last utterance. "Okay." also acknowledges the last utterance, but carries more hint of agreement than {je'e}. To show that nearly anyone would understand an utterance, English speakers sometimes use the word "Duh!". In English people say "Huh?" or "Wha?" or "What?" to denote similar meanings. co'o. A Lojban speaker says {co'o} to another Lojban speaker shortly before ending conversation or close proximity to the second Lojban speaker. The second Lojban speaker often replies {co'o}. As with most other vocatives, I can follow {co'o} with a name. English phrases with similar meanings include "Goodbye.", "So long.", and "See you later.". re'i. This word signifies that the speaker can listen to the listener. I can follow {re'i} with a name like most vocatives to signify the listener. English phrases with similar meanings include "Go ahead.", "I'm all ears.", and "I'm listening." la daniel. cusku zo be'e .i la kleir. cusku zo re'i Daniel says, "May I have a word with you?". Claire says, "Go ahead.". In English {re'inai} translate to "Sorry, I'm busy.", "I'm not accepting visitors.", and "I can't listen right now." zo. In English, I might put a word in quotes italics to quote it. If I only wanted to quote one word, I might say "the word foo". I can talk about the word {zo} as a word by saying {zo zo}. {zo nai} quotes the word {nai} instead of meaning the opposite of {zo}. ma. In asking another Lojban speaker for information, a Lojban speaker might say give a bridi describing their information with a blank for the listener to insert their answer. The asker would signify that blank with {ma}. The answerer would probably not repeat the entire le bridi, but instead just the information to replace {ma} with. In English, a person might say "What" or "blank" instead. la. zo la gadri mi. If I wanted to say something that didn't mean much. I would say, {mi'e mi}, pointing out the speaker as myself. "Does {minai} mean {do}?" "I believe that {minai} would mean anyone but yourself." gismu. smuni mun smu meaning x1 is a meaning/interpretation of x2 recognized/seen/accepted by x3 [referential meaning (=selsni, snismu)]; (cf. jimpe, sinxa, valsi, tanru, gismu, lujvo, cmavo, jufra) gismu gim gi'u root word x1 is a (Lojban) root word expressing relation x2 among argument roles x3, with affix(es) x4 [gismu list, if physical object (= (loi) gimste); referring to the mental construct (e.g. propose adding a new gismu to the gismu list = gimpoi, gimselcmi, gimselste)]; (cf. cmavo, cmene, lujvo, smuni, sumti, tanru, valsi) lujvo luv jvo affix compound x1 (text) is a compound predicate word with meaning x2 and arguments x3 built from metaphor x4 (cf. stura, cmavo, gismu, rafsi, smuni) tanru tau phrase compound x1 is a binary metaphor formed with x2 modifying x3, giving meaning x4 in usage/instance x5 (x2 and x3 are both text or both si'o concept) (cf. gismu, smuni) sumti sum su'i argument x1 is a/the argument of predicate/function x2 filling place x3 (kind/number) (x1 and x2 are text); (cf. bridi, darlu, gismu) bridi bri predicate x1 (text) is a predicate relationship with relation x2 among arguments (sequence/set) x3 [also: x3 are related by relation x2 (= terbri for reordered places)]; (x3 is a set completely specified); (cf. sumti, fancu) cmavo ma'o structure word x1 is a structure word of grammatical class x2, with meaning/function x3 in usage (language) x4 [x4 may be a specific usage (with an embedded language place) or a massified language description; x3 and x4 may be merely an example of cmavo usage or refer to an actual expression; cmavo list, if physical object (= (loi) ma'oste); referring to the mental construct (e.g. propose adding a new cmavo to the cmavo list = ma'orpoi, ma'orselcmi, ma'orselste)]; (cf. gismu, lujvo, gerna, smuni, valsi) cmene cme me'e name x1 (quoted word(s)) is a/the name/title/tag of x2 to/used-by namer/name-user x3 (person) [also: x2 is called x1 by x3 (= selcme for reordered places)]; (cf. cmavo list me'e, gismu, tcita, valsi, judri) Exercises. In Exercises 1 to 11, translate the Lojban sentence to English.<br> 1. coi. braun. e'apei mi ba te cmene do lu la bab. li'u<br> 2. be'e meiris. mi'o ca cliva<br> 3. ko'a cusku lu le lujvo cu lujvo li'u .i ko'e cusku zo je'e<br> 4. ko'a cusku lu mi cmavo li'u .i ko'e cusku lu je'enai li'u<br> 5. co'o .ednas. ko ba klama mi<br> 6. la daniel. cusku zo be'e .i la kleir. cusku zo re'i<br> 7. mi cusku lu be'e. reitcel. li'u le nanmu pe la reitcel. cusku lu la reitcel. cusku lu re'inai li'u li'u<br> 8. mi cusku zo bridi .i mi na cusku tanru<br> 9. mi cusku lu lu smuni cmene li'u tanru ma ma li'u .i la keven. cusku lu smuni cmene li'u tanru zo smuni zo cmene li'u<br> 10. mi'e la mark.<br> 11. le prenu pe mi te cmene mi lu la brai'an. li'u In Exercises, 100 to 131, translate le jufra (the sentence) given.<br> 100. le se bridi cu smuni le selbri mi .i<br> 101. zo coi smuni zoi gy. hello .gy mi .i<br> 102. gy. goodbye .gy smuni zo co'o mi .i<br> 103. lu mi'e. brai'an. li'u smuni lu mi me la brai'an. li'u mi .i<br> 104. fi la'o smuni. George Bush .smuni goi ko'a smuni fa ko'a la'o smuni. Mr. President .smuni .i<br> 105. le ve gismu cu smuni le rafsi mi .i<br> 106. zoi ly. gi'u .ly ve gismu zo gismu .i<br> 107. zo smuni gismu .i<br> 108. zo gismu gismu fi le te gismu .i<br> 109. zo selbri gismu le du'u se bridi .i<br> 110. zo selbri lujvo lu se bridi li'u .i<br> 111. zo selbri lujvo zo'e le te lujvo be fa zo bridi .i<br> 112. zo selbri se ve se lujvo lu se bridi li'u .i<br> 113. zo selma'o lujvo fo lu se cmavo li'u .i<br> 114. zo selma'o lujvo fi le se cmavo .i<br> 115. zo selma'o lujvo lu se cmavo li'u le ve cmavo lu se cmavo li'u .i<br> 116. zo selbri lujvo lu se bridi li'u le bridi lu se bridi li'u .i<br> 117. zo tertau lujvo lu te tanru li'u le tanru lu te tanru li'u .i<br> 118. lu gismu smuni li'u tanru zo gismu zo smuni .i<br> 119. lu gismu lujvo li'u tanru zo gismu zo lujvo lu gismu co lujvo li'u .i<br> 120. lu le tanru li'u cu smuni lu le ve lujvo li'u mi .i<br> 121. zo tanru gismu zo'e le se tanru zoi ly. tau .ly .i<br> 122. le gismu sumti dei li pa .i<br> 123. nei sumti dei li re .i<br> 124. li ci sumti dei li ci .i<br> 125. zo sumti gismu .i zo sumti sumti di'u li pa .i<br> 126. mi klama le se klama le te klama .i le te klama sumti di'u li ci .i<br> 127. dei bridi le du'u bridi dei<br> 128. lu le ninmu klama le nanmu li'u bridi le du'u klama le nanmu<br> 129. do nanmu .i di'u bridi le du'u nanmu do .i<br> 130. di'e bridi le du'u cliva la'o gy. Elvis .gy .i la'o gy. Elvis .gy cliva .i<br> 131. zo .ui cmavo zoi selma'o. UI .selma'o lu mi gleki li'u la lojban. In Exercises 200 to 226, give an English translation of each place of each le sumti given.<br> 201. le smuni<br> 202. le se smuni<br> 203. le te smuni<br> 204. le gismu<br> 205. le se gismu<br> 206. le te gismu<br> 207. le ve gismu<br> 208. le lujvo<br> 209. le se lujvo<br> 210. le te lujvo<br> 211. le ve lujvo<br> 212. le tanru<br> 213. le se tanru<br> 214. le te tanru<br> 215. le ve tanru<br> 216. le xe tanru<br> 217. le sumti<br> 218. le se sumti<br> 219. le te sumti<br> 220. le bridi<br> 221. le se bridi<br> 222. le te bridi<br> 223. le cmavo<br> 224. le se cmavo<br> 225. le te cmavo<br> 226. le ve cmavo In Exercises 301 to 321, use the best word in the vocabulary of this lesson to fill in each blank of each sentence. You may use each word more than once.<br> 301. Teacher: _____ is the capital of Kentucky?<br> Pupil: Frankfort.<br> <br> 302. Mother: Did you hear what I just said?<br> Daughter: _____, except I missed the part about chocolate.<br> <br> 303. I said "_____", and she told me, "Sorry, I can listen right now."<br> 304. _____ name is Jessica, but my friends call me Jessie.<br> 305. Welcome to _____ .alaskas.!<br> 306. When I say "_____ Eliza", that means I'm talking to you.<br> 307. I wish I could stay longer. _____<br> 308. If I knew le _____, I wouldn't have asked you for a definition.<br> 309. Say "doi" and then le _____ of the person you wish to talk to.<br> 310. _____ Robert! It's so nice to see you after all these years.<br> 311. I wouldn't have said "_____" if I wasn't all ears.<br> 312. Did you rent the movie, "_____, Myself & Irene"?<br> 313. Which le rafsi did you use to make that le _____?<br> 314. How can you call that le _____, when a phrase compound needs at least two words?<br> 315. If f(x) = y, then f is the function and yby. _____ fy.<br> 316. That's na ____ because any decent predicate needs at least pa le selbri.<br> 317. ro le attitudinals are a type of word called le _____.<br> 318. _____, but I would feel happy to listen another time.<br> 319. ____ la romeos. _____ la romeos. Wherefore art thou Romeo?<br> 320. _____ blue begins with the letter "b".<br> 321. Lojban has 1342 le _____. Answers to exercises. 1. Hello Brown. May I call you Bob?<br> 2. May I have a word with you, Mary? Let's leave.<br> The Lojban means more "We leave." than the English. Maybe I could change that with an attitudinal meaning "suggestion" or {ko} and {mi} instead of {mi'o}.<br> 3. The first person says, "The affix compound qualifies as an affix compound." The second person says, "I understand."<br> 4. The first person says, "I qualify as a structure word.". The second person says, "Huh?".<br> 5. Goodbye, Edna. Come see me in the future.<br> 6. Daniel says, "May I have a word with you?". Claire says, "Go ahead.".<br> 7. I said, "May I speak with you, Rachel?" The man associated with Rachel said, "Rachel said, 'I can't listen right now.'"<br> 8. I said the word {bridi}. I did not say the word {tanru}.<br> 9. I said, "What modifies what in the metaphor 'meaning sort of name'?" Kevin said, "In the metaphor 'meaning sort of name', 'meaning' modifies 'name'."<br> 10. I go by the name Mark.<br> 11. People associated with me call me "Brian". 100. According to me, "the relationship of a sentence" means "the relationship of a sentence".<br> 101. I see "Hello" meaning {coi}.<br> 102. I see {co'o} as meaning "Goodbye".<br> 103. I accept the interpretation "I am Brian." for the sentence "I am Brian.".<br> 104. George Bush accepts the interpretation of Mr. President as himself.<br> 105. I recognize the interpretation of the affixes of a root word as the affixes of a word.<br> 106. The word {gismu} (meaning root word) has the affix {gi'u}.<br> 107. The word {smuni} qualifies as a root word.<br> 108. The relationship of the word {gismu} has a role for the roles of the relationship of a root word.<br> 109. The word {selbri} denotes the relationship {se bridi}.<br> 110. The affix compound {selbri} means {se bridi}.<br> 111. The relationship of the compound word {selbri} has the same roles as the compound word {bridi}.<br> 112. The compound word {selbri} comes from the metaphor {se bridi}.<br> 113. The word {selma'o} comes from the metaphor {se cmavo}.<br> 114. The relationship of the word {selma'o} involves the grammatical class of a structure word.<br> 115. The compound word {selma'o} means {se cmavo}, and its relationship involves its meaning, and it comes from the metaphor {se cmavo}.<br> 116. The compound word {selbri} means {se bridi}, and its relationship involves the predicate, and it comes from the metaphor {se bridi}.<br> 117. The compound word {tertau} means {te tanru}, and its relationship involves a binary metaphor, and it comes from the metaphor {te tanru}.<br> 118. "Root word sort of meaning" qualifies a binary metaphor with "root word" modifying "meaning".<br> 119. In binary metaphor "Root word sort of compound word", "root word" modifies "compound word", and it means "compound word of root word sort".<br> 120. According to me, "metaphor made into compound word" means "binary metaphor".<br> 121. The root word {tanru} denotes the relationship involving the modifier of the metaphor, and has the affix {tau}.<br> 122. The root word is in the current utterance filling the first role.<br> 123. The current utterance is in the current predicate filling the second role.<br> 124. Three is in the current utterance filling the third role.<br> 125. The word {sumti} qualifies as a root word. The word {sumti} is in the previous utterance filling the first role.<br> 126. I go to the destination from the origin. The destination is in the previous utterance filling the third place.<br> 127. The current utterance qualifies as a predicate with the predicate relationship and the role the current utterance.<br> 128. The predicate "The woman goes to the man." involves the going relationship and the role of the man.<br> 129. You qualify as a man. The last utterance involves the man relationship and the argument you.<br> 130. The next utterance qualifies as a predicate involving the leaving relationship and Elvis. Elvis leaves.<br> 131. The structure word {.ui} comes from the grammatical class {UI}, means I feel happiness, and is used in the Lojban language. 201. meaning<br> 202. symbol with meaning<br> 203. interpreter of meaning<br> 204. root word<br> 205. relationship expressed by root word<br> 206. roles in relationship expressed by root word<br> 207. affixes of root word<br> 208. compound word<br> 209. meaning of compound word<br> 210. roles of relationship of compound word<br> 211. metaphor used to make compound word<br> 212. binary metaphor<br> 213. modifier of metaphor<br> 214. modified of metaphor<br> 215. meaning of metaphor<br> 216. usage of metaphor<br> 217. argument<br> 218. predicate of argument<br> 219. role filled by argument<br> 220. predicate<br> 221. relationship of predicate<br> 222. argument of predicate<br> 223. structure word<br> 224. grammatical class of structure word<br> 225. meaning of structure word<br> 226. language of structure word 301. ma<br> 302. je'e<br> 303. be'e<br> 304. mi<br> 305. la<br> 306. doi<br> 307. co'o<br> 308. smuni<br> 309. cmene<br> 310. coi<br> 311. re'i<br> 312. mi<br> 313. lujvo<br> 314. tanru<br> 315. sumti<br> 316. bridi<br> 317. cmavo<br> 318. re'inai<br> 319. doi, doi<br> 320. zo<br> 321. gismu

Physics Study Guide/Sound. Sound is defined as mechanical sinosodial vibratory longitudinal impulse waves which oscillate the pressure of a transmitting medium by means of adiabatic compression and decompression consequently resulting in the increase in the angular momentum and hence rotational kinetic energy of the particles present within the transmitting medium producing frequencies audible within hearing range, that is between the threshold of audibility and the threshold of pain on a Fletchford Munson equal loudness contour diagram. Intro. When two glasses collide, we hear a sound. When we pluck a guitar string, we hear a sound. Different sounds are generated from different sources. Generally speaking, the collision of two objects results in a sound. Sound does not exist in a vacuum; it travels through the materials of a medium. Sound is a longitudinal wave in which the mechanical vibration constituting the wave occurs along the direction of the wave's propagation. The velocity of sound waves depends on the temperature and the pressure of the medium. For example, sound travels at different speeds in air and water. We can therefore define sound as a mechanical disturbance produced by the collision of two or more physical quantities from a state of equilibrium that propagates through an elastic material medium. =Sound= The amplitude is the magnitude of sound pressure change within a sound wave. Sound amplitude can be measured in pascals (Pa), though its more common to refer to the "sound (pressure) level" as Sound intensity(dB,dBSPL,dB(SPL)), and the "perceived sound level" as Loudness(dBA, dB(A)). Sound intensity is flow of sound energy per unit time through a fixed area. It has units of watts per square meter. The reference Intensity is defined as the minimum Intensity that is audible to the human ear, it is equal to 10-12 W/m2, or one picowatt per square meter. When the intensity is quoted in decibels this reference value is used. Loudness is sound intensity altered according to the frequency response of the human ear and is measured in a unit called the A-weighted decibel (dB(A), also used to be called phon). The Decibel. The decibel is not, as is commonly believed, the unit of sound. Sound is measured in terms of pressure. However, the decibel is used to express the pressure as very large variations of pressure are commonly encountered. The decibel is a dimensionless quantity and is used to express the ratio of one power quantity to another. The definition of the decibel is formula_1, where x is a squared quantity, ie pressure squared, volts squared etc. The decibel is useful to define relative changes. For instance, the required sound decrease for new cars might be 3 dB, this means, compared to the old car the new car must be 3 dB quieter. The absolute level of the car, in this case, does not matter. Definition of terms. "Sample equation:" Change in sound intensity<br> Δβ = β2 - β1<br> = 10 log("I"2/"I"0) - 10 log("I"1/"I"0)<br> = 10 [log("I"2/"I"0) - log("I"1/"I"0)]<br> = 10 log[("I"2/"I"0)/("I"1/"I"0)]<br> = 10 log("I"2/"I"1)<br> where log is the base-10 logarithm. Doppler effect. <br>f' is the observed frequency, f is the actual frequency, v is the speed of sound (formula_2), T is temperature in degrees Celsius formula_3 is the speed of the observer, and formula_4 is the speed of the source. If the observer is approaching the source, use the top operator (the +) in the numerator, and if the source is approaching the observer, use the top operator (the -) in the denominator. If the observer is moving away from the source, use the bottom operator (the -) in the numerator, and if the source is moving away from the observer, use the bottom operator (the +) in the denominator. Example problems. A. An ambulance, which is emitting a 400 Hz siren, is moving at a speed of 30 m/s towards a stationary observer. The speed of sound in this case is 339 m/s. formula_5 B. An M551 Sheridan, moving at 10 m/s is following a Renault FT-17 which is moving in the same direction at 5 m/s and emitting a 30 Hz tone. The speed of sound in this case is 342 m/s. formula_6

Physics Study Guide/Reviews. Our first review of the is in, by email to the author: Thanks karl! <br> it's very helpful!!!!

