text:
Fermat's Last Theorem/Appendix

This appendix collects some proofs and studies in depth some mathematical concepts that can be interesting in order to examine in depth some aspects of the book. It seeks to maintain a simple approach but the proofs being correct, in some cases however it was necessary to make recourse to some non immediate concepts and passages that have been specified and clarified where possible.

Pythagoras’ theorem
Being one of the most noted theorems in the history of mathematics, many proofs exist, the work of astronomers, stockbrokers, and even one by Leonardo da Vinci. Probably, together with quadratic reciprocity, it contends for the prize for the theorem with the most absolute proofs. It will be proved in a graphical manner utilising only the concepts of elementary geometry. Pythagoras’ proof will not be quoted being very complex and not immediate.

The proof is very simple, as one sees from the graphic one constructs first a square formed by four triangles and by two squares, one of side a and the second of side b. The area of a square is calculated multiplying the side by itself or in modern notation the area is the side raised to the power two. The area of the large square is therefore the sum of the areas of the squares values a2 and b2 plus the sum of the four triangles. In the second square we have again four triangles and a square of area c2. The four triangles being present both to the left of the equality and to the right can be eliminated. Therefore remaining in the equation:

a2 + b2 = c2

As one wished to prove. It is to be noted that the proof is generic and effectively covers every possible right angled triangle given that numbers are not utilised in the proof but only generic segments length a, b and c. The proof depends solely on the fact that the triangles are right angled and on the fact that one is utilising Euclidean geometry. This is a small gallery of some geometrical proofs of the theorem even if as was said above there are very many proofs and in fact there are also purely algebraic proofs, proofs that utilise complex numbers and even proofs written in the form of sonnets.

Fundamental theory of arithmetic
The fundamental theory of arithmetic states that every natural number that is not 1 admits one and only one factorisation in prime numbers not taking account of the order of the factors. (The exclusion of 1 is due to the fact that it does not have prime factors.) This theorem was the basis of the proofs of Gabriel Lamé and Augustin Luis Cauchy and as was said in general is not valid for complex numbers therefore it cannot be utilised for Fermat’s theorem but given its importance it was decided however to include the proof in the appendix. The statement is easily verifiable for “small” natural numbers: it is easy to discover that 70 is equal to 2 × 5 × 7 while 100 equates to 2 × 2 × 5 × 5 or 22 × 52, and furthermore it is easy to verify that for these numbers other decompositions into prime factors cannot exist. Conversely the general proof is rather longer: Here is an extract of it. It deals with a proof for absurd: that is it starts from the hypothesis contrary to that of the statement in order to be able to prove it unfounded.

One supposes that there exist some number reducible into prime factors in more than one way, and one calls the smallest m. Firstly one proves that, given two factorisations of m, the prime numbers that present themselves in the first factorisation are all distinct from those in the second factorisation. They are in fact two different factorisations:

 * $$m = p_1 p_2 p_3 \dots p_s$$

 * $$m = q_1 q_2 q_3 \dots q_t$$

where pi and qj are prime. (Note: within a single factorisation there can be repeated factors, naturally: for example, 100 = 2 × 2 × 5 × 5). Were there to be an identical factor ph = qk, we could divide m by such a factor and obtain a number m' , less than m, that would also itself have two distinct factorisations. At this point we know that p1 is different from q1; without loss of generality we can suppose that p1 < q1. We put then

 * $$ n = (q_1-p_1)q_2 q_3\dots q_t $$

Evidently, n < m, given that [3] can be written as:

 * $$n = q_1 q_2 q_3 \dots q_t - p_1 q_2 q_3 \dots q_t = m - p_1 q_2 q_3 \dots q_t\;\!$$.

We now demonstrate that n admits at least two distinct factorisations. We begin by considering if the first factor of n, q1 - p1, can or cannot be prime; in the case that it was not, we suppose factorising it. The factorisation of n thus obtained does not admit p1 among its factors. In fact, from the first part of the proof, we know that p1 is different from q2, q3, ..., qt; but it cannot none the less appear in the eventual factorisation of q1  - p1. If in fact it happened that would mean that

 * $$q_1-p_1= p1\cdot b \Rightarrow q_1 = p_1(1+b) $$

and therefore q1 would be divisible by p1, which is not possible in as much as q1 is a prime number. Taking now the final equality [4] and substituting for m the value from [1], we obtain:

 * $$n= p_1p_2p_3\dots p_s-p_1q_2q_3\dots q_t \rightarrow n = p_1(p_2p_3\dots p_s- q_2q_3\dots q_t)$$

In whatever way the second factor in [5], may be factorised, we will have obtained a factorisation of n that contains p1, and that therefore is different from that in [3], contrary to the hypothesis that m was the smallest number that admitted more than one factorisation. The theorem is therefore proved.

Principle of Induction
The Principle of induction states that  If $$U$$ is a subset of the set $$\mathbb N$$ of natural numbers that satisfy the following two properties: then $$U$$ coincides with all of the set of natural numbers $$\mathbb N$$
 * $$U$$ contains $$0$$,
 * every time that $$U$$ contains a number $$n$$ $$U$$ contains also the successive number $$n+1$$,

This is found in general within the axioms of Peano and furnishes a potent instrument for proofs in all sectors of mathematics. In the book it is recalled at times given that many mathematicians have sought to prove a base case of Fermat's theorem and then of generalising the solution in order to be able include therein the successive cases by means of this principle.

Proof by induction
In order to prove that a certain assertion $$P(n)$$ in which appears a natural number $$n$$ valid for whatever $$n \in \mathbb N$$ one must apply the principle of induction in the following way:

One puts $$U=\{n\in \mathbb N: \mbox{vale } P(n)\}$$, and therefore one concludes that the set $$U$$ of numbers for which $$P(n)$$ is valid is valid coincides with all the set of natural numbers. Point 1 is generally called base of the induction, point 2 the inductive step.
 * 1) one proves $$P(0)$$ as valid, that is that $$0$$ is in the set of natural numbers $$U$$ for which $$P(n)$$ is valid;
 * 2) one assumes as a hypothesis that the assertion $$P(n)$$ may be valid for a generic  $$n$$ and from such an assumption one also proves that $$P(n+1)$$ (that is that $$n\in U \Rightarrow n+1\in U$$)

The following is an intuitive mode in which one can look at this type of proof: if we have available a proof of the base $$P(0)$$ of the inductive step $$P(n) \Rightarrow P(n+1)$$ then clearly we can make use of these proofs in order to prove $$P(1)$$ using the logical rule modus ponens on $$P(0)$$ (the base) and $$P(0) \Rightarrow P(1)$$ (which is a particular case of the inductive step for $$n=0$$), then we can prove $$P(2)$$ since now we are using the modus ponens on $$P(1)$$ and $$P(1) \Rightarrow P(2)$$, thus for $$P(3)$$, $$P(4)$$, etcetera... it is clear at this point that we can produce a proof in a finite number of steps (eventually very lengthy) of $$P(n)$$ for whatever natural number $$n$$, from which we deduce that $$P(n)$$ is true for every  $$n \in \N$$.

An example
We will prove