Physics Study Guide/Torque. Torque and Circular Motion. Circular motion is the motion of a particle at a set distance (called radius) from a point. For circular motion, there needs to be a force that makes the particle turn. This force is called the 'centripetal force.' Please note that the centripetal force is "not" a new type of force-it is just a force causing rotational motion. To make this clearer, let us study the following examples: Thus, we see that the centripetal force acting on a body is always provided by some other type of force -- centripetal force, thus, is simply a name to indicate the force that provides this circular motion. This centripetal force is "always" acting inward toward the center. You will know this if you swing an object in a circular motion. If you notice carefully, you will see that you have to continuously pull inward. We know that an opposite force should exist for this centripetal force(by Newton's 3rd Law of Motion). This is the centrifugal force, which exists only if we study the body from a non-inertial frame of reference(an accelerating frame of reference, such as in circular motion). This is a so-called 'pseudo-force', which is used to make the Newton's law applicable to the person who is inside a non-inertial frame. e.g. If a driver suddenly turns the car to the left, you go towards the right side of the car because of centrifugal force. The centrifugal force is equal and opposite to the centripetal force. It is caused due to inertia of a body. Average angular velocity is equal to one-half of the sum of initial and final angular velocities assuming constant acceleration, and is also equal to the angle gone through divided by the time taken. Angular acceleration is equal to change in angular velocity divided by time taken. Angular momentum. Angular momentum of an object revolving around an external axis formula_3 is equal to the cross-product of the position vector with respect to formula_3 and its linear momentum. Angular momentum of a rotating object is equal to the moment of inertia times angular velocity. Rotational Kinetic Energy is equal to one-half of the product of moment of inertia and the angular velocity squared. The equations for rotational motion are analogous to those for linear motion-just look at those listed above. When studying rotational dynamics, remember:

Lojban/Vocabulary. Vocabulary 1. "See Vocabulary 1." Vocabulary 2. "See Vocabulary 2."

Lojban/Vocabulary 2. cmavo. le LE the described non-veridical descriptor: the one(s) described as ... cu CU selbri separator elidable marker: separates selbri from preceding sumti, allows preceding terminator elision ti KOhA6 this here pro-sumti: this here; immediate demonstrative it; indicated thing/place near speaker ta KOhA6 that there pro-sumti: that there; nearby demonstrative it; indicated thing/place near listener tu KOhA6 that yonder pro-sumti: that yonder; distant demonstrative it; indicated thing far from speaker&listener goi GOI pro-sumti assign sumti assignment; used to define/assign ko'a/fo'a series pro-sumti; Latin 'sive' ko'a KOhA4 it-1 pro-sumti: he/she/it/they #1 (specified by goi) zo'o UI5 humorously attitudinal modifier: humorously - dully - seriously cf. xajmi, junri) zo'onai UI*5 seriously attitudinal modifier: humorously - dully - seriously gismu. broda rod predicate var 1 1st assignable variable predicate (context determines place structure) (cf. cmavo list bu'a) blanu bla blue x1 is blue [color adjective] (cf. skari, blabi, xekri, zirpu, kandi, carmi, cicna) cusku cus sku express x1 (agent) expresses/says x2 (sedu'u/text/lu'e concept) for audience x3 via expressive medium x4 [also says]; (cf. bacru, tavla, casnu, spuda, cmavo list cu'u, bangu, dapma, jufra, pinka) ciska ci'a write ' scribe ' x1 inscribes/writes x2 on display/storage medium x3 with writing implement x4; x1 is a scribe [also x3 writing surface]; (cf. papri, penbi, pinsi, tcidu, xatra, pixra, prina, finti for 'author' or specific authorial works, barna, pinka) prenu pre person x1 is a person/people (noun) [not necessarily human]; x1 displays personality/a persona (cf. nanmu, ninmu, remna, zukte, sevzi) remna rem re'a human x1 is a human/human being/man (non-specific gender-free sense); (adjective:) x1 is human (cf. nanmu, ninmu, prenu) nanmu nau man x1 is a man/men; x1 is a male humanoid person [not necessarily adult] [word dispreferred in metaphor/example as sexist; (use remna or prenu)]; (cf. ninmu, remna, prenu, makcu, nanla, bersa) ninmu nim ni'u woman ' women ' x1 is a woman/women; x1 is a female humanoid person [not necessarily adult] [word dispreferred in metaphor/example as sexist; (use remna or prenu)]; (cf. nanmu, remna, prenu, makcu, nixli) gasnu gau do x1 [person/agent] is an agentive cause of event x2; x1 does/brings about x2 (cf. cmavo list gau, gunka, zukte, rinka, fasnu for non-agentive events, jibri, kakne, pilno) zukte zuk zu'e act x1 is a volitional entity employing means/taking action x2 for purpose/goal x3/to end x3 [also acting at, undertaking, doing; agentive cause with volition/purpose; also x3 objective, end]; (cf. cmavo list zu'e, bapli, gunka, jalge, krinu, mukti, rinka, snuti, gasnu, fasnu, minji, prenu, ciksi, jibri, pilno, pluta, tadji, tutci) rinka rik ri'a cause x1 (event/state) effects/physically causes effect x2 (event/state) under conditions x3 [x1 is a material condition for x2; x1 gives rise to x2]; (cf. gasnu, krinu, nibli, te zukte, se jalge, bapli, jitro, cmavo list ri'a, mukti, ciksi, xruti)

French/Appendices/Typing characters. French accents on computers. While French keyboards are available, some French students may need to enter accented characters on an English keyboard. If you are on the Internet, many sites have a virtual keyboard that allows you to mouse-select the characters. Google Translate, for example, has a virtual keyboard icon for entering text in the form window. Windows Operating System. If you are using Microsoft Windows Operating System, then you can use the Character Map application, located under: Some word processing programs allow the user to enter accents using a key combination, while others may require an Alt code. The ALT code is entered by holding down the ALT key, and enter the number (all digits given) using the keypad (only the keypad). In most applications, you will need the "numlock" turned on to avoid undesirable effects. Mac Operating System. If you are using the Mac Operating System, there is a simple system that can be used with the Option (⌥) key. Open the System Preferences application (found in your Applications folder by default and in the Apple menu in the upper-left corner) and navigate to "Language and Text" preferences. Under the Input Sources tab, select U. S. Extended. Now you can use the following key combinations with the Option (⌥) key to form French accents. For instance: Press and hold ⌥ and then press e. Now you have a floating acute accent. Press e again to put the accent over that letter and form é. In the same way ⌥ - 6, then o will give you ô, etc. These shortcuts work throughout the operating system and do not depend on the application in which they are used. Linux Operating System. If you are using Ubuntu Linux with Gnome you select the Compose key from System: Preferences: Keyboard then Layouts: Layout Options: Compose key position. You can select one of Right Alt key, Left Win-key, Right Win-key, Menu key, Right Ctrl key or Caps Lock key (for a USA keyboard layout). The Keyboard preferences dialog has an area you can use to test the settings. See below for how to use the Compose key. Ubuntu with a different window manager, such as KDE should have a similar keyboard preferences utility. If you are using Unix or a derivative operating system (such as Linux) with XFree86, you can define a compose key by opening a terminal window and typing: 'To use the Windows menu key (between the right Windows key and right Ctrl key: 'To use the right Windows key: 'To use the right Alt key:' To use the Compose key, press and release the Compose key, then type two characters. Combinations useful for typing in French follow:

Physics Study Guide/Waves. =Waves= Wave is defined as the movement of any periodic motion like a spring, a pendulum, a water wave, an electric wave, a sound wave, a light wave, etc. Any periodic wave that has amplitude varied with time, phase sinusoidally can be expressed mathematically as Wave speed is equal to the frequency times the wavelength. It can be understood as how frequently a certain distance (the wavelength in this case) is traversed. Frequency is equal to speed divided by wavelength. Period is equal to the inverse of frequency. Variables<br> Definition of terms Image here The wave’s extremes, its peaks and valleys, are called antinodes. At the middle of the wave are points that do not move, called nodes. "Examples of waves:" Water waves, sound waves, light waves, seismic waves, shock waves, electromagnetic waves … Oscillation. A wave is said to oscillate, which means to move back and forth in a regular, repeating way. This fluctuation can be between extremes of position, force, or quantity. Different types of waves have different types of oscillations. Longitudinal waves: Oscillation is parallel to the direction of the wave. Examples: sound waves, waves in a spring. Transverse waves: Oscillation is perpendicular to direction of the wave. Example: light Interference. When waves overlap each other it is called interference. This is divided into constructive and destructive interference. Constructive interference: the waves line up perfectly and add to each others’ strength. Destructive interference: the two waves cancel each other out, resulting in no wave.This happens when angle between them is 180degrees. Resonance. In real life, waves usually give a mishmash of constructive and destructive interference and quickly die out. However, at certain wavelengths standing waves form, resulting in resonance. These are waves that bounce back into themselves in a strengthening way, reaching maximum amplitude. "Resonance is a special case of forced vibration when the frequency of the impressed periodic force is equal to the natural frequency of the body so that it vibrates with increased amplitude, spontaneously."

German/Appendices/Grammar I. Personal Pronoun Tables: nominative, genitive, dative & accusative cases. Nominative case personal pronouns. The nominative case is used as the subject of a verb. Genitive case personal pronouns. The genitive case corresponds to the possessive case in English or to the English objective case preceded by 'of' and denoting possession. The use of genitive personal pronouns is very rare in German and many Germans are unable to use them correctly. Examples: Dative case personal pronouns. The personal pronouns in the dative case are used as indirect objects of verbs and after the prepositions aus, außer, bei, mit, nach, seit, von, zu. Accusative case personal pronouns. The personal pronouns in the accusative case are used as direct objects of transitve verbs and after the prepositions durch, für, gegen, ohne, um.

Physics Study Guide/Standing waves. =Standing waves= Wave speed is equal to the square root of tension divided by the linear density of the string. Linear density of the string is equal to the mass divided by the length of the string. The fundamental wavelength is equal to two times the length of the string. Variables<br> Definition of terms Fundamental frequency: the frequency when the wavelength is the longest allowed, this gives us the lowest sound that we can get from the system. In a string, the length of the string is half of the largest wavelength that can create a standing wave, called its fundamental wavelength.

Physics Study Guide/Wave overtones. =Wave overtones= For resonance in a taut string, the first harmonic is determined for a wave form with one antinode and two nodes. That is, the two ends of the string are nodes because they do not vibrate while the middle of the string is an antinode because it experiences the greatest change in amplitude. This means that one half of a full wavelength is represented by the length of the resonating structure. The frequency of the first harmonic is equal to wave speed divided by twice the length of the string. (Recall that wave speed is equal to wavelength times frequency.) The wavelength of the first harmonic is equal to double the length of the string. The "nth" wavelength is equal to the fundamental wavelength divided by n. Harmonics for a taut string* Definition of terms The first overtone is the first "allowed" harmonic above the fundamental frequency ("F"1). In the case of a system with two different ends (as in the case of a tube open at one end), the closed end is a node and the open end is an antinode. The first resonant frequency has only a quarter of a wave in the tube. This means that the first harmonic is characterized by a wavelength four times the length of the tube. The wavelength of the first harmonic is equal to four times the length of the string. The "nth" wavelength is equal to the fundamental wavelength divided by n. Note that "n" must be odd in this case as only odd harmonics will resonate in this situation. Harmonics for a system with two different ends* <br> Vs: "velocity of sound"<br>

General Astronomy. Astronomy is the scientific study of celestial bodies in the visible universe, from the scale of a few meters to the macro scale, including: the underlying physics governing those bodies, what they are made of, their properties, distribution, relation, distance, movement, creation, age and demise. Our understanding of the universe has dramatically improved due to the progress of technology. Astronomy has been one of the most modernized areas of scientific study, but it is also one of the oldest sciences — practiced by all ancient civilizations to some degree. Sadly, people have increasingly started to lose connection with the observable universe, something that was previously even required for measuring time, and defining seasons. Astronomy is among our species' first technological steps, but today only passingly remarked about when it verifies something thought about in theoretical physics. Even in a highly industrialized global civilization, defined by consumerism only a few of us had the chance to go beyond simple images and concepts and have in considering what is around our blue dot and its implications for us. This Wikibook introduces the reader to that tapestry and the process that revealed it to humanity. It presents astronomy not only as a field of knowledge, but also as a human endeavor in science. Also on Wikimedia. Wikibooks is a Web site where this and other free textbooks are developed. In addition to this book, Wikibooks is the host of related textbook projects.

General Astronomy/The Solar System. General Astronomy > The Solar System « Astronomy | The Sun » The Solar System may be broadly defined as that portion of the universe under the gravitational influence of the Sun. This includes the Sun itself as well as all planets, moons, asteroids, comets, dust, and ice orbiting the Sun. The Solar System is an example of a star system, which is similarly defined as that portion of the universe under the gravitational influence of one or more co-orbiting stars. The Solar System is a unitary star system, as it has only one star (Sol, our Sun). Components of the Solar System. The largest, most massive, and most prominent element of the Solar System is, of course, the Sun. The Sun makes up 99.8% of the mass of the Solar System. It is literally the point around which the entire Solar System turns. The Sun is virtually at the center of the Solar System; although gravity tugs by the planets may move the center of the System slightly away from the center of the Sun, it always resides deep within the Sun's core. The next largest objects in the Solar System are the planets. There are generally considered to be eight planets in the Solar System. They can be divided into two types: (1) the gas giant planets, which include Jupiter, Saturn, Uranus, and Neptune and (2) the terrestrial planets Mercury, Venus, Earth, and Mars. All eight planets orbit the Sun in elliptical, roughly circular orbits, in approximately the same plane. However, no planet orbits in exactly a circular orbit or exactly in the plane of the Sun's rotation. The orbit of Jupiter is the closest to the plane and circularity; the orbit of Pluto (a dwarf planet) deviates the most from both the plane and from circularity. After the eight major planets are the minor planets, asteroids and comets. Asteroids and comets are smaller objects than planets, but also orbit the Sun. Asteroids and comets are distinguished by their content: asteroids are primarily made up of rock, while comets are primarily made of ices and volatile compounds. Minor planets may be found anywhere in the Solar System, in orbits varying from circular to highly elliptical. Most, however, are found in three belts. The main asteroid belt is found between the planets Mars and Jupiter. As the name implies, it is made almost entirely of asteroids. The ../Kuiper Belt/ is found outside the orbit of Neptune, and encompasses the area from 30 to 100 astronomical units from the Sun. The Kuiper belt contains mainly comets, including very large comet-like objects called cubewanos or plutinos. Some astronomers also consider Pluto to be part of the Kuiper belt. The ../Oort Cloud/ is another belt of comets, and is believed to extend out to approximately one light-year from the Sun. Its existence is deduced from the frequent visitation of long-period comets, comets with extremely elliptical or even hyperbolic orbits. Arrangement of the Solar System. The Solar System may be divided by its components into three major regions: the inner system, the near outer system, and the far outer system. The near outer system might also be referred to as the middle system. The general term outer system refers to both the near and far outer systems. The inner system is composed of the Sun (the largest mass), the terrestrial planets (rocky and closer to the sun) and their moons(moons are drawn to planets because of their gravitational force), close-orbiting asteroids and comets, and the main asteroid belt. Objects in the inner system are almost exclusively composed of rock, with either no atmosphere or an atmosphere that composes little of the object's mass. The inner system's boundary is defined by the main asteroid belt, which separates it from the near outer system. The near outer system is composed of the gas giant planets and their moons, and asteroids and comets that orbit between the main asteroid belt and the Kuiper belt. Objects in the near outer system may have rock, liquid, gas, and ice as significant components. The near outer system's boundary is defined by the orbit of Neptune. The far outer system is composed of the ice planet Pluto, the Kuiper belt, the Oort Cloud, and comets that orbit between the belt and the cloud. Objects in the far outer system may have some rock components, but are mainly composed of ices. Boundary of the Solar System. The boundary of the Solar System is defined in two ways. The gravitational boundary may be described as the point at which objects no longer orbit the Sun. This boundary includes the Oort Cloud, but is poorly defined, as an object is not compelled to orbit the Sun at any point. Another definition is to declare the heliopause as the boundary of the Solar System. This boundary is more easily detectable and definable, but resides well within the Oort Cloud. « Astronomy | The Solar System | The Sun » | Stars, Clusters and Nebulae »

German/Appendices/Resources. Appendix 3 ~ Online Resources for German Language Students Online Wörterbücher - Dictionary. Slideshows with pictures and pronunciations. Language courses German at the time of insertion there is only one file about fruit - I will try to add new ones every week-end. Tandem. Tandem by E-Mail The Mixxer Tandem via Skype

Windows Programming. Introduction. This book aims to be a comprehensive source for any developer who is interested in programming for the Windows platform. It starts at the lowest level, with the Win32 API (C and VB Classic) and then goes over to MFC (C++). Beyond these basic sections, it will cover COM, and the creation of ActiveX modules from a variety of languages. Next, it delves into the Windows DDK, and talk about programming device drivers for Windows platform. Finally, it moves on to the highest-level programming tasks, including shell extensions, shell scripting, and finally ASP and WSH. Other topics that will be discussed here are: Writing screen-savers, creating HTML help modules, and compiling DLL files. This book will focus on topics that are specific to Windows, and avoids general programming topics. For related material the reader is encouraged to look into Wikibooks other works, they will cover general programming, ASM, C, C++, Visual Basic and Visual Basic.NET and other languages and concepts in greater detail. Appropriate links to these books are provided. The reader is assumed to have a previous knowledge of the programming languages involved. Specifically, prior knowledge in C, C++, and Visual Basic is required for certain sections of this book. Further Reading. Wikimedia Resources. Programming Languages: Information about Windows: Related topics:

Physics Study Guide/Vectors and scalars. Vectors are quantities that are characterized by having both a numerical quantity (called the "magnitude" and denoted as |"v"|) and a direction. Velocity is an example of a vector; it describes the time rated change in position with a numerical quantity (meters per second) as well as indicating the direction of movement. The definition of a vector is any quantity that adds according to the parallelogram law (there are some physical quantities that have magnitude and direction that are not vectors). Scalars are quantities in physics that have no direction. Mass is a scalar; it can describe the quantity of matter with units (kilograms) but does not describe any direction. Frequently Asked Questions about Vectors. When are scalar and vector compositions essentially the same? Answer: when multiple vectors are in same direction then we can just add the magnitudes.so, the scalar and vector composition will be same as we do not add the directions. What is a "dot-product"? (work when force not parallel to displacement). Answer: Let's take gravity as our force. If you jump out of an airplane and fall you will pick up speed. (for simplicity's sake, let's ignore air drag). To work out the kinetic energy at any point you simply multiply the "value" of the force caused by gravity by the "distance" moved in the direction of the force. For example, a 180 N boy falling a distance of 10 m will have 1800 J of extra kinetic energy. We say that the man has had 1800 J of work done on him by the force of gravity. Notice that energy is "not" a vector. It has a value but no direction. Gravity and displacement are vectors. They have a value plus a direction. (In this case, their directions are down and down respectively) The reason we can get a scalar energy from vectors gravity and displacement is because, in this case, they happen to point in the same direction. Gravity acts downwards and displacement is also downwards. When two vectors point in the same direction, you can get the scalar product by just multiplying the "value" of the two vectors together and ignoring the direction. But what happens if they don't point in the same direction? Consider a man walking up a hill. Obviously it takes energy to do this because you are going against the force of gravity. The steeper the hill, the more energy it takes every step to climb it. This is something we all know unless we live on a salt lake. In a situation like this we can still work out the work done. In the diagram, the green lines represent the displacement. To find out how much work "against" gravity the man does, we work out the "projection" of the displacement along the line of action of the force of gravity. In this case it's just the y component of the man's displacement. This is where the cos θ comes in. θ is merely the angle between the velocity vector and the force vector. If the two forces do not point in the same direction, you can still get the scalar product by multiplying the projection of one force in the direction of the other force. Thus: There is another method of defining the dot product which relies on components. What is a "cross-product"? (Force on a charged particle in a magnetic field). Answer: Suppose there is a charged particle moving in a constant magnetic field. According to the laws of electromagnetism, the particle is acted upon by a force called the Lorentz force. If this particle is moving from left to right at 30 m/s and the field is 30 Tesla pointing straight down perpendicular to the particle, the particle will actually curve in a circle spiraling out of the plane of the two with an acceleration of its charge in coulombs times 900 newtons per coulomb! This is because the calculation of the Lorentz force involves a cross-product.when cross product can replace the sin0 can take place during multiplication. A cross product can be calculated simply using the angle between the two vectors and your right hand. If the forces point parallel or 180° from each other, it's simple: the cross-product does not exist. If they are exactly perpendicular, the cross-product has a magnitude of the product of the two magnitudes. For all others in between however, the following formula is used: But if the result is a vector, then what is the direction? That too is fairly simple, utilizing a method called the "right-hand rule". The right-hand rule works as follows: Place your right-hand flat along the first of the two vectors with the palm facing the second vector and your thumb sticking out perpendicular to your hand. Then proceed to curl your hand towards the second vector. The direction that your thumb points is the direction that cross-product vector points! Though this definition is easy to explain visually it is slightly more complicated to calculate than the dot product. How to draw vectors that are in or out of the plane of the page (or board). Answer: Vectors in the plane of the page are drawn as arrows on the page. A vector that goes into the plane of the screen is typically drawn as circles with an inscribed X. A vector that comes out of the plane of the screen is typically drawn as circles with dots at their centers. The X is meant to represent the fletching on the back of an arrow or dart while the dot is meant to represent the tip of the arrow.

Physics Study Guide/Work (Advanced). Work is equal to the integral of force times velocity times displacement times time. An integral, if the force isn't constant.

Linear Algebra/Linear Transformations. A linear transformation is an important concept in mathematics because many real world phenomena can be approximated by linear models. Unlike a linear function, a linear transformation works on vectors as well as numbers. Motivations and definitions. Say we have the vector formula_1 in formula_2, and we rotate it through 90 degrees, to obtain the vector formula_3. Another example instead of rotating a vector, we stretch it, so a vector formula_4 becomes formula_5, for example. formula_6 becomes formula_7 Or, if we look at the "projection" of one vector onto the "x" axis - extracting its "x" component - , e.g. from formula_6 we get formula_9 These examples are all an example of a "mapping" between two vectors, and are all linear transformations. If the rule transforming the matrix is called formula_10, we often write formula_11 for the mapping of the vector formula_4 by the rule formula_10. formula_10 is often called the transformation. Note we do not always write brackets like when we write functions. However we "should" write brackets, especially when we want to express the mapping of the sum or the product or the combination of many vectors. Definitions. Linear Operators. Suppose one has a field K, and let x be an element of that field. Let O be a function taking values from K where O(x) is an element of a field J. Define O to be a linear form if and only if: Linear Forms. Suppose one has a vector space V, and let x be an element of that vector space. Let F be a function taking values from V where F(x) is an element of a field K. Define F to be a linear form if and only if: Linear Transformation. This time, instead of a field, let us consider functions from one vector space into another vector space. Let T be a function taking values from one vector space V where L(V) are elements of another vector space. Define L to be a linear transformation when it: Note that not all transformations are linear. Many simple transformations that are in the real world are also non-linear. Their study is more difficult, and will not be done here. For example, the transformation "S" (whose input and output are both vectors in R2) defined by formula_15 We can learn about nonlinear transformations by studying easier, linear ones. We often "describe" a transformation T in the following way This means that T, whatever transformation it may be, maps vectors in the vector space V to a vector in the vector space W. The actual transformation "could" be written, for instance, as Examples and proofs. Here are some examples of some linear transformations. At the same time, let's look at how we can prove that a transformation we may find is linear or not. Projection. Let us take the projection of vectors in R2 to vectors on the "x"-axis. Let's call this transformation T. We know that T maps vectors from R2 to R2, so we can say and we can then write the transformation itself as Clearly this is linear. ("Can you see why, without looking below?") Let's go through a proof that the conditions in the definitions are established. Scalar multiplication is preserved. We wish to show that for all vectors v and all scalars λ, T(λv)=λT(v). Let Then Now If we work out λT(v) and find it is the same vector, we have proved our result. This is the same vector as above, so under the transformation T, "scalar multiplication is preserved". Addition is preserved. We wish to show for all vectors x and y, T(x+y)=Tx+Ty. Let and Now Now if we can show Tx+Ty is this vector above, we have proved this result. Proceed, then, So we have that the transformation T "preserves addition". Zero vector is preserved. Clearly we have Conclusion. We have shown T preserves addition, scalar multiplication and the zero vector. So T must be linear. Disproof of linearity. When we want to "disprove" linearity - that is, to "prove" that a transformation is "not" linear, we need only find one counter-example. If we can find just one case in which the transformation does not preserve addition, scalar multiplication, or the zero vector, we can conclude that the transformation is not linear. For example, consider the transformation We suspect it is not linear. To prove it is not linear, take the vector then but so we can immediately say T is not linear because it doesn't preserve scalar multiplication. Problem set. Given the above, determine whether the following transformations are in fact linear or not. Write down each transformation in the form T:V -> W, and identify V and W. (Answers follow to even-numbered questions): Images and kernels. We have some fundamental concepts underlying linear transformations, such as the "kernel" and the "image" of a linear transformation, which are analogous to the "zeros" and "range" of a function. Kernel. The "kernel" of a linear transformation T: V -> W is the set of all vectors in V which are mapped to the zero vector in W, ie., Coincidentally because of the matr to the matrix equation Ax=0. The kernel of a transform T: V->W is always a subspace of V. The dimension of a transform or a matrix is called the "nullity".. Image. The "image" of a linear transformation T:V->W is the set of all vectors in W which were mapped from vectors in V. For example with the trivial mapping T:V->W such that Tx=0, the image would be 0. ("What would the kernel be?"). More formally, we say that the image of a transformation T:V->W is the set Isomorphism. A linear transformation T:V -> W is an isomorphic transformation if it is:

Ecology/Introduction. Chapter 1 Chapter 1. Introduction to Basic Ecology The objective of this wikibook, "A Study Guide to Basic Ecology", is to give the reader a better understanding of the way life functions on Earth, and how it is organized. This section will introduce basic concepts and definitions required to establish a course that is both biological and ecological in approach. You will learn that there are numerous terms in ecology which basically mean the same thing, and that there are also a plethora of views on precise definitions. As ecology emerged in the 19th and early 20th centuries, many concepts of ecological organization were proposed. These came from both zoologists and botanists—whom seldom read the other's literature—and from different schools of thought. Definition of Ecology. The term oekologie () was coined in 1866 by the German biologist, from the Greek "oikos" meaning "house" or "dwelling", and "logos" meaning "science" or "study". Thus, ecology is the "study of the household of nature". Haeckel intended it to encompass the study of an animal in relation to both the physical environment and other plants and animals with which it interacted. A contemporary definition of ecology is: The scientific study of the distribution and abundance of organisms and the interactions that determine distribution and abundance. This definition encompasses not only the plants and animals that Haeckel recognized but microscopic organisms such as , and , as well. The interactions that determine an organism's distribution and abundance are processes that include energy flow, growth, reproduction, predation, competition and many others. Basic Ecology Definitions. To fully understand the science of ecology, there are some common terms that must be defined. The term environment describes, in an unspecified way, the sum total of physical and biotic conditions that influence an organism (Kendeigh, 1961). The subset of the planet earth "environment" into which life penetrates is termed the biosphere. With respect to the planet earth, the biosphere penetrates only a limited distance into the rock beneath the land and the oceans, and a limited distance out away from the planet towards space. All human effort so far has failed to demonstrate that the biosphere extends beyond these limits or that other biospheres exist elsewhere in the universe. We cannot therefore conclude that they do not exist, only that we know nothing of that existence. Ecosystem is perhaps the most widely used term in ecology. It is defined as the system of organisms and physical factors under study or consideration. Although the boundaries of ecosystems are sometimes quite difficult to define in nature, ecosystems—however bounded—comprise the basic units of that nature (Tansley, 1935). Habitat is generally considered by biologists to be the physical conditions that surround a species, or species population, or assemblage of species, or community (Clements and Shelford, 1939). The basic physical units of the biosphere are the lithosphere (the land), hydrosphere (the water), and atmosphere (the air). Apparently there is no permanent biota of the atmosphere, although insects and birds among others utilize that environment extensively (Hesse, et al., 1951). These basic units are easily recognized in any landscape, as for example shown in the scene at right from Belarus in Europe. NOTE: Definitions of terms used in this textbook have been collected into various glossaries, the basic one being Basic Ecology Glossary. Scope of Ecology. Humanity has been studying nature for thousands of years and formally for several centuries under the science of biology, so why do we say that Ecology is a relatively new science? (Note, the term "ecology" is only about 150 years old). What is it that ecologists do or study that biologists might not? Kendeigh (1961, p. 3) wrote that "[e]cology is one of three main divisions of biology; the other two being morphology [organism structural aspects] and physiology [organism functional aspects]". The behavioral sciences encompass one facet of the interaction of an organism with its physical and biological surroundings, and therefore are part of ecology. Several techniques are used to study Ecology; one of the methods is known as strong inference. Strong inference is defined as the method of testing a hypothesis by deliberately attempting to demonstrate the falsity of the hypothesis (Kinraide and Denison, 2003). Performing experiments is the preferred method of using strong inference. The point of an experiment is to control variables and/or patterns and to predict the outcomes. Traditionally, Ecology is based more on weak inference (the other type of inference) rather than strong inference. In weak inference there are no experiments; rather, there are correlations between observations. Weak inference is defined as a "common sense" approach using simple system models to build understanding (Elner and Vadas). Both weak and strong inference have been used throughout many different science courses over the last several thousands of years (Kinraide and Denison). However, strong inference is said to be more advantageous because weak inference is more prone to error. Weak inference makes people try to cling to one point of view; whereas strong inference (doing experimentation) causes people to think from more than one point of view and keep coming up with different hypotheses to test as their old hypotheses get falsified. Ecology incorporates and overlaps with many other disciplines in both the biological and physical sciences. Certainly on one level, there is no information about the natural environment that does not have some applicability to ecology. On the other hand, such interrelationships between the sciences are much more the norm than most people realize. Ecology, according to Kendeigh (1961, p. 1), is a distinct science because of the way information about the natural world is organized; and because of its unique methodologies and point-of-view by which knowledge is extracted from such information. It may be helpful here to list the phenomenon that ecologists are particularly interested in if only to better clarify the boundaries of this text covering basic ecology (list modified from Kendeigh, 1961, p 1). Ecologists study: Ecology is both a biological and an environmental science, something that should certainly be evident from the definition provided above. Many environmental sciences are minimally concerned with biology (meteorology, for example) and others (environmental toxicology, for example) necessarily combine physical and biological sciences. Environmentalism on the other hand is a political position involved with various aspects of managing the environment. There are many subcategories of Ecology. Plant Ecology looks at the differences and similarities of various plants in differing climates and habitats. The origins of Animal Ecology can be traced to two Europeans, R. Hesse of and of . Physiological Ecology, or , studies the responses of the individual organism to the environment. The idea of was brought forward by two famous men, , who looked at the similarities and dissimilarities of populations and how they replaced each other over time, and . The last subcategory is , which brought about terms such as , introduced by A. Thienemann. Early History of Ecology. Because ecology is a facet of biology, it is not possible to clearly define a time or person that represents the beginning of ecological thought as distinct from biology. One of the first ecologists was probably Theophrastus, a contemporary and student of Aristotle. Theophrastus described various interrelationships between animals and between animals and their environment as early as the 4th century BC (Ramalay, 1940). Over the next several centuries biological knowledge gradually expanded as naturalists, such as Bufon and Linnaeus, contributed to a growing understanding of the nature of plants and animals. These early naturalists of course understood that organisms had a relationship with the environment, and especially that the distribution of forms was related to physical aspects of the geography. The modern ecological concept of integrated communities of organisms began in the 19th century with the studies of August Grisebach (1838), a German botanist. A contemporary and fellow countryman, Ernst Haeckel, coined the term "ecology" in 1866. Other biologists followed Grisbach's ecological approach to natural history studies: K. Möbius (1877) investigating Danish oyster banks, Stephen A. Forbes (1887), describing a lake community as a microcosm, J. E. B. Warming (1895), describing Danish plant communities, and C. C. Adams conducting ecological stuidies in northern Michigan (1905) and at Isle Royale (1909). References. Tansley, A. G. 1935. The use and abuse of vegetational concepts and terms. Ecology, 16(3): 284-307.

C Programming/Simple input and output. Machines process things. We feed stuff into a machine and get different stuff out. A saw turns trees into planks. An internal combustion engine turns gasoline into rotational energy. A computer is no different. But instead of physical materials, computers process information for us. We feed information into the computer, tell the computer what do with it, and then get a result back out. The information we put into a computer is called input and the information we receive from the computer is called output. Input can come from just about anywhere. Keystrokes on a keyboard, data from an internet connection, or sound waves converted to electrical signals are examples of input. Output can also take many forms such as video played on a monitor, a string of text displayed in a terminal, or data we save onto a hard drive. The collection of input and generation of output is known under the general term, "input/output", or I/O for short, and is a core function of computers. Interestingly, the C programming language doesn't have I/O abilities built into it. It does, however, provide us with an external library containing I/O functions which we can compile and link into our programs. We have already used an output library function in the Hello, World! example at the beginning of this text: codice_1. You may recall this function resided in the codice_2 library file. As that file's name implies, codice_2 contains standardized I/O functions for adding input and output capability to our programs. This section of the text will explore some of these functions. Output using codice_1. Recall from the beginning of this text the demonstration program duplicated below: int main(void) printf("Hello, World!"); return 0; If you compile and run this program, you will see the sentence below show up on your screen: This amazing accomplishment was achieved by using the "function" codice_1. A function is like a "black box" that does something for you without exposing the internals inside. We can write functions ourselves in C, but we will cover that later. You have seen that to use codice_1 one puts text, surrounded by quotes, in between the parentheses. We call the text surrounded by quotes a "literal string" (or just a "string"), and we call that string an "argument" to printf. As a note of explanation, it is sometimes convenient to include the opening and closing parentheses after a function name to remind us that it is, indeed, a function. However usually when the name of the function we are talking about is understood, it is not necessary. As you can see in the example above, using codice_1 can be as simple as typing in some text, surrounded by double quotes (note that these are double quotes and not two single quotes). So, for example, you can print any string by placing it as an argument to the codice_1 function: And once it is contained in a proper codice_9 function, it will show: Printing numbers and escape sequences. Placeholder codes. The codice_1 function is a powerful function, and is probably the most-used function in C programs. For example, let us look at a problem. Say we want to calculate: 19 + 31. Let's use C to get the answer. We start writing: // can't be used without this header int main(void) printf("19+31 is"); But here we are stuck! codice_1 only prints strings! Thankfully, printf has methods for printing numbers. What we do is put a "placeholder" format code in the string. We write: printf("19+31 is %d", 19+31); The placeholder codice_12 literally "holds the place" for the actual number that is the result of adding 19 to 31. These placeholders are called format specifiers. Many other format specifiers work with codice_1. If we have a floating-point number, we can use codice_14 to print out a floating-point number, decimal point and all. Other format specifiers are: A complete listing of all the format specifiers for codice_1 is on Wikipedia. Tabs and newlines. What if, we want to achieve some output that will look like: 1905 312 + codice_1 will not put line breaks in at the end of each statement: we must do this ourselves. But how? What we can do is use the newline "escape character". An escape character is a special character that we can write but will do something special onscreen, such as make a beep, write a tab, and so on. To write a newline we write codice_24. All escape characters start with a backslash. So to achieve the output above, we write: printf(" 1905\n312 +\n-----\n"); or to be a bit clearer, we can break this long printf statement over several lines. So our program will be: int main(void) printf(" 1905\n"); printf("312 +\n"); printf("-----\n"); printf("%d", 1905+312); return 0; There are other escape characters we can use. Another common one is to use codice_25 to write a tab. You can use codice_26 to ring the computer's bell, but you should not use this very much in your programs, as excessive use of sound is not very friendly to the user. Other output methods. codice_27. The codice_27 function is a very simple way to send a string to the screen when you have no placeholders or variables to be concerned about. It works very much like the codice_1 function we saw in the "Hello, World!" example: puts("Print this string."); will print to the screen: Print this string. followed by the newline character (as discussed above). (The codice_30 function appends a newline character to its output.) Input using codice_31. The codice_31 function is the input method equivalent to the codice_1 output function - simple yet powerful. In its simplest invocation, the scanf "format string" holds a single "placeholder" representing the type of value that will be entered by the user. These placeholders are mostly the same as the codice_1 function - codice_12 for integers, codice_14 for floats, and codice_37 for doubles. There is, however, one variation to codice_31 as compared to codice_1. The codice_31 function requires the memory address of the variable to which you want to save the input value. While "pointers" (variables storing memory addresses) can be used here, this is a concept that won't be approached until later in the text. Instead, the simple technique is to use the "address-of" operator, &. For now it may be best to consider this "magic" before we discuss pointers. A typical application might be like this: int main(void) int a; printf("Please input an integer value: "); scanf("%d", &a); printf("You entered: %d\n", a); return 0; If you were to describe the effect of the codice_31 function call above, it might read as: "Read in an integer from the user and store it at the address of variable "a" ". If you are trying to input a "string" using "scanf", you should not include the & operator. The code below will produce a runtime error and the program will likely crash: scanf("%s", &a); The correct usage would be: scanf("%s", a); This is because, whenever you use a format specifier for a string (codice_20), the variable that you use to store the value will be an array and, the array names (in this case - a) themselves point out to their base address and hence, the address of operator is not required. Note that using codice_31 to collect keyboard input from the user can make your code vulnerable to Buffer overflow issues and lead to other undesirable behavior if you are not very careful. Consider using codice_44 instead of codice_31. Note on inputs: When data is typed at a keyboard, the information does not go straight to the program that is running. It is first stored in what is known as a buffer - a small amount of memory reserved for the input source. Sometimes there will be data left in the buffer when the program wants to read from the input source, and the codice_31 function will read this data instead of waiting for the user to type something. Some may suggest you use the function codice_47, which may work as desired on some computers, but isn't considered good practice, as you will see later. Doing this has the downfall that if you take your code to a different computer with a different compiler, your code may not work properly.

Calculus/Power series. The study of power series is aimed at investigating series which can approximate some function over a certain interval. Motivations. Elementary calculus (differentiation) is used to obtain information on a line which touches a curve at one point (i.e. a tangent). This is done by calculating the gradient, or slope of the curve, at a single point. However, this does not provide us with reliable information on the curve's actual "value" at given points in a wider interval. This is where the concept of power series becomes useful. An example. Consider the curve of formula_1 , about the point formula_2 . A naïve approximation would be the line formula_3 . However, for a more accurate approximation, observe that formula_4 looks like an inverted parabola around formula_2 - therefore, we might think about which parabola could approximate the shape of formula_4 near this point. This curve might well come to mind: In fact, this is the best estimate for formula_4 which uses polynomials of degree 2 (i.e. a highest term of formula_9) - but how do we know this is true? This is the study of power series: finding optimal approximations to functions using polynomials. Definition. A "power series" (in one variable) is a infinite series of the form or, equivalently, Radius of convergence. When using a power series as an alternative method of calculating a function's value, the equation can only be used to study formula_14 where the power series converges - this may happen for a finite range, or for all real numbers. The size of the interval (around its center) in which the power series converges to the function is known as the "radius of convergence". An example. this converges when formula_16 , the range formula_17 , so the radius of convergence - centered at 0 - is 1. It should also be observed that at the "extremities" of the radius, that is where formula_18 and formula_19 , the power series does not converge. Another example. Using the ratio test, this series converges when the ratio of successive terms is less than one: which is always true - therefore, this power series has an infinite radius of convergence. In effect, this means that the power series can "always" be used as a valid alternative to the original function, formula_24 . Abstraction. If we use the ratio test on an arbitrary power series, we find it converges when and diverges when The radius of convergence is therefore If this limit diverges to infinity, the series has an infinite radius of convergence. Differentiation and Integration. Within its radius of convergence, a power series can be differentiated and integrated term by term. Both the differential and the integral have the same radius of convergence as the original series. This allows us to sum exactly suitable power series. For example, This is a geometric series, which converges for formula_16 . Integrating both sides, we get which will also converge for formula_16 . When formula_19 this is the harmonic series, which "diverges"; when formula_18 this is an alternating series with diminishing terms, which "converges" to formula_36 - this is testing the extremities. It also lets us write series for integrals we cannot do exactly such as the error function: The left hand side can not be integrated exactly, but the right hand side can be. This gives us a series for the sum, which has an infinite radius of convergence, letting us approximate the integral as closely as we like. Note that this is not a power series, as the power of formula_39 is not the index.

Calculus/Integration techniques. Infinite Sums Derivative Rules and the Substitution Rule Integration by Parts Trigonometric Substitutions Trigonometric Integrals Rational Functions by Partial Fraction Decomposition Tangent Half Angle Substitution Reduction Formula Irrational Functions Numerical Approximations

French/Lessons/The house. Note that "quitter" must be followed by a direct object, usually a room or building. , meaning "to inhabit", "to dwell", or "to reside", is used to say in what city or area you live: "Habiter" is also used more specifically: "Habiter rue …" is used to state on what street a person lives: "Habiter" refers to occupying a location, and does not mean "to live" more generally. (The irregular "vivre" is used instead.) The verb "faire" is translated to "to do" or "to make". It is irregularly conjugated (it does not count as a regular "-re" verb). Examples. "Faire" conjugated, followed by an infinitive, means "to have something done for oneself": The direct object pronouns "me", "te", "nous", and "vous" mean "me", "you", and "us": "Me", "te", "nous", and "vous" are also indirect object pronouns, and mean "to me", "to you", and "to us": These pronouns come before the verb they modify: "Me" becomes "m'" and "te" becomes "t'" before a vowel: Examples. The preposition means "in" or "into", in the sense of "inside", "from outside", or "to inside": also means "in" in the sense of "within a period of time": As in English, describes abstract situations and state: can also mean "out of" or "from": The preposition is used instead to indicate "in" in other senses.

Romanian/Contents. Romanian is a Romance language spoken mainly in Romania and Moldova, as well as in some parts of Hungary, Serbia, Bulgaria and Ukraine. It is part of the Romance group of the Indoeuropean family of languages. It is easiest to learn if someone already knows a related language such as Spanish, Catalan, French, Galician, Portuguese or Italian. The most closely related are the other Romance languages, Italian being the closest, but any knowledge of Spanish, French, Galician or Portuguese might be very useful, especially because of the lexical and vocabulary similarities and the grammatical structure. A bit of knowledge of the Latin grammar might be useful as well. Even more distant Indo-European languages have many similarities in both grammar and even common words, as many languages, like English have borrowed extensively words from Latin. It is useful to know the language if travelling in Romania, especially in rural areas. Many people who know English and Romanian will understand any of its relatives, especially Spanish, French or Italian. Note that in Romanian, there is a formal and informal form when addressing people. The informal is tu (you - singular) and voi (also you - plural). Use tu when addressing friends or people you know well. When addressing strangers, use Dumneavoastră or vă. Dumneavoastră is used for stressed pronouns, which are optional, "vă" is used for non-stressed pronouns, which are mandatory for direct and indirect objects. For instance, Vă mulțumesc means "Thank you" (accusative case, direct object), and Vă dau un telefon means "I telephone (to) you" (dative case, indirect object). The formal form of address requires the second person plural form of the verb at all times, even when addressing a single person. (This is similar to the French construction, and, to an extent, German.) Using the singular form can be considered rude or even insulting.

Systematic Phonics/Syllable types. There are six different types of syllables in the English language. Schwa: This can end in a consonant or not, and is an unemphasized syllable whose vowel is somewhat swallowed and pronounced like "uh". Other syllable types can be reclassified as a schwa based on experience of how a word is regionally pronounced. In a dictionary, the schwa sound is written like an upside-down, lower case "e". Long and short vowels. Long vowels are the same sound as the name of the vowel, "a", "e", "i", "o", and "u". Short vowels are the hardest vowel sounds to pronounce in English. "ah" as in cat, "eh" as in pet, "ih" as in sit, "oo" as in not, "uh" as in nut.

GCSE Science/Induction. GCSE Science/Electricity So far we have looked at the effect of putting a current in a magnetic field and seeing that there is a force on the wire that carries the current. On this page we will look at a related effect known as "induction". The best way to learn about induction is to consider the results of a simple experiment. In fact if your school has a spot galvanometer, you should really take a look at these results "in the flesh". Otherwise you'll just have to take my word for it. Experimental set up to demonstrate induction. Look at the diagram below. A coil of wire (solenoid) is attached to the inputs of a spot galvanometer. The solenoid can be made by winding a piece of plastic coated wire a round a paper tube. A spot galvanometer (also known as a mirror galvanometer) looks like a fancy piece of kit, and it is pretty fancy, delicate and expensive, but it does a very simple job. It's really just a very sensitive ammeter. It measures current just like any other ammeter but is much more sensitive than the normal sort you usually see. It can detect "tiny" currents. The only other thing that is needed is an ordinary bar magnet. Experimental results. So, once the apparatus has been set up as in the diagram above, we can look and see what happens. Conclusions. Q1) What effect will reversing the magnet and the direction of movement have on any induced current ? Theoretic explanation of what's going on (Advanced). So now we know what happens we have to come up with an explanation. Look at the diagram below. In this diagram the green line represents a wire that is going into the screen or page. It is at right angles to the magnetic field between the two bar magnets. The is moved downwards so that it "cuts" the field lines. This induces an e.m.f. (voltage) across the length of wire. It is this e.m.f. that causes a current to flow if a complete circuit is made. So now we know why you get a current. It's caused by the induced voltage, but why do you get a voltage? Look at the diagram below. This is a close up of the wire seen end on. The blue circles represent where the magnetic field lines stick out of the screen or page. They are coming straight out of the screen. The wire is made of a metal and so has many free electrons. As the wire moves downwards each individual electron travels downwards too. They effectively form loads of little current flowing down. From the motor effect we know that if a current flows in a magnetic field there will be a force. in this case the force pushes the electrons to the right. It is the electrons all moving up to the right end of the wire that causes the voltage difference. So you see, Induction is really the motor effect. Q2) A student uses a stronger magnet. What effect do you think this will have on any induced current? Q3) Imagine more than one loop of wire cutting through the magnetic field. Each loop of wire has its own e.m.f. induced on it. If the wires are joined up, it's as if they are little cells in series. Fill in the blanks " As the number of windings on the solenoid "increases" the value of the induced voltage ______________. Q4) An engineer wants to uses the induction to create electrcity. He gets a couple of students to push an enormous magnet into and out of a huge coil (he uses a whip to make 'em go fast). In what way will the electricity that this set up produces be different to a the electricity produced by a battery? «The motor effect

GCSE Science/Transformers. Transformers are devices that use induction to transform a high a.c. voltage to a low one or vice versa. They are incredibly important devices, and (even more importantly) they are examiners' favourites. On this page you will be looking at how a transformer works and how they are used. You will also be given some practice in using some simple equations that let you work out what the output voltage and current must be. How a transformer works. There is nothing new to learn in this section. You've already covered GCSE Science/Magnetic effects of a current and GCSE Science/Induction. This section used ideas from those two pages to understand a transformer. The simplest transformer consists of a soft iron core with two coils of wire independently wrapped around it. The first coil called the "primary coil" is connected to an a.c. power supply. The other coil, called the "secondary coil" is connected to the output. The current in the primary coil causes a magnetic field. It's just an electromagnet but because the current is a.c. the magnetic field is constantly changing. If we consider one end of the soft iron core, it's first a north pole, then the field gets weaker and weaker until it becomes zero, then it starts to build up and the end becomes a south pole. The process repeats and the end becomes a north pole again. Now let's think about what is going on in the secondary coil. The magnetic field of the first coil passes right through the secondary coil, what's more the field is constantly changing. This changing field induces a current in the secondary coil. So even though the coils are not physically connected, the current in one, causes the current through the other. If you imagine the lines of field they appear to pulse as the field grows stronger and weaker. When the field grows weak they sweep inwards cutting the secondary coil. Q1) What would the current in the secondary coil be like if you used d.c. in the primary coil? - d.c. in the primary coil will not create any current in the secondary coil. Transformers are used to change the voltage. If the number of turns in the secondary coil is greater than the number of turns in the primary coil, then the voltage in the secondary coil will be higher than that in the primary coil. This is called a "step-up transformer". Conversely, if the secondary coil has fewer turns than the primary coil, then the voltage will be lower, and it is called a "step-down transformer". A simple demonstration transformer. Your teacher may show you a demonstration of a transformer. (see here for details on how to set up a simple transformer). Look at the diagram below. The second coil is on a separate soft iron core. This core can be brought up to the primary coil. At large distances the bulb is off, but as the coils are brought closer together they suddenly attract one another (the primary coil is a powerful electromagnet). Once the two cores are stuck together the bulb in the secondary coil starts to glow. The brightness of the bulb depends on the number of turns on the secondary coil. The more windings there are, the brighter the bulb. Important equations. There are two things you need to remember about transformers. Step up and Step down transformers. Because the voltage in the secondary coil depends on the number of turns, we can use a transformer to "transform" one voltage to another. For example let's assume that the primary coil has 300 turns of wire and the secondary coil has 900 turns. This transformer will step up the voltage by a factor of 3. So if the primary coil has 2V applied to it, the secondary coil will have 6V across it. A step down transformer is the opposite of a step up transformer. Let's say the primary has 900 turns and the secondary has 450 turns. This time the voltage will be half on the secondary as it is on the primary. So if the primary has 2V applied, the secondary will have only 1V across it. Strategy for answering questions. Questions on transformers will often be of the form "A coil has 3000 turns of wire on a soft iron. Another coil of 12000 turns is brought into contact with the first coil. This second coil has a 12V bulb attached to it completing a circuit.What voltage should applied to the first coil?" to answer a question like this: Uses of transformers. The most important use of transformers is in the routing of mains electricity. The power dissipated by a cable = I2R, where I is the current and R is the resistance. There is little that can be done to lower the resistance, so in order to lose as little energy as possible in heating up the cable, the current needs to be kept as low as possible. This is done using a step up transformer which increases the voltage to many thousands of volts. Because power is voltage times current, a high voltage means a low current for a given power value.(Notice that transormers do not obey Ohm's law). At the other end of the distribution network, the voltage is stepped down using another transformer so that the voltage going into homes and factories is not excessively high.

Spanish/Pronunciation. Pronouncing Spanish based on the written word is much simpler than pronouncing English based on written English. This is because, with few exceptions, each letter in the Spanish alphabet represents a single sound, and even when there are many possible sounds, simple rules tell us which is the correct one. In contrast, many letters and letter combinations in English represent multiple sounds (such as the "ou" and "gh" in words like "cough", "rough", "through", "though", "plough", etc.). Letter-sound correspondences in Spanish. The table below presents letter-sound correspondences in the order of the traditional Spanish alphabet. (Refer to the article Spanish orthography in Wikipedia for details on the Spanish alphabet and alphabetization.) One letter, one sound. Pronouncing Spanish based on the written word is much simpler than pronouncing English based on written English. Each vowel represents only one sound. With some exceptions (such as "w" and "x"), each consonant also represents one sound. Many consonants sound very similar to their English counterparts. As the table indicates, the pronunciation of some consonants (such as "b") does vary with the position of the consonant in the word, whether it is between vowels or not, etc. This is entirely predictable, so it doesn't really represent a breaking of the "one letter, one sound" rule. The University of Iowa has a very visual and detailed explanation of the Spanish pronunciation. Here is another page with links to the audio files of the letters. Only five letters may be doubled, and they are the ones in CLEAR. Examples: A"cc"ento, amari"ll"o, l"ee"r, Is"aa"c, and a"rr"iba. Word stress. In Spanish there are two levels of stress when pronouncing a syllable: stressed and unstressed. To illustrate: in the English word ""thinking", "think" is pronounced with stronger stress than "ing". If both syllables are pronounced with the same stress, it sounds like "thin king"". With one category of exceptions ("-mente" adverbs), all Spanish words have one stressed syllable. If a word has an accent mark (´; explicit accent), the syllable with the accent mark is stressed and the other syllables are unstressed. If a word has no accent mark (implicit accent), the stressed syllable is predictable by rule (see below). If you don't put the stress on the correct syllable, the other person may have trouble understanding you. For example: "esta", which has an implicit accent in the letter "e", means "this (feminine)"; and "está", which has an explicit accent in the letter "a", means "is." "Inglés" means "English," but "ingles" means "groins." Adverbs ending in "-mente" are stressed in two places: on the syllable where the accent falls in the adjectival root and on the "men" of "-mente". For example: "estúpido" → "estúpidamente". The vowel of an unstressed syllable should be pronounced with its true value, as shown in the table above. Don't reduce unstressed vowels to neutral schwa sounds, as occurs in English. Rules for pronouncing the implicit accent. There are only the following rules for pronouncing the implicit accent. The stressed syllable is in bold letters: Any exception to these rules is marked by writing an acute accent ("máximo", "paréntesis", "útil", "acción"). In those exceptions, the stressed syllable is the one where the acute accent (called "tilde" in Spanish) appears. The diéresis ( ¨ ). In the clusters "gue" and "gui", the "u" is not pronounced; it serves simply to give the "g" a hard-"g" sound, like in the English word "gut" ("gue" → [ge]; "gui" → [gi]). However, if the "u" has a the diaeresis mark (¨), it is pronounced like an English "w" ("güe" → [gwe]; "güi" → [gwi]). This mark is rather rare. Examples:

Romanian/Pronunciation and alphabet. Even though Romanian spelling is very phonetic, a lot of foreigners find the language difficult. The accent and sounds are very similar to Italian (with slight Slavic influences), so remember to sound every letter clearly. Also, sounds very rarely differ between words (i.e. the letter s is always pronounced the same, everytime, unlike in English). In the pronunciation guide, X-SAMPA will be used to help those people who are familiar with it, or the IPA (International Phonetic Alphabet), in pronouncing Romanian. For those unfamiliar with it, the IPA is a phonetic alphabet designed to help in the description of foreign sounds, and is used extensively by linguists. A good place to start learning the IPA is here. X-SAMPA is an ASCII method of transcribing the IPA. A guide to it can be found here.

German/Level III/Tour de France. Lernen 7-2 ~ Tour de France. (aus Wikipedia, der freien Enzyklopädie)<br> Die "Tour de France" ist eines der berühmtesten und wichtigsten sportlichen Großereignisse überhaupt. Seit 1903 wird die Tour alljährlich - mit Ausnahme der Zeit des Ersten und Zweiten Weltkriegs - drei Wochen lang im Juli ausgetragen und führt dabei in wechselnder Streckenführung quer durch Frankreich und das nahe Ausland. Eine Tour de France der Frauen ("grande boucle féminine") mit deutlich kürzeren Etappen wird seit 1984 gefahren. Sie steht medial völlig im Schatten ihres männlichen Pendants. Vokabeln 7A. die Ausnahme exception die Enzyklopädie encyclopedia der Erste Weltkrieg WW I das Großereignis major event der Juli July das Radrennen bicycle race die Welt world die Woche, die Wochen week, weeks die Zeit time, period der Zweite Weltkrieg WW II (bei weitem) berühmteste among the most widely renowned, the most popular alljährlich every year bei among (one of) berühmteste most celebrated, most renowned frei, freien (Akkusativ) free seit since sportlich athletic überhaupt altogether, generally während during drei Wochen lang three weeks lasting weit broad, wide wichtig important

Puzzles/Decision puzzles/Yet Another Weighing. Puzzles | Decision puzzles | Yet another Weighing You have a balance and the following items of which you know the weights: a stapler weighing 80g, a pen weighing 40g, an eraser weighing 20g, a ruler weighing 10g, and a small coin weighing 5g. "How many different weights can you measure with these items?" solution

Systematic Phonics/Dividing syllables. Systematic Phonics If we can divide a word into syllables, it essentially divides it into easy, bite-size chunks that very easy to pronounce. In this way anyone can pronounce even very large and difficult words. There are a few simple steps to divide a word into syllables. Consonant patterns. Take a word and grab any two talking vowels (the two vowels should not have any other talking vowels in-between them). These are the bookends, the beginning and the end of the part of the word that we are going to look at. There are just five possible combinations of vowels and consonants that can occur: VV. This vowel pattern always starts with an open syllable. If the vowels make different sounds, split them. If not, keep them together. VCV. This is the trickiest one of the five, the only one that will trip you up if you are not careful. First, tentatively divide the syllables between the first vowel and the consonant. Then pronounce the result. If it sounds right, this is the correct division. If it does not sound right, try dividing the syllables between the consonant and the second vowel. How do you know how to pronounce the syllables ? If the syllable ends with a consonant, it is a short vowel. If it ends in a vowel, it is a long vowel. Think about it this way: imagine that an ending consonant has hands, and can use them to shut things like a Jack-in-the-box. If the box is shut by that ending consonant, the Jack-in-the-box is stuffed down in the box and real short, just like the vowel will be short. If there is no consonant to shut the box, the Jack-in-the-box springs out and is real long, just like the vowel will be real long. VCCV. Always break syllables between the two consonants. Almost always, even if the two consonants are the same one repeated, like a double "s". The only exception would be if the two consonants are a single diagraph such as "th" and "sh". With three to five, find the blends, glued sounds, or digraphs, and split. But… if it's a compound, it's the middle point.

Systematic Phonics/Blend. Systematic Phonics Blends or clusters are groups of consonants whose sounds blend together. They can be composed of two or three consonants and can begin or end a syllable. Examples include br, cr, dr, fr, gr, pr, tr, bl, cl, fl, gl, pl, sl, sm, sn, sp, st, str, sw, sc, sk, scr, squ, spl, spr, thr, tw, rl, ng, nt, nk, lk, mp, lt, nd, and rt.

Systematic Phonics/Why use systematic phonics. Systematic phonics is a toolbox designed to enable and empower a person to read. It is useful for children first learning to read, non-native speakers who are learning to read, and even the many native adult English speakers who have not yet learned to read. With systematic phonics, a reader can break down any word, even the most difficult, into maneagable pieces called syllables. When a person can correctly divide a word, he can then pronounce each part and then the whole word. Systematic phonics was developed decades ago by language experts as a way to decode the entire English language. Extensive studies support that the method is effective. However, systematic phonics has not been adopted by most educators, who tend to use "whole language" or "holistic learning" to teach kids to read. Proponents of systematic phonics claim that the failure of many students to read to level can be traced to the use of other, less systematic, teaching methods. Systematic phonics an be an important part of learning English as a Second Language.

Graphic Design/Project List. A great way to learn to do design is to stretch your graphic design muscles. That is, push up your shirtsleeves and get down to doing some projects. Don't worry if the stuff turns out bad or people hate it, it's all a process of learning. Business card design. Every professional needs a business card. The US standard is 2" x 3.5" (89 mm x 51 mm). Use a .125" (3.175 mm) margin on all sides. Using a desktop publishing program, such as Scribus, make a business card for yourself, with typography and graphic elements. Plan layout with an eye for hierarchy. Symbol design. Using Adobe Illustrator or a similar vector-graphics tool, design a stylized icon or symbol representing an animal, taking care to communicate the socially perceived emotional connotations of this animal. The icon should be scalable to the point that it can be used on office stationary as well as blown up to billboard size. The symbol should employ limited colors so as to be easily and inexpensively printable. Compact disc design. Find an existing or imagined compact disc recording and design a complete package for it, including all copy appropriate for a disc to be sold in a store (song list, copyright information, etc.) You may use photography that you take yourself or any drawings or other computer art, etc. that you create yourself or commission for the project. Design the inside and outside of the CD case as well as the disc itself, keeping yourself open to the possibilities of non-traditional CD cases (transparent, etc.) Typeface design. Design a complete alphabet with special characters of your own, original font. You may choose a serif or sans-serif font, or a decorative font. Give samples of bold, extra bold, and italic versions of some letters. Webpage design. Design, using appropriate tools, an entire webpage devoted to a social or political cause of your choosing. Use colors, images, and a style that conforms to the page's message. Importantly don't forget - that the page you are designing for the Visitors only. So first classify your visitors, and use the color schemes which they impress most. And try to design a user friendly navigation system with a low flashy images. Toy design. Design a novel toy, optimized for maximum "fun-ness" for an audience of your choosing, and its complete packaging. Include suggestions for a marketing campaign promoting the toy. Personal projects. Design a project that personally touches you. Whether it be a collage or a poster for something you believe in, it is important to perform your skills for your own use as well as for your clients. Combine tools (Adobe with Macromedia with ink, pencil, highlighters and your trusty scanner). Have fun.

Biochemistry/pKa values. Biochemistry « Metabolism and energy It is difficult to discuss the subject of biochemistry without a firm foundation in general chemistry and organic chemistry, but if one doesn't remember the concept of the Acid Dissociation Constant (p"K"a) from Organic Chemistry, one can read up on the topic below. "Buffers" are essential to biochemical reactions, as they provide a (more or less) stable pH value for reactions to take place under constantly changing circumstances. The pH value in living cells tends to fall between 7.2 and 7.4, and this pH level is generally maintained by weak acids. (The pH values in lysosomes and peroxisomes differ from this value, as do the pH measurements of the stomach and other organs found in various types of plants and animals.) An "acid" is here defined simply as any molecule that can release a proton (H+) into a solution. Stronger acids are more likely to release a proton, due to their atomic and molecular properties. The tendency of an acid to release a proton is called the "dissociation constant" ("K"a) of that substance, with for HA <-> H+ + A-. A larger "K"a value means a greater tendency to dissociate a proton, and thus it means the substance is a stronger acid. The pH at which 50% of the protons are dissociated can therefore be calculated as: This equation is known as the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation is derived from the adjacent Ka expression. By taking the logarithm of base ten to both sides, the next part of the equation is obtained. Using the logarithmic property of multiplication, the [H+] breaks from the expression. Since log Ka is equal to -pKa and log [H+] is equal to -pH, they are then substituted. To obtain what is known as the Henderson-Hasselbalch equation, -pKa and -pH are subtracted from their respective sides to yield a positive equation. The Henderson-Hasselbalch equation interestingly enough predicts the behavior of buffer solutions. A solution of 1 M ethanoic (acetic) acid [HA] and 1 M sodium ethanoate [A-] will have a pH equal to the p"K"a of ethanoic acid: 4.76. If we added acid to pure water up to a concentration of 0.1 M, the pH would become 1. If we add the same concentration of acid to the buffer solution, it will react with the ethanoate to form ethanoic acid. The ethanoate concentration would drop to 0.9 M and the ethanoic acid concentration should rise to 1.1 M. The pH becomes 4.67 - very different from the pH=1 "without" a buffer. Similarly, adding 0.1 M alkali changes the pH of the buffer to 4.85, instead of pH=13 without buffer. Due to the amphipathic nature of amino acids - which are the monomer building blocks of all proteins, physiological conditions are always considered to be buffered, which plays a major role in the conformations and reactivities of substrates in the cell's liquid interior, its cytosol. A very small (which would include a large negative value) p"K"a indicates a very strong acid. A p"K"a value between 4 and 5 is the most common range for organic acid compounds. « Metabolism and energy

Graphic Design/Drawing. =Drawing= It's a good idea for a student of graphic design to learn how to draw. Sure, you can bypass this and do everything by computer, but drawing by hand trains your mind and your eye to seek out details and improve your grasp of visual forms. It develops different parts of your mind that relate to composition, color, anatomy, depth and mood, and helps you directly perceive things and interpret them. Much of what we relate to in our lives is linear. For effective visual communication you need to develop a nonlinear, direct connection to the actual tensions, feelings, and dimesions you are interpreting and expressing in your work. Drawing can be an invaluable way to develop a direct connection to the world around you and develop your own outlook. The ultimate aim of the graphic designer is to understand, use and coordinate the tools of the craft (typeface, art, photography, printing, etc.) and create a message that rises above them. As in music, you do not pay attention to the instruments alone but to the composition as a whole. Draw some architecture, some life studies, and some abstract compositions. Start with basic media like pencil and charcoal, and then try some things in color. Look at master drawings for ideas and inspiration. In interpreting three dimensions on a flat surface with a defined page shape, you encounter a number of issues. Evaluate how light falls across an object and how you can make shapes out of shadows. Shading, the gradation of darkness, is one of the most important factors when you draw an object. Shading and defining basic forms can provide a truer understanding of a dimensional object on a flat surface, and can make the difference between a really shoddy piece and a proper drawing. Get beyond outlining in your definition of form. Appreciate your overall use of the page. Be familiar with positive and negative space (negative space is that space that falls between the objects) and understand they are all part of the overall composition. To be successful at graphic design you need to develop a taste for solving visual problems and a set of strategies for resolving them.

Graphic Design/Type. =Typography= Typeforms are an integral part of modern communication. Since the invention of the printing press, people have used printed —and more recently— electronic type to communicate. Could you imagine a newspaper or magazine where all the articles were handwritten and copied? Imagine how difficult it would be to compose an e-mail or use desktop publishing software to create party invitations without the existence of typefaces. Typefaces are used in print and electronic media not just to communicate a legible message, but as an expressive tool of the author or designer. Each typeface can be used to convey a different style or atmosphere. There are typefaces evocative of Art Deco, The old American West, Weddings and other traditionally formal ceremonies, childhood, The Middle Ages, handwritten text, and an endless variety of other styles. It is almost imperative as a graphic designer, and "absolutely" imperative as a typographer, to develop an appreciation and understanding of both modern and historic typography. In everyday life, one should pay attention to the stylistic and practical uses of typefaces in various kinds of media. Note what feelings the designer was hoping to convey, or what style they were attempting to mimic. Classification. A typeface is a style of lettering, such as Helvetica or Times. A font is the set of a typeface, used to produce the letters. On a computer, it is a file used by the system. People often confuse "font" with "typeface". For example, Helvetica, point 12 is a different font from Helvetica, point 14, even though both are of the same typeface. A set of similar typefaces is called a "family." Within a family, typefaces are categorized as parent (e.g. Times, Helvetica) or relative (e.g. bold, italic). Typefaces are categorized also according to style (e.g. italic, book), weight (e.g. bold or light), and width (e.g. expanded). Type is measured in points, from top to bottom of the letters' invisible bounding boxes. Since each letter fills up a percentage of that bounding box, when the size of the box is increased, the letter size increases. The divisions you may already be familiar with are the serif and sans-serif fonts. Serif fonts, like Times, have the little feet and variable line width characters which make them easy to read. Sans-serif fonts, like Helvetica and Verdana, are drawn with more even-width lines and don't have the little feet, which gives them a clean, modern feel. Usage in Design. Text can have a number of different purposes in a design. It can be used for pure graphic appeal —or aesthetically— a case in which legibility may be less important than aesthetics. An example of graphical use of text is possibly that of major titles. Text may also, more commonly, be used for communication on a linguistic basis rather than visual, in which case, legibility is always the priority of the designer. A few examples of usage of text for linguistic communication are: the body text of an article or book, the text of a restaurant menu, or in product descriptions in a catalog. A font may be used either successfully or poorly, depending on its degree of relevance in the project and the skill of the designer. The designer must pay careful attention to letter, word, and line spacing as well as the size of the typeface and its stylistic contribution to the overall aesthetic of the project. He or she must optimize the properties of the text for its purpose in the overall design (aesthetic or communicative) and maintain legibility where it is necessary, and the designer is also expected to add visual variety with formatting and layout, as well as possible font changes where applicable. Choosing a Font. A designer has to choose a font that is not only appropriate to the mood of the design, but that is appropriate for the text's purpose in the design. For example, there are many kinds of decorative typefaces that one would not want to set an entire article in. This is because a purely decorative typeface tends to be distracting to the content of the message and tire the reader's eyes when used in large portions. Our eyes are most comfortable reading less idiosyncratic typefaces. Decorative typefaces are better suited for display type (greater than 14 points), while simpler type is better used for text (less than 14 points). To maintain readability in large blocks of text —such as in an article— stay consistent, and use only one family. Readability in Different Media. Standard graphic design wisdom holds that of the categories of serif and sans-serif, serif fonts are easier to read. This is because when reading, the eye quickly scans the tops of the letterforms, and a serif font has more immediately recognizable features thanks to the tiny 'eye-holds' provided by the serifs. There is a notion slowly gaining acceptance, that, for the purposes of purely electronic design, the reverse is sometimes true. Sans-serif fonts are more readable in this case because a screen has a lower resolution than a printed page, so the serifs only serve to smudge the letter forms. Some typefaces such as Times, originally designed for the London Times newspaper, or Futura, designed as a letterpress (raised plate) type for printing on paper, were intended for the printed page. Others such as Georgia and Verdana were designed for the lower resolution of text on a screen. The shapes of these typefaces are developed to optimize visibility in smaller sizes on a computer monitor. In larger sizes, these differences don't matter as much. "For maximum readability on the page: Serif; On the screen: Sans." Typeface Sizing. Keep the typeface at a reasonable size for reading. The numbered size of a typeface may reflect the overall height of the lines that stick out of the type, but not the readability size that relates to the inner dimensions of the letters. The type size should be chosen on a visual basis, and not purely on that of font size numbers. Usually, type that is proportioned so that the lower case size is larger in proportion to the overall height of the font, can produce a greater amount of legible words into an equivalent space. Typeface Spacing. Word spacing should be so that the reader is aware of the beginnings and endings of words with little or no difficulty. Experiment with spacing settings to find the best one. Letter spacing and line spacing may be used to expand on the expressivity of the font. Leave enough space between the lines so that the text is legible. Experimentation is important here, too. The reader's eyes should be pulled to the next word as they read, not to the lines above and below. The letter spacing should be that so the reader can easily differentiate between different characters. Yet again: experiment, experiment, experiment. When to Break Rules. With text used purely for graphical or display purposes, spacing, fonts, or colors that would be considered otherwise unreasonable can be utilized to create a visually appealing effect. The legibility rules that are extremely important in body text aren't as critical to effect the larger typeface size. Make sure that before deciding to use more untraditional methods of formatting text, you consider the desires of your client, and/or the stylistic effect the formatting will have on the overall design. Is it supposed to be a classic, elegant wedding invitation, or is this a layout for a skateboarding magazine article? Consider the circumstances and break or follow the rules of tradition appropriately. Remember that a common amateur mistake is to break too many —or the wrong— formatting rules in rebellion of the idea that aesthetics have constraints. Then, they end up with a horrible mess of a design that looks good under no circumstances. "The purpose of a graphic designer is to merge optimal form and function". Remember: anything can be art, but not anything can look good! Layout. A good layout is one that shows good use of the elements and principles of design. Most importantly, a designer should use the principles of design to draw the reader's eye both to and through the design easily. The elements of design are: color, value, texture, shape, form, space, and line. The principles of design are: contrast, emphasis, balance, unity, pattern, movement, and rhythm. The specifics of both the principles and elements vary from source to source, but the idea remains the same. If you haven't studied the principles and elements of design before, read more in the chapter Principles of Design, or scroll down to view the external links. =External Links=

Graphic Design/Photography. Like drawing, you can skip photography and still be a salary-earning graphic design professional. However, some familiarity with the craft will make you an even better designer. Kids today have many more options open to them than we did back when I graduated three years ago. That is, you can take digital pictures and save the money and time needed to develop the film.

Graphic Design/Form and Function. =Form and function= Just like in architecture, one of the fundamental debates in graphic design is between form and function. Form is defined as the shape or visual quality of something. It refers to aesthetics, how a piece looks. Much of graphic design centers on how to make a work appealing (or unappealing, or any other quality depending on the project goals). Function relates to getting the job done. Function is pragmatic and business-oriented. Printing newspaper on glossy magazine paper is too expensive, and printing it on tissue paper would fall apart. An artistic photograph of a mountain may not convey a message appropriate to an Arctic cruise.

Graphic Design/Statistics about graphic designers. =Statistics= Looking at designers as a whole, only about 60 percent of entering designers stay in the field after two years. By five years, about 30 percent are left. Princeton Review

Graphic Design/Authors. This book was started by , a graduate of the acclaimed University of Cincinnati College of Design, Architecture, Art and Planning (DAAP). Note from the author. There are not many textbooks published on the discipline of graphic design. Perhaps this is due in part to the abstract, subjective nature of many of its aspects, and the fact that there are few universally-agreed-upon rules like there are for mathematics or the hard sciences. This book is an attempt to formalize some of the concepts that were taught to me while in design school. The material was difficult and sometimes even overwhelming for me at the time. I did not graduate at the top of my class. However DAAP is a widely respected school and I did receive the vigorous training that characterizes its graphic design department. In this book I will try to break down in a simple and understandable way the basics of what I learned.

Geometry/Congruency and Similarity. Congruency. "Congruent" shapes are the same size with corresponding lengths and angles equal. In other words, they are exactly the same size and shape. They will fit on top of each other perfectly. Therefore if you know the size and shape of one you know the size and shape of the others. For example: Each of the above shapes is congruent to each other. The only difference is in their orientation, or the way they are rotated. If you traced them onto paper and cut them out, you could see that they fit over each other exactly. Having done this, right away we can see that, though the angles correspond in size and position, the sides do not. Therefore it is proved the triangles are not congruent. Similarity. "Similar" shapes are like congruent shapes in that they must be the same shape, but they don't have to be the same size. Their corresponding angles are congruent and their corresponding sides are in proportion.

GCSE Science/Generating electricity. GCSE Science/Electricity On the last page we looked at induction. That is how the motor effect acting on electrons in wires causes them to move and create a current. On this page we will look at some practical uses of induction and how electricity is made in power stations. Look at the diagram of an electric motor. As the coil rotates it cuts the field lines in a downwards direction then an upwards direction. This means that the electricity produced alternates. The current flows one way then the other. The frequency depends on the speed of rotation. Q1) A motor is rotated manually to produce a current. An oscilloscope is used to investigate this current and produces a trace like the one shown. The time is on the x axis and voltage is on the y axis. The motor is speeded up. Which one of the following shows the new trace? Alternating Current. In the section above you learned that a dynamo produces a.c. If you've ever looked closely at a school power pack you will probably have noticed that it has a.c. and d.c. outputs. D.c. stands for direct current. The current flows in one direction only and (apart from when it is switched on or off) doesn't change in value. A.c. constantly changes. An a.c. curve is typically that of a sine wave. The current switches back and forth and the value of the current is constantly changing.(This fact is important when we come to study transformers.) Some devices work equally well with either a.c. or d.c. Others must have the correct type or they won't work. For example think about a child's train on a track. If a.c. electricity is used the train will not go anywhere! This is because the current is 'telling' the motor to go forwards, go backwards, no, go forwards and so on. Anything with a small electric motor in it has to use d.c. (Special electric motors which use a.c. do exist. However, the ones you'll come across in school or in any toy application will almost certainly be d.c. motors.) On the other hand a bulb has no problem working on a.c. This is because a bulb converts the energy of the electric current to heat and light. It makes no difference which way the current flows, the energy is still there. So bulbs, electric fires, cookers and so on do not care if they use a.c. or d.c. Transformers (which we will study in the next section) will only work with a.c. This is because a transformer needs to have a constantly varying current, and d.c. only varies when it is switched on or off. What useful electrical component was the engineer thinking of?---- Answers | Transformers»

English in Use/Verbs. Verbs are often called action words that show what the subject (a noun or pronoun) is doing. A verb is a word that signifies to be, to act, or to be acted on: as, "I am, I rule, I am ruled, I love, you love, he loves". Verbs are so called, from the Latin "verbum", a word; because the verb is that word which most essentially contains what is said in any clause or sentence. Although described as "action words", they can describe abstract concepts. They are a requirement of any sentence. Verbs have modifications of four kinds: moods, tenses, persons and numbers. Morphological forms. An English verb has four morphological forms (forms of word formation) ever needful to be ascertained in the first place: the present, the past, the present participle, and the past participle. The third person singular is the fifth morphological form. The present is that form of the verb, which is the root of all the rest; the verb itself; or that simple term which we should look for in a dictionary: as, "be, act, rule, love, defend, terminate". The past is that simple form of the verb, which denotes time past; and which is always connected with some noun or pronoun, denoting the subject of the assertion: as, "I was, I acted, I ruled, I loved, I defended". The present participle is that form of the verb, which ends commonly in "ing", and implies a continuance of the being, action, or passion: as, "being, acting, ruling, loving, defending, terminating". The past participle is that form of the verb, which ends commonly in "d" or "ed", and implies what has taken place: as, "been, acted, ruled, loved". Regularity. English, like many Germanic languages, contains both strong (or irregular, which is not "quite" the same as strong) and weak (regular) verbs. Irregular verbs are one of the most difficult aspects of learning English. Each irregular verb must be memorized, because they are not often easy to identify otherwise. Verbs are divided, with respect to their regularity, into four classes: regular and irregular, redundant and defective. A regular verb is a verb that forms the past and the past participle by assuming "d" or "ed": as, "love, loved, loving, loved". An irregular verb is a verb that does not form the past and the past participle by assuming "d" or "ed": as, "see, saw, seeing, seen". A redundant verb is a verb that forms the past or the past participle in two or more ways, and so as to be both regular and irregular: as, "thrive, thrived or throve, thriving, thrived or thriven". A defective verb is a verb that forms no participles, and is used in but few of the moods and tenses: as, "beware, ought, quoth". Persons and numbers. The person and number of a verb are those modifications in which it agrees with its subject. There are three persons and two numbers: thus, Where the verb is varied, the third person singular in the present tense, is regularly formed by adding "s" or "es": as, "I see, he sees; I give, he gives; I go, he goes; I fly, he flies; I vex, he vexes; I lose, he loses". Where the verb is not varied to denote its person and number, these properties are inferred from its subject: as, "if I love, if he love; if we love, if you love, if they love". Tenses. Tenses are those modifications of the verb, which distinguish time. There are three tenses - Each of the above category lists subcategories. One could even say there are twelve tenses because each of those comes in simple and in progressive forms, which have different meaning. The past tense is sometimes called imperfect, but the names perfect and imperfect do not fit their meaning. These names were derived from Latin where they were correct. The Present Simple Present Tense is that which expresses what now exists, is normal or correlated to senses. It is used with adverbs like "always", "generally". Present Continuous Tense is that which expresses what is temporary: Present perfect tense is that which expresses what has taken place, within some period of time not yet fully past, or is still valid. It is used with adverbs like "ever", "never", "today", "this week". Present perfect continuous tense is that which which started in the past and has not yet finished. The Past Simple Past tense is that which expresses what took place in time fully past. It is used with adverbs like "yesterday", " last week". Past continuous tense is that which expresses what was taking place when (suddenly) something else occurred. Past perfect tense is that which expresses what had taken place, at some past time mentioned, before something other happened. Past perfect continuous tense is that which expresses what had started before and was still going on, when something else occurred. The Future Simple Future Tense is that which expresses what will take place hereafter. Future continuous tense is that which expresses what will be currently taking place at a certain time in future. Future Perfect Tense is that which expresses what will have taken place at some future time mentioned. Future Perfect continuous Tense is that which expresses what will have started at some time and will still be ongoing, at some future time mentioned. Signification. An active verb is a verb in an active sentence, in which the subject performs the verb: as, An active verb can be transitive or intransitive, but not passive or neuter. Verbs are divided again, with respect to their signification, into four classes: transitive, intransitive, passive, and neuter. A transitive verb is a verb that expresses an action which has some person or thing for its object: as, An intransitive verb is a verb that expresses an action which has no person or thing for its object: as, A passive verb is a verb in a passive sentence (passive voice) that represents its subject, or what the nominative expresses, as being acted on: as, In a passive sentence, the action is performed on the subject. These sentences have the same denotative meaning, but their connotative meaning is quite different; active verbs are much more powerful and personal. A neuter verb or impersonal passive verb is a verb that expresses neither action nor passion, but simply being, or a state of being: as, Voice. Voice of speech can be active or passive. Principally in passive voice the same tenses can be used as in active voice. There are two forms of passive voice (the second form is preferred): There are however some things to note. Here active and passive do not really have the same meaning. If for example you describe a picture where people build a house, the first sentence is perfectly correct. The second sentence however will be interpreted as the static perfect of the sentence This is, the house is now ready and not under construction. So the correct passive form is Passive voice can be built quite formally by adhering to some rules. You will however not find normally all tenses as in active voice. Formal rules will lead you to monstrosities like the following, you will certainly never hear (already the active sentence is quite monstrous): Moods. Moods are different forms of the verb, each of which expresses the being, action, or passion, in some particular manner. There are five moods; the infinitive, the indicative, the potential, the subjunctive, and the imperative. The infinitive mood is that form of the verb, which expresses the being, action, or passion, in an unlimited manner, and without person or number: as, The indicative mood is that form of the verb, which simply indicates or declares a thing: as, or asks a question: as, The potential mood is that form of the verb which expresses the power, liberty, possibility, or necessity, of the being, action, or passion: as, The subjunctive mood is that form of the verb, which represents the being, action, or passion, as conditional, doubtful, and contingent: as, The imperative mood is that form of the verb which is used in commanding, exhorting, entreating, or permitting: as, Conjugation. The conjugation of a verb is a regular arrangement of its moods, tenses, persons, numbers, and participles. An auxiliary, or a sign of a verb, is a short verb prefixed to one of the morphological forms of another verb, to express some particular mode and time of the being, action, or passion. The auxiliaries are "do, be, have, shall, will, may, can", and "must", with their variations. "Do", "be", and "have" express the indicative mood. Most often, the auxiliaries are used in the following way: Shall and will. Often confused with each other in modern English. These auxiliaries have distinct meanings, and, as signs of the future, they are interchanged thus: Present tense, sign of the indicative first-future. Past tense, sign of aorist, or indefinite. See also: Shall and will by Wikipedia Must. If "must" is ever used in the sense of the past tense, the form is the same as that of the present: this word is entirely invariable. Is being. English grammar has changed, no longer means the same as The first sentence refers to an ongoing action, the second to a completed one. Forms of conjugation. Verb may be conjugated in four ways: The verbs would be conjugated affirmatively, unless said otherwise. Love, conjugated in simple form. The verb "love" is a regular active verb. Simple form, active or neuter. The simplest form of an English conjugation, is that which makes the present and past tenses without auxiliaries; but, even in these, auxiliaries are required for the potential mood, and are often preferred for the indicative. Infinite mood. The infinitive mood is that form of the verb, which expresses the being, action, or passion, in an unlimited manner, and without person or number. It is used only in the present and perfect tenses. Present tense. This tense is the root, or radical verb; and is usually preceded by the preposition to, which shows its relation to some other word: thus, Perfect tense. This tense prefixes the auxiliary have to the past participle; and, like the infinitive present, is usually preceded by the preposition to: thus, Indicative mood. The indicative mood is that form of the verb, which simply indicates or declares a thing, or asks a question. It is used in all the tenses. Present tense. The present indicative, in its simple form, is essentially the same as the present infinitive, or radical verb; except that the verb "be" has "am" in the indicative. The simple form of the present tense is varied thus: This tense may also be formed by prefixing the auxiliary "do" to the verb: thus, Past tense. This tense, in its simple form is the past; which, in all regular verbs, adds "d" or "ed" to the present, but in others is formed variously. The simple form of the past tense is varied thus: This tense may also be formed by prefixing the auxiliary "did" to the present: thus, Perfect tense. This tense prefixes the auxiliary "have" to the past participle: thus, Past perfect tense. This tense prefixes the auxiliary "had" to the past participle: thus, First-future tense. This tense prefixes the auxiliary "shall or will" to the present: thus, Second-future tense. This tense prefixes the auxiliaries "shall have or will have" to the past participle: thus, Potential mood. The potential mood is that form of the verb, which expresses the power, liberty, possibility, or necessity of the being, action, or passion. It is used in the first four tenses; but the potential past is properly an aorist: its time is very indeterminate: as, Present tense. This tense prefixes the auxiliary "may, can, or must", to the radical verb: thus, Past tense. This tense prefixes the auxiliary "might, could, would, or should", to the radical verb: thus, Perfect tense. This tense prefixes the auxiliaries, "may have, can have, or must have", to the past participle: thus, Past perfect tense. This tense prefixes the auxiliaries, "might have, could have, would have, or should have", to the past participle: thus, Subjunctive mood. The subjunctive mood is that form of the verb, which represents the being, action, or passion, as conditional, doubtful, or contingent. This mood is generally preceded by a conjunction: as, "if, that, though, lest, unless, except". But sometimes, especially in poetry, it is formed by a mere placing of the verb before the nominative: as, It does not vary its termination at all, in the different persons. It is used in the present, and sometimes in the past tense; rarely, and perhaps never properly, in any other. As this mood can be used only in a dependent clause, the time implied in its tenses is always relative, and generally indefinite: as, Present tense. This tense is generally used to express some condition on which a future action or event is affirmed. It is therefore erroneously considered by some grammarians, as an elliptical form of the future. In this tense, the auxiliary "do" is sometimes employed: as, Past tense. This tense, like the past of the potential mood, with which it is frequently connected, is properly an aorist, or indefinite tense; for it may refer to time past, present, or future: as, Imperative mood. The imperative mood is that form of the verb, which is used in commanding, exhorting, entreating, or permitting. It is commonly used only in the second person of the present tense. See, conjugated in simple form. The verb "see" is an irregular active verb. Participles. Present Past Past Perfect Seeing. Seen. Having seen. Be, conjugated in simple form. The verb "be" is an irregular neuter verb. Morphological forms. Present Past Present Participle Past Participle. Be. Was. Being. Been. Participles. Present Past Past Perfect Being. Been. Having been. Read, conjugated in progressive form. The verb "read" is an irregular active verb. Compound or progressive form. Active and neuter verbs may also be conjugated, by adding the present participle to the auxiliary verb "be", through all its changes: as, This form of the verb denotes a continuance of the action or state of being, and is, on many occasions, preferable to the simple form of the verb. Morphological forms of the simple verb. Present Past Present Participle Past Participle Read. Read. Reading. Read. Participles. Present Past Past Perfect Being reading. ———————— Having been reading. Be loved, conjugated in simple form. The verb "be loved" is a regular passive verb. Form of passive verbs. Passive verbs, in English, are always of a progressive form; being made from transitive verbs, by adding the past participle to the auxiliary verb "be", through all its changes: thus from the active transitive verb "love", is formed the passive verb "be loved". Love, conjugated negatively. Form of negation. A verb is conjugated negatively, by placing the adverb "not" and participles take the negative first: as, not to love, not to have loved; not loving, not loved, not having loved. Love, conjugated interrogatively. Form of question. A verb is conjugated interrogatively, in the indicative and potential moods, by placing the nominative after it, or after the first auxiliary: as, Love, conjugated interrogatively and negatively. Form of question with negation. A verb is conjugated interrogatively and negatively, in the indicative and potential moods, by placing the nominative and the adverb "not" after the verb, or after the first auxiliary: as, Irregular verbs. An irregular verb is a verb that does not form the past and the past participle by assuming "d" or "ed": as, "see, saw, seeing, seen". Of this class of verbs there are about one hundred and ten, beside their several derivatives and compounds. Methods of learning irregular verbs: List of the top irregular verbs: Redundant verbs. A redundant verb is a verb that forms the past or the past participle in two or more ways, and so as to be both regular and irregular: as, "thrive, thrived or throve, thriving, thrived or thriven". Of this class of verbs, there are about ninety-five, beside sundry derivatives and compounds. List of the redundant verbs: Defective verbs. A defective verb is a verb that forms no participles, and is used in but few of the moods and tenses: as, "beware, ought, quoth". List of the defective verbs: A short syntax. The finite verb must agree with its subject, as "The birds fly", except the following cases: the conjunction "and", as "Rhetoric and logic are allied," one person or thing, as "Flesh and blood has not revealed it," empathy, as "Consanguinity, and not affinity, is the ground," "each", "every", or "no", as "No one is the same," and the conjunction "or", as "Fear or jealousy affects him."

Puzzles/Easy Sequence 7/Solution. < They are the sum of two numbers before (also known as the Fibonacci-sequence): 2 3 5 8 13 21 34 55 89 That is, 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13 and so on...

Puzzles/Easy Sequence 9/Solution. These numbers are sorted by reverse alphabet: two, three, six, seven, one, nine, four, five, eight 2 3 6 7 1 9 4 5 8

Physics with Calculus. This textbook is designed for use with first- and second-year college level physics for engineers and scientists. While the content is not mathematically complicated or very advanced, the students are expected to be familiar with differential calculus and some integral calculus. Unlike the Modern Physics textbook, this textbook will stay with the traditional order in presentation of topics in mechanics, thermodynamics, electromagnetism, and geometric optics. These consist the first two semesters and perhaps first few weeks of the third semester. The topics in modern physics, which can be covered during the third semester in the remaining time, can be presented or read in any order. In keeping with maintaining the orthodox order, we will also maintain the traditional chapter-section organization. A few suggested break points between semesters are shown below as well. These break points are marked by a horizontal line between chapters. "(Note to editors: For the purpose of hierarchical organization, at least until the organization of the book is settled down, it should be: "Physics with Calculus/General Topic/Specific Topic", where "General Topic" is any of the following: Mechanics, Thermodynamics, Waves, Electromagnetism, Optics, Modern. No additional "general topic" should be necessary. "Specific Topic" is what it sounds like it is. It can be as specific as necessary, such as "Conservation of Angular Momentum in Spin-Orbit Coupling", or as general as necessary, such as "Newton's Laws". More specific information, such as ordering of chapters will be kept in this module only. This should minimize the need to rename books each time one section moves from one chapter to another, without the unclear "Part I" or "Unit I".)"

C Programming/Program flow control. Very few programs follow exactly one control path and have each instruction stated explicitly. In order to program effectively, it is necessary to understand how one can alter the steps taken by a program due to user input or other conditions, how some steps can be executed many times with few lines of code, and how programs can appear to demonstrate a rudimentary grasp of logic. C constructs known as conditionals and loops grant this power. From this point forward, it is necessary to understand what is usually meant by the word "block". A block is a group of code statements that are associated and intended to be executed as a unit. In C, the beginning of a block of code is denoted with { (left curly), and the end of a block is denoted with }. It is not necessary to place a semicolon after the end of a block. Blocks can be empty, as in {}. Blocks can also be nested; i.e. there can be blocks of code within larger blocks. Conditionals. There is likely no meaningful program written in which a computer does not demonstrate basic decision-making skills. It can actually be argued that there is no meaningful human activity in which some sort of decision-making, instinctual or otherwise, does not take place. For example, when driving a car and approaching a traffic light, one does not think, "I will continue driving through the intersection." Rather, one thinks, "I will stop if the light is red, go if the light is green, and if yellow go only if I am traveling at a certain speed a certain distance from the intersection." These kinds of processes can be simulated in C using conditionals. A conditional is a statement that instructs the computer to execute a certain block of code or alter certain data only if a specific condition has been met. The most common conditional is the If-Else statement, with conditional expressions and Switch-Case statements typically used as more shorthanded methods. Before one can understand conditional statements, it is first necessary to understand how C expresses logical relations. C treats logic as being arithmetic. The value 0 (zero) represents false, and all other values represent true. If you chose some particular value to represent true and then compare values against it, sooner or later your code will fail when your assumed value (often 1) turns out to be incorrect. Code written by people uncomfortable with the C language can often be identified by the usage of #define to make a "TRUE" value. Because logic is arithmetic in C, arithmetic operators and logical operators are one and the same. Nevertheless, there are a number of operators that are typically associated with logic: Relational and Equivalence Expressions:. New programmers should take special note of the fact that the "equal to" operator is ==, not =. This is the cause of numerous coding mistakes and is often a difficult-to-find bug, as the expression codice_1 sets codice_2 equal to codice_3 and subsequently evaluates to codice_3; but the expression codice_5, which is usually intended, checks if codice_2 is equal to codice_3. It needs to be pointed out that, if you confuse = with ==, your mistake will often not be brought to your attention by the compiler. A statement such as codice_8 is considered perfectly valid by the language, but will always assign 20 to codice_9 and evaluate as true. A simple technique to avoid this kind of bug (in many, not all cases) is to put the constant first. This will cause the compiler to issue an error, if == got misspelled with =. Note that C does not have a dedicated boolean type as many other languages do. 0 means false and anything else true. So the following are equivalent: if (foo()) { // do something and if (foo() != 0) { // do something Often codice_10 and codice_11 are used to work around the lack of a boolean type. This is bad practice, since it makes assumptions that do not hold. It is a better idea to indicate what you are actually expecting as a result from a function call, as there are many different ways of indicating error conditions, depending on the situation. if (strstr("foo", bar) >= 0) { // bar contains "foo" Here, codice_12 returns the index where the substring foo is found and -1 if it was not found. Note: this would always fail with the codice_13 definition mentioned in the previous paragraph. It would also not produce the expected results if we omitted the codice_14. One other thing to note is that the relational expressions do not evaluate as they would in mathematical texts. That is, an expression codice_15 does not evaluate as you probably think it might. Mathematically, this would test whether or not "value" is between "myMin" and "myMax". But in C, what happens is that "value" is first compared with "myMin". This produces either a 0 or a 1. It is this value that is compared against myMax. Example: int value = 20; if (0 < value < 10) { // don't do this! it always evaluates to "true"! /* do some stuff */ Because "value" is greater than 0, the first comparison produces a value of 1. Now 1 is compared to be less than 10, which is true, so the statements in the if are executed. This probably is not what the programmer expected. The appropriate code would be: int value = 20; if (0 < value && value < 10) { // the && means "and" /* do some stuff */ Logical Expressions. Here's an example of a larger logical expression. In the statement: e = ((a && b) || (c > d)); e is set equal to 1 if a and b are non-zero, or if c is greater than d. In all other cases, e is set to 0. C uses short circuit evaluation of logical expressions. That is to say, once it is able to determine the truth of a logical expression, it does no further evaluation. This is often useful as in the following: int myArray[12]; if (i < 12 && myArray[i] > 3) { In the snippet of code, the comparison of i with 12 is done first. If it evaluates to 0 (false), i would be out of bounds as an index to myArray. In this case, the program never attempts to access myArray[i] since the truth of the expression is known to be false. Hence we need not worry here about trying to access an out-of-bounds array element if it is already known that i is greater than or equal to zero. A similar thing happens with expressions involving the or || operator. while (doThis() || doThat()) ... doThat() is never called if doThis() returns a non-zero (true) value. The If-Else statement. If-Else provides a way to instruct the computer to execute a block of code only if certain conditions have been met. The syntax of an If-Else construct is: if (/* condition goes here */) { /* if the condition is non-zero (true), this code will execute */ } else { /* if the condition is 0 (false), this code will execute */ The first block of code executes if the condition in parentheses directly after the "if" evaluates to non-zero (true); otherwise, the second block executes. The "else" and following block of code are completely optional. If there is no need to execute code if a condition is not true, leave it out. Also, keep in mind that an "if" can directly follow an "else" statement. While this can occasionally be useful, chaining more than two or three if-elses in this fashion is considered bad programming practice. We can get around this with the Switch-Case construct described later. Two other general syntax notes need to be made that you will also see in other control constructs: First, note that there is no semicolon after "if" or "else". There could be, but the block (code enclosed in { and }) takes the place of that. Second, if you only intend to execute one statement as a result of an "if" or "else", curly braces are not needed. However, many programmers believe that inserting curly braces anyway in this case is good coding practice. The following code sets a variable c equal to the greater of two variables a and b, or 0 if a and b are equal. if (a > b) { c = a; } else if (b > a) { c = b; } else { c = 0; Consider this question: why can't you just forget about "else" and write the code like: if (a > b) { c = a; if (a < b) { c = b; if (a == b) { c = 0; There are several answers to this. Most importantly, if your conditionals are not mutually exclusive, "two" cases could execute instead of only one. If the code was different and the value of a or b changes somehow (e.g.: you reset the lesser of a and b to 0 after the comparison) during one of the blocks? You could end up with multiple "if" statements being invoked, which is not your intent. Also, evaluating "if" conditionals takes processor time. If you use "else" to handle these situations, in the case above assuming (a > b) is non-zero (true), the program is spared the expense of evaluating additional "if" statements. The bottom line is that it is usually best to insert an "else" clause for all cases in which a conditional will not evaluate to non-zero (true). The conditional expression. A conditional expression is a way to set values conditionally in a more shorthand fashion than If-Else. The syntax is: (/* logical expression goes here */) ? (/* if non-zero (true) */) : (/* if 0 (false) */) The logical expression is evaluated. If it is non-zero (true), the overall conditional expression evaluates to the expression placed between the ? and :, otherwise, it evaluates to the expression after the :. Therefore, the above example (changing its function slightly such that c is set to b when a and b are equal) becomes: c = (a > b) ? a : b; Conditional expressions can sometimes clarify the intent of the code. Nesting the conditional operator should usually be avoided. It's best to use conditional expressions only when the expressions for a and b are simple. Also, contrary to a common beginner belief, conditional expressions do not make for faster code. As tempting as it is to assume that fewer lines of code result in faster execution times, there is no such correlation. The Switch-Case statement. Say you write a program where the user inputs a number 1-5 (corresponding to student grades, A(represented as 1)-D(4) and F(5)), stores it in a variable grade and the program responds by printing to the screen the associated letter grade. If you implemented this using If-Else, your code would look something like this: if (grade == 1) { printf("A\n"); } else if (grade == 2) { printf("B\n"); } else if /* etc. etc. */ Having a long chain of if-else-if-else-if-else can be a pain, both for the programmer and anyone reading the code. Fortunately, there's a solution: the Switch-Case construct, of which the basic syntax is: switch (/* integer or enum goes here */) { case /* potential value of the aforementioned int or enum */: /* code */ case /* a different potential value */: /* different code */ /* insert additional cases as needed */ default: /* more code */ The Switch-Case construct takes a variable, usually an int or an enum, placed after "switch", and compares it to the value following the "case" keyword. If the variable is equal to the value specified after "case", the construct "activates", or begins executing the code after the case statement. Once the construct has "activated", there will be no further evaluation of "case"s. Switch-Case is syntactically "weird" in that no braces are required for code associated with a "case". Very important: Typically, the last statement for each case is a break statement. This causes program execution to jump to the statement following the closing bracket of the switch statement, which is what one would normally want to happen. However if the break statement is omitted, program execution continues with the first line of the next case, if any. This is called a "fall-through". When a programmer desires this action, a comment should be placed at the end of the block of statements indicating the desire to fall through. Otherwise another programmer maintaining the code could consider the omission of the 'break' to be an error, and inadvertently 'correct' the problem. Here's an example: switch (someVariable) { case 1: printf("This code handles case 1\n"); break; case 2: printf("This prints when someVariable is 2, along with...\n"); /* FALL THROUGH */ case 3: printf("This prints when someVariable is either 2 or 3.\n" ); break; If a "default" case is specified, the associated statements are executed if none of the other cases match. A "default" case is optional. Here's a switch statement that corresponds to the sequence of if - else if statements above. Back to our example above. Here's what it would look like as Switch-Case: switch (grade) { case 1: printf("A\n"); break; case 2: printf("B\n"); break; case 3: printf("C\n"); break; case 4: printf("D\n"); break; default: printf("F\n"); break; A set of statements to execute can be grouped with more than one value of the variable as in the following example. (the fall-through comment is not necessary here because the intended behavior is obvious) switch (something) { case 2: case 3: case 4: /* some statements to execute for 2, 3 or 4 */ break; case 1: default: /* some statements to execute for 1 or other than 2,3,and 4 */ break; Switch-Case constructs are particularly useful when used in conjunction with user defined "enum" data types. Some compilers are capable of warning about an unhandled enum value, which may be helpful for avoiding bugs. Loops. Often in computer programming, it is necessary to perform a certain action a certain number of times or until a certain condition is met. It is impractical and tedious to simply type a certain statement or group of statements a large number of times, not to mention that this approach is too inflexible and unintuitive to be counted on to stop when a certain event has happened. As a real-world analogy, someone asks a dishwasher at a restaurant what he did all night. He will respond, "I washed dishes all night long." He is not likely to respond, "I washed a dish, then washed a dish, then washed a dish, then...". The constructs that enable computers to perform certain repetitive tasks are called loops. While loops. A while loop is the most basic type of loop. It will run as long as the condition is non-zero (true). For example, if you try the following, the program will appear to lock up and you will have to manually close the program down. A situation where the conditions for exiting the loop will never become true is called an infinite loop. int a = 1; while (42) { a = a * 2; Here is another example of a while loop. It prints out all the powers of two less than 100. int a = 1; while (a < 100) { printf("a is %d \n", a); a = a * 2; The flow of all loops can also be controlled by break and continue statements. A break statement will immediately exit the enclosing loop. A continue statement will skip the remainder of the block and start at the controlling conditional statement again. For example: int a = 1; while (42) { // loops until the break statement in the loop is executed printf("a is %d ", a); a = a * 2; if (a > 100) { break; } else if (a == 64) { continue; // Immediately restarts at while, skips next step printf("a is not 64\n"); In this example, the computer prints the value of a as usual, and prints a notice that a is not 64 (unless it was skipped by the continue statement). Similar to If above, braces for the block of code associated with a While loop can be omitted if the code consists of only one statement, for example: int a = 1; while (a < 100) a = a * 2; This will merely increase a until a is not less than 100. When the computer reaches the end of the while loop, it always goes back to the while statement at the top of the loop, where it re-evaluates the controlling condition. If that condition is "true" at that instant -- even if it was temporarily 0 for a few statements inside the loop -- then the computer begins executing the statements inside the loop again; otherwise the computer exits the loop. The computer does not "continuously check" the controlling condition of a while loop during the execution of that loop. It only "peeks" at the controlling condition each time it reaches the codice_16 at the top of the loop. It is very important to note, once the controlling condition of a While loop becomes 0 (false), the loop will not terminate until the block of code is finished and it is time to reevaluate the conditional. If you need to terminate a While loop immediately upon reaching a certain condition, consider using break. A common idiom is to write: int i = 5; while (i--) { printf("java and c# can't do this\n"); This executes the code in the while loop 5 times, with i having values that range from 4 down to 0 (inside the loop). Conveniently, these are the values needed to access every item of an array containing 5 elements. For loops. For loops generally look something like this: for ("initialization"; "test"; "increment") { /* code */ The "initialization" statement is executed exactly once - before the first evaluation of the "test" condition. Typically, it is used to assign an initial value to some variable, although this is not strictly necessary. The "initialization" statement can also be used to declare and initialize variables used in the loop. The "test" expression is evaluated each time before the code in the "for" loop executes. If this expression evaluates as 0 (false) when it is checked (i.e. if the expression is not true), the loop is not (re)entered and execution continues normally at the code immediately following the FOR-loop. If the expression is non-zero (true), the code within the braces of the loop is executed. After each iteration of the loop, the "increment" statement is executed. This often is used to increment the loop index for the loop, the variable initialized in the initialization expression and tested in the test expression. Following this statement execution, control returns to the top of the loop, where the "test" action occurs. If a "continue" statement is executed within the "for" loop, the increment statement would be the next one executed. Each of these parts of the for statement is optional and may be omitted. Because of the free-form nature of the for statement, some fairly fancy things can be done with it. Often a for loop is used to loop through items in an array, processing each item at a time. int myArray[12]; int ix; for (ix = 0; ix < 12; ix++) { myArray[ix] = 5 * ix + 3; The above for loop initializes each of the 12 elements of myArray. The loop index can start from any value. In the following case it starts from 1. for (ix = 1; ix <= 10; ix++) { printf("%d ", ix); which will print 1 2 3 4 5 6 7 8 9 10 You will most often use loop indexes that start from 0, since arrays are indexed at zero, but you will sometimes use other values to initialize a loop index as well. The "increment" action can do other things, such as "decrement". So this kind of loop is common: for (i = 5; i > 0; i--) { printf("%d ", i); which yields 5 4 3 2 1 Here's an example where the test condition is simply a variable. If the variable has a value of 0 or NULL, the loop exits, otherwise the statements in the body of the loop are executed. for (t = list_head; t; t = NextItem(t)) { /* body of loop */ A WHILE loop can be used to do the same thing as a FOR loop, however a FOR loop is a more condensed way to perform a set number of repetitions since all of the necessary information is in a one line statement. A FOR loop can also be given no conditions, for example: for (;;) { /* block of statements */ This is called an infinite loop since it will loop forever unless there is a break statement within the statements of the for loop. The empty test condition effectively evaluates as true. It is also common to use the comma operator in for loops to execute multiple statements. int i, j, n = 10; for (i = 0, j = 0; i <= n; i++, j += 2) { printf("i = %d , j = %d \n", i, j); Special care should be taken when designing or refactoring the conditional part, especially whether using < or <= , whether start and stop should be corrected by 1, and in case of prefix- and postfix-notations. ( On a 100 yards promenade with a tree every 10 yards there are 11 trees. ) int i, n = 10; for (i = 0; i < n; i++) printf("%d ", i); // processed n times => 0 1 2 3 ... (n-1) printf("\n"); for (i = 0; i <= n; i++) printf("%d ", i); // processed (n+1) times => 0 1 2 3 ... n printf("\n"); for (i = n; i--;) printf("%d ", i); // processed n times => (n-1) ...3 2 1 0 printf("\n"); for (i = n; --i;) printf("%d ", i); // processed (n-1) times => (n-1) ...4 3 2 1 printf("\n"); Do-While loops. A DO-WHILE loop is a post-check while loop, which means that it checks the condition after each run. As a result, even if the condition is zero (false), it will run at least once. It follows the form of: do { /* do stuff */ } while (condition); Note the terminating semicolon. This is required for correct syntax. Since this is also a type of while loop, break and continue statements within the loop function accordingly. A continue statement causes a jump to the test of the condition and a "break" statement exits the loop. It is worth noting that Do-While and While are functionally almost identical, with one important difference: Do-While loops are always guaranteed to execute at least once, but While loops will not execute at all if their condition is 0 (false) on the first evaluation. One last thing: goto. goto is a very simple and traditional control mechanism. It is a statement used to immediately and unconditionally jump to another line of code. To use goto, you must place a label at a point in your program. A label consists of a name followed by a colon (:) on a line by itself. Then, you can type "goto "label";" at the desired point in your program. The code will then continue executing beginning with "label". This looks like: MyLabel: /* some code */ goto MyLabel; The ability to transfer the flow of control enabled by gotos is so powerful that, in addition to the simple if, all other control constructs can be written using gotos instead. Here, we can let "S" and "T" be any arbitrary statements: if ("cond") { S; } else { T; /* ... */ The same statement could be accomplished using two gotos and two labels: if ("cond") goto Label1; T; goto Label2; Label1: S; Label2: Here, the first goto is conditional on the value of "cond". The second goto is unconditional. We can perform the same translation on a loop: while ("cond1") { S; if ("cond2") break; T; /* ... */ Which can be written as: Start: if (!"cond1") goto End; S; if ("cond2") goto End; T; goto Start; End: As these cases demonstrate, often the structure of what your program is doing can usually be expressed without using gotos. Undisciplined use of gotos can create unreadable, unmaintainable code when more idiomatic alternatives (such as if-elses, or for loops) can better express your structure. Theoretically, the goto construct does not ever "have" to be used, but there are cases when it can increase readability, avoid code duplication, or make control variables unnecessary. You should consider first mastering the idiomatic solutions, and use goto only when necessary. Keep in mind that many, if not most, C style guidelines "strictly forbid" use of goto, with the only common exceptions being the following examples. One use of goto is to break out of a deeply nested loop. Since break will not work (it can only escape one loop), goto can be used to jump completely outside the loop. Breaking outside of deeply nested loops without the use of the goto is always possible, but often involves the creation and testing of extra variables that may make the resulting code far less readable than it would be with goto. The use of goto makes it easy to undo actions in an orderly fashion, typically to avoid failing to free memory that had been allocated. Another accepted use is the creation of a state machine. This is a fairly advanced topic though, and not commonly needed. Examples. int main(void) int years; printf("Enter your age in years : "); fflush(stdout); errno = 0; if (scanf("%d", &years) != 1 || errno) return EXIT_FAILURE; printf("Your age in days is %d\n", years * 365); return 0;

C Programming/Procedures and functions. In C programming, all executable code resides within a function. Note that other programming languages may distinguish between a "function", "subroutine", "subprogram", "procedure", or "method" -- in C, these are all functions. Functions are a fundamental feature of any high level programming language and make it possible to tackle large, complicated tasks by breaking tasks into smaller, more manageable pieces of code. At a lower level, a function is nothing more than a memory address where the instructions associated with a function reside in your computer's memory. In the source code, this memory address is usually given a descriptive name which programmers can use to call the function and execute the instructions that begin at the function's starting address. The instructions associated with a function are frequently referred to as a block of code. After the function's instructions finish executing, the function can return a value and code execution will resume with the instruction that immediately follows the initial call to the function. If this doesn't make immediate sense to you, don't worry. Understanding what is happening inside your computer at the lowest levels can be confusing at first, but will eventually become very intuitive as you develop your C programming skills. For now, it's enough to know that a function and its associated block of code is often executed (called) several times, from several different places, during a single execution of a program. As a basic example, suppose you are writing a program that calculates the distance of a given (x,y) point to the x-axis and to the y-axis. You will need to compute the absolute value of the whole numbers x and y. We could write it like this (assuming we don't have a predefined function for absolute value in any library): /*this function computes the absolute value of a whole number.*/ int abs(int x) if (x>=0) return x; else return -x; /*this program calls the abs() function defined above twice.*/ int main() int x, y; printf("Type the coordinates of a point in 2-plane, say P = (x,y). First x="); scanf("%d", &x); printf("Second y="); scanf("%d", &y); printf("The distance of the P point to the x-axis is %d. \n Its distance to the y-axis is %d. \n", abs(y), abs(x)); return 0; The next example illustrates the usage of a function as a procedure. It's a simplistic program that asks students for their grade for three different courses and tells them if they passed a course. Here, we created a function, called codice_1 that can be called as many times as we need to. The function saves us from having to write the same set of instructions for each class the student has taken. /*the 'check' function is defined here.*/ void check(int x) if (x<60) printf("Sorry! You will need to try this course again.\n"); else printf("Enjoy your vacation! You have passed.\n"); /*the program starts here at the main() function, which calls the check() function three times.*/ int main() int a, b, c; printf("Type your grade in Mathematics (whole number). \n"); scanf("%d", &a); check(a); printf("Type your grade in Science (whole number). \n"); scanf("%d", &b); check(b); printf("Type your grade in Programming (whole number). \n"); scanf("%d", &c); check(c); /* this program should be replaced by something more meaningful.*/ return 0; Notice that in the program above, there is no outcome value for the 'check' function. It only executes a procedure. This is precisely what functions are for. More on functions. It's useful to conceptualize a function like a machine in a factory. On the input side of the machine, you dump in the "raw materials," or the input data, that you want the machine to process. Then the machine goes to work and and spits out a finished product, the "return value," to the output side of the machine which you can collect and use for other purposes. In C, you must tell the machine exactly what raw materials it is expected to process and what kind of finished product you want the machine to return to you. If you supply the machine with different raw materials than it expects, or if you try to return a product that's different than what you told the machine to produce, the C compiler will throw an error. Note that a function isn't required to take any inputs. It doesn't have to return anything back to us, either. If we modify the example above to ask the user for their grade inside the codice_2 function, there would be no need to pass the grade value into the function. And notice that the codice_2 doesn't pass a value back. The function just prints out a message to the screen. You should be familiar with some basic terminology related to functions: Writing functions in C. It's always good to learn by example. Let's write a function that will return the square of a number. int square(int x) int square_of_x; square_of_x = x * x; return square_of_x; To understand how to write such a function like this, it may help to look at what this function does as a whole. It takes in an int, x, and squares it, storing it in the variable square_of_x. Now this value is returned. The first int at the beginning of the function declaration is the type of data that the function returns. In this case when we square an integer we get an integer, and we are returning this integer, and so we write int as the return type. Next is the name of the function. It is good practice to use meaningful and descriptive names for functions you may write. It may help to name the function after what it is written to do. In this case we name the function "square", because that's what it does - it squares a number. Next is the function's first and only argument, an int, which will be referred to in the function as x. This is the function's "input". In between the braces is the actual guts of the function. It declares an integer variable called square_of_x that will be used to hold the value of the square of x. Note that the variable square_of_x can only be used within this function, and not outside. We'll learn more about this sort of thing later, and we will see that this property is very useful. We then assign x multiplied by x, or x squared, to the variable square_of_x, which is what this function is all about. Following this is a return statement. We want to return the value of the square of x, so we must say that this function returns the contents of the variable square_of_x. Our brace to close, and we have finished the declaration. Written in a more concise manner, this code performs exactly the same function as the above: int square(int x) return x * x; Note this should look familiar - you have been writing functions already, in fact - main is a function that is always written. In general. In general, if we want to declare a function, we write "type" "name"("type1" "arg1", "type2" "arg2", ...) /* "code" */ We've previously said that a function can take no arguments, or can return nothing, or both. What do we write if we want the function to return nothing? We use C's void keyword. void basically means "nothing" - so if we want to write a function that returns nothing, for example, we write void sayhello(int number_of_times) int i; for(i=1; i <= number_of_times; i++) { printf("Hello!\n"); Notice that there is no return statement in the function above. Since there's none, we write void as the return type. (Actually, one can use the return keyword in a procedure to return to the caller before the end of the procedure, but one cannot return a value as if it were a function.) What about a function that takes no arguments? If we want to do this, we can write for example float calculate_number(void) float to_return=1; int i; for(i=0; i < 100; i++) { to_return += 1; to_return = 1/to_return; return to_return; Notice this function doesn't take any inputs, but merely returns a number calculated by this function. Naturally, you can combine both void return and void in arguments together to get a valid function, also. Recursion. Here's a simple function that does an infinite loop. It prints a line and calls itself, which again prints a line and calls itself again, and this continues until the stack overflows and the program crashes. A function calling itself is called recursion, and normally you will have a conditional that would stop the recursion after a small, finite number of steps. // don't run this! void infinite_recursion() printf("Infinite loop!\n"); infinite_recursion(); A simple check can be done like this. Note that ++depth is used so the increment will take place before the value is passed into the function. Alternatively you can increment on a separate line before the recursion call. If you say print_me(3,0); the function will print the line Recursion 3 times. void print_me(int j, int depth) if(depth < j) { printf("Recursion! depth = %d j = %d\n",depth,j); //j keeps its value print_me(j, ++depth); Recursion is most often used for jobs such as directory tree scans, seeking for the end of a linked list, parsing a tree structure in a database and factorising numbers (and finding primes) among other things. Static functions. If a function is to be called only from within the file in which it is declared, it is appropriate to declare it as a static function. When a function is declared static, the compiler will know to compile an object file in a way that prevents the function from being called from code in other files. Example: static int compare( int a, int b ) return (a+4 < b)? a : b; Using C functions. We can now "write" functions, but how do we use them? When we write main, we place the function outside the braces that encompass main. When we want to use that function, say, using our calculate_number function above, we can write something like float f; f = calculate_number(); If a function takes in arguments, we can write something like int square_of_10; square_of_10 = square(10); If a function doesn't return anything, we can just say say_hello(); since we don't need a variable to catch its return value. Functions from the C Standard Library. While the C language doesn't itself contain functions, it is usually linked with the C Standard Library. To use this library, you need to add an #include directive at the top of the C file, which may be one of the following from C89/C90: The functions available are: Variable-length argument lists. Functions with variable-length argument lists are functions that can take a varying number of arguments. An example in the C standard library is the printf function, which can take any number of arguments depending on how the programmer wants to use it. C programmers rarely find the need to write new functions with variable-length arguments. If they want to pass a bunch of things to a function, they typically define a structure to hold all those things -- perhaps a linked list, or an array -- and call that function with the data in the arguments. However, you may occasionally find the need to write a new function that supports a variable-length argument list. To create a function that can accept a variable-length argument list, you must first include the standard library header stdarg.h. Next, declare the function as you would normally. Next, add as the last argument an ellipsis ("..."). This indicates to the compiler that a variable list of arguments is to follow. For example, the following function declaration is for a function that returns the average of a list of numbers: float average (int n_args, ...); Note that because of the way variable-length arguments work, we must somehow, in the arguments, specify the number of elements in the variable-length part of the arguments. In the average function here, it's done through an argument called n_args. In the printf function, it's done with the format codes that you specify in that first string in the arguments you provide. Now that the function has been declared as using variable-length arguments, we must next write the code that does the actual work in the function. To access the numbers stored in the variable-length argument list for our average function, we must first declare a variable for the list itself: va_list myList; The va_list type is a type declared in the stdarg.h header that basically allows you to keep track of your list. To start actually using myList, however, we must first assign it a value. After all, simply declaring it by itself wouldn't do anything. To do this, we must call va_start, which is actually a macro defined in stdarg.h. In the arguments to va_start, you must provide the va_list variable you plan on using, as well as the name of the last variable appearing before the ellipsis in your function declaration: float average (int n_args, ...) va_list myList; va_start (myList, n_args); va_end (myList); Now that myList has been prepped for usage, we can finally start accessing the variables stored in it. To do so, use the va_arg macro, which pops off the next argument on the list. In the arguments to va_arg, provide the va_list variable you're using, as well as the primitive data type (e.g. int, char) that the variable you're accessing should be: float average (int n_args, ...) va_list myList; va_start (myList, n_args); int myNumber = va_arg (myList, int); va_end (myList); By popping n_args integers off of the variable-length argument list, we can manage to find the average of the numbers: float average (int n_args, ...) va_list myList; va_start (myList, n_args); int numbersAdded = 0; int sum = 0; while (numbersAdded < n_args) { int number = va_arg (myList, int); // Get next number from list sum += number; numbersAdded += 1; va_end (myList); float avg = (float)(sum) / (float)(numbersAdded); // Find the average return avg; By calling average (2, 10, 20), we get the average of 10 and 20, which is 15.

C Programming/Basics of compilation. Having covered the basic concepts of C programming, we can now briefly discuss the process of "compilation". Like any programming language, C by itself is completely incomprehensible to a microprocessor. Its purpose is to provide an intuitive way for humans to provide instructions that can be easily converted into machine code that "is" comprehensible to a microprocessor. The compiler is what translates our human-readable source code into machine code. To those new to programming, this seems fairly simple. A naive compiler might read in every source file, translate everything into machine code, and write out an executable. That could work, but has two serious problems. First, for a large project, the computer may not have enough memory to read all of the source code at once. Second, if you make a change to a single source file, you would have to recompile the "entire" application. To deal with these problems, compilers break the job into steps. For each source file (each codice_1 file), the compiler reads the file, reads the files it references via the codice_2 directive, and translates them to machine code. The result of this is an "object file" (codice_3). After all the object files are created, a "linker" program collects all of the object files and writes the actual executable program. That way, if you change one source file, only that file needs to be recompiled, after which, the application will need to be re-linked. Without going into details, it can be beneficial to have a superficial understanding of the compilation process. Preprocessor. The preprocessor provides the ability for the inclusion of so called header files, macro expansions, conditional compilation and line control. These features can be accessed by inserting the appropriate preprocessor directives into your code. Before compiling the source code, a special program, called the preprocessor, scans the source code for tokens, or special strings, and replaces them with other strings or code according to specific rules. The C preprocessor is not technically part of the C language and is instead a tool offered by your compiler's software. All preprocessor directives begin with the hash character (#). You can see one preprocessor directive in the Hello world program. Example: #include <stdio.h> This directive causes the stdio header to be included into your program. Other directives such as codice_4 control compiler settings and macros. The result of the preprocessing stage is a text string. You can think of the preprocessor as a non-interactive text editor that modifies your code to prepare it for compilation. The language of preprocessor directives is agnostic to the grammar of C, so the C preprocessor can also be used independently to process other kinds of text files. Syntax Checking. This step ensures that the code is valid and will sequence into an executable program. Under most compilers, you may get messages or warnings indicating potential issues with your program (such as a conditional statement always being true or false, etc.) When an error is detected in the program, the compiler will normally report the file name and line that is preventing compilation. Object Code. The compiler produces a machine code equivalent of the source code that can be linked into the final program. At this point the code itself can't be executed, as it requires linking to do so. It's important to note after discussing the basics that compilation is a "one way street". That is, compiling a C source file into machine code is easy, but "decompiling" (turning machine code into the C source that creates it) is not. Decompilers for C do exist, but the code they create is hard to understand and only useful for reverse engineering. Linking. Linking combines the separate object files into one complete program by integrating libraries and the code and producing either an or a . Linking is performed by a linker program, which is often part of a compiler suite. Common errors during this stage are either missing or duplicate functions. Automation. For large C projects, many programmers choose to automate compilation, both in order to reduce user interaction requirements and to speed up the process by recompiling only modified files. Most Integrated Development Environments (IDE's) have some kind of project management which makes such automation very easy. However, the project management files are often usable only by users of the same integrated development environment, so anyone desiring to modify the project would need to use the same IDE. On UNIX-like systems, make and Makefiles are often used to accomplish the same. Make is traditional and flexible and is available as one of the standard developer tools on most Unix and GNU distributions. Makefiles have been extended by the GNU Autotools, composed of Automake and Autoconf for making software compilable, testable, translatable and configurable on many types of machines. Automake and Autoconf are described in detail in their respective manuals. The Autotools are often perceived to be complicated and various simpler build systems have been developed. Many components of the GNOME project now use the declarative Meson build system which is less flexible, but instead focuses on providing the features most commonly needed from a build system in a simple way. Other popular build systems for programs written in the C language include CMake and Waf. Once GCC is installed, it can be called with a list of c source files that have been written but not yet compiled. e.g. if the file main.c includes functions described in myfun.h and implemented in myfun_a.c and myfun_b.c, then it is enough to write gcc main.c myfun_a.c myfun_b.c myfun.h is included in main.c, but if it is in a separate header file directory, then that directory can be listed after a "-I " switch. In larger programs, Makefiles and GNU make program can compile c files into intermediate files ending with suffix .o which can be linked by GCC. How to compile each object file is usually described in the Makefile with the object file as a label ending with a colon followed by two spaces (tabs often cause problems) followed by a list of other files that are dependencies, e.g. .c files and .o files compiled in another section, and on the next line, the invocation of GCC that is required. Typing codice_5 or codice_6 often gives the information needed to on how to use make, as well as GCC. Although GCC has a lot of option switches, one often used is -g to generate debugging information for gdb to allow gdb to show source code during a step-through of the machine code program. gdb has an 'h' command that shows what it can do, and is usually started with 'gdb a.out' if a.out is the anonymous executable machine code file that was compiled by GCC.

Discrete Mathematics/Finite fields. Introduction. Recall from the previous section that we considered the case where F["x"]/<m("x")> analogous to modular arithmetic but with polynomials, and that when we are looking at numbers modulo "n", we have a field iff Zn is a field if "n" is prime. Can we say something similar about F["x"]/<m("x")>? Indeed, if m("x") is irreducible then F["x"]/<m("x")> is a field. This section deals with these kinds of fields, known as a finite field. Definitions. We have the object F["x"]/<m("x")> where this is the set of polynomials in F["x"] are divided by the polynomial m("x"). Of the elements in F["x"]/<m("x")> we can easily define addition, subtraction, multiplication, division and so on normally but with a reduction modulo m("x") to get the desired remainder. We have that F["x"]/<m("x")> is a commutative ring with identity, and if m("x") is irreducible then F["x"]/<m("x")> is a field. If m("x") has degree "n", then If F is Zp (so "p" is prime) then formula_2 Properties. Now remember with complex numbers C, we have "invented" the symbol i to stand for the root of the solution "x"2+1=0. In fact, we have C=R["x"]/<"x"2+1>. When we have a "general" finite field, we can do this also. We write this often as F["x"]/<m("x")>=F(α) where α is "the root of" m("x") - we "define" α to be the root of m("x"). F(α) in fact is the smallest field which contains F and α. Finite field theorems. We have a number of theorems associated with finite fields. Some examples. Let's look at a few examples that go through these ideas. The complex numbers. Complex numbers, briefly, are numbers in the form where "i" is the solution to the equation "x"2+1=0 These numbers in fact form a field, however it is not a finite field. Take m("x")="x"2+1, with the field F being R. Then we can form the complex numbers as F/<m("x")>. Now F/<m("x")> = { "a"+"bx" | "a", "b" ∈ R} because the remainders must be of degree less than m("x") - which is 2. So then ("a"+"bx")("c"+"dx")="ac"+"bdx"2+("ad"+"bc")"x". But remember that we are working in F/<m("x")>. So "x"2 modulo "x"2+1, can be written as ("x"2+1)-1=-1, and substituting -1 above yields a rather familiar expression. If we let the symbol "i" to be the "root of "x"2+1", then "i"2+1=0 and "i"2=-1. The rest of the field axioms follow from here. We can then say the complex numbers C=R/<"x"2+1>=R("i"). The Zp case. We can still do this for some field in general. Let's take Z3 for example, and pick m("x")="x"2+"x"+2. m("x") is irreducible - m(0)=2, m(1)=4=1, m(2)=4+2+2=8=2. So Z3/<"x"2+"x"+2> is a finite field. Assume α is a root of m("x"). Then Z3(α) = { "a"+"b"α|"a", "b" ∈ Z3}. Since Z3/<"x"2+"x"+2> is finite, we can list out all its elements. We have the constant terms, then the α terms, then the α+constant terms, and so on. We have {0, 1, 2, α, α+1, α+2, 2α, 2α+1, 2α+2}. Now we have α2+α+2=0, then We can verify multiplication works mod m("x") - for example Reducing coefficients normally mod 3 we get Now using the formula above for α2 Verify for yourself that multiplication and other operations work too. Primitive elements. Recall from ../Modular arithmetic/ that the order of a number "a" modulo "n", in a field, is the least power such that "a""k"-1=1 in Zn, with "k" the size of this field. Since the order is defined over a field, this leads us to consider whether we have primitive elements in F["x"]/<m("x")> - which we do. If we have F(α), just like in Zn, α is primitive iff the order of α is "q"-1 where "q" is the number of elements in F["x"]/<m("x")>. Let's take Z2/<"x"2+"x"+1>. Is α (root of "x"2+"x"+1) primitive? First, if α is a root of "x"2+"x"+1, Now, let us calculate powers of α Recall that the size of this field is 4 (the "n" in Zn, in this case, 2, raised to the power of the degree of the polynomial, in this case 2). Now we have α3=α4-1=1, and α is primitive. We generally want to look at powers of α in F(α), to see whether they are primitive, since we already know about the orders of the constants in F(α) - which we've looked at in ../Modular arithmetic/.

General Biology/Getting Started/Introduction. The word biology means, "the science of life", from the Greek bios, "life", and logos, "word" or "knowledge." Therefore, Biology is the science of Living Things. That is why Biology is sometimes known as Life Science. The science has been divided into many subdisciplines, such as botany, bacteriology, anatomy, zoology, histology, mycology, embryology, parasitology, genetics, molecular biology, systematics, immunology, microbiology, physiology, cell biology, cytology, ecology, and virology. Other branches of science include or are comprised in part of biology studies, including paleontology, taxonomy, evolution, phycology, helimentology, protozoology, entomology, biochemistry, biophysics, biomathematics, bio engineering, bio climatology and anthropology. Characteristics of life. Not all scientists agree on the definition of just what makes up life. Various characteristics describe most living things. However, with most of the characteristics listed below we can think of one or more examples that would seem to break the rule, with something nonliving being classified as living or something living classified as nonliving. Therefore we are careful not to be too dogmatic in our attempt to explain which things are living or nonliving. An easy way to remember this is GRIMNERD C All organisms; - Grow, Respire, Interact, Move, Need Nutrients, Excrete (Waste), Reproduce,Death, Cells (Made of) Living things are organized in the microscopic level from atoms up to cells. Atoms are arranged into molecules, then into macromolecules, which make up organelles, which work together to form cells. Beyond this, cells are organized in higher levels to form entire multicellular organisms. Cells together form tissues, which make up organs, which are part of organ systems, which work together to form an entire organism. Of course, beyond this, organisms form populations which make up parts of an ecosystem. All of the Earth's ecosystems together form the diverse environment that is the earth. Example:- sub atoms, atoms, molecules, cells, tissues, organs, organ systems, organisms, population, community, eco systems, biosphere Emergent property is viewed in the biological organization of life, ranging from the subatomic level to the entire biosphere. Emergent properties are not unique to life, but biological systems are far more complex, making the emergent properties of life difficult to study. Systems biology is a biology-based inter-disciplinary field of study that focuses on complex interactions within biological systems, using a holistic approach. Biologists study properties of life, with reductionist approach and holistic approach. Nature of science. Science is a methodology for learning about the world. It involves the application of knowledge. The scientific method deals with systematic investigation, reproducible results, the formation and testing of hypotheses, and reasoning. Reasoning can be broken down into two categories, induction (specific data is used to develop a generalized observation or conclusion) and deduction (general information leads to specific conclusion). Most reasoning in science is done through induction. Science as we now know it arose as a discipline in the 17th century. Scientific method. The scientific method is not a step by step, linear process. It is an intuitive process, a methodology for learning about the world through the application of knowledge. Scientists must be able to have an "imaginative preconception" of what the truth is. Scientists will often observe and then hypothesize the reason why a phenomenon occurred. They use all of their knowledge and a bit of imagination, all in an attempt to uncover something that might be true. A typical scientific investigation might go like so: Scientists first make observations that raise a particular question. In order to explain the observed phenomenon, they develop a number of possible explanations, or hypotheses. This is the inductive part of science, observing and constructing plausible arguments for why an event occurred. Experiments are then used to eliminate one or more of the possible hypotheses until one hypothesis remains. Using deduction, scientists use the principles of their hypothesis to make predictions, and then test to make sure that their predictions are confirmed. After many trials (repeatability) and all predictions have been confirmed, the hypothesis then may become a theory. Quick Definitions The scientific method is based primarily on the testing of hypotheses by experimentation. This involves a control, or subject that does not undergo the process in question. A scientist will also seek to limit variables to one or another very small number, single or minimum number of variables. The procedure is to form a hypothesis or prediction about what you believe or expect to see and then do everything you can to violate that, or falsify the hypotheses. Although this may seem unintuitive, the process serves to establish more firmly what is and what is not true. A founding principle in science is a lack of absolute truth: the accepted explanation is the most likely and is the basis for further hypotheses as well as for falsification. All knowledge has its relative uncertainty. Theories are hypotheses which have withstood repeated attempts at falsification. Common theories include evolution by natural selection and the idea that all organisms consist of cells. The scientific community asserts that much more evidence supports these two ideas than contradicts them. Charles Darwin. Charles Darwin is most remembered today for his contribution of the theory of evolution through natural selection. The seeds of this theory were planted in Darwin's mind through observations made on a five-year voyage through the New World on a ship called the Beagle. There, he studied fossils and the geological record, geographic distribution of organisms, the uniqueness and relatedness of island life forms, and the affinity of island forms to mainland forms. Upon his return to England, Darwin pondered over his observations and concluded that evolution must occur through natural selection. He declined, however, to publish his work because of its controversial nature. However, when another scientist, Wallace, reached similar conclusions, Darwin was convinced to publish his observations in 1859. His hypothesis revolutionized biology and has yet to be falsified by empirical data collected by mainstream scientists. After Darwin. Since Darwin's day, scientists have amassed a more complete fossil record, including microorganisms and chemical fossils. These fossils have supported and added subtleties to Darwin's theories. However, the age of the Earth is now held to be much older than Darwin thought. Researchers have also uncovered some of the preliminary mysteries of the mechanism of heredity as carried out through genetics and DNA, areas unknown to Darwin. Another growing area is comparative anatomy including homology and analogy. Today we can see a bit of evolutionary history in the development of embryos, as certain (although not all) aspects of development recapitulate evolutionary history. The molecular biology study of slowly mutating genes reveal considerable evolutionary history consistent with fossil and anatomical record. Challenges to Darwin. Darwin and his theories have been challenged many times in the last 150 years. The challenges have been primarily religious based on a perceived conflict with the preconceived notion of creationism. Many of those who challenge Darwin have been adherents to the young earth hypothesis that says that the Earth is only some 6000 years old and that all species were individually created by a god. Some of the proponents of these theories have suggested that chemical and physical laws that exist today were different or nonexistent in earlier ages. However, for the most part, these theories are either not scientifically testable and fall outside the area of attention of the field of biology, or have been disproved by one or more fields of science. References. "This text is based on notes very generously donated by Dr. Paul Doerder, Ph.D., of Cleveland State University."

Puzzles/How do you ... ?/Ten Apples and a Basket. Puzzles | How do you... ? | Ten Apples and A Basket Ten Apples and A Basket puzzle You have a basket containing ten apples. You have ten friends, who each desire an apple. You give each of your friends one apple. After ten minutes, each of your friends has one apple each. Yet there is one remaining apple in the basket. How is this possible? Solution

Puzzles/How do you ... ?/Ten Apples and a Basket/Solution. < Back to Problem Solutions: //Solutions below are only humorous and not Logical //

General Biology/Getting Started/Matter. Matter. Matter is defined as anything that has mass (an amount of matter in an object) and occupies space (which is measured as volume). Water. Hydrogen bonding. Water organizes nonpolar molecules Ionization of water: H2O -> H+ + OH- pH Buffer References. "This text is based on notes very generously donated by Dr. Paul Doerder, Ph.D., of the Cleveland State University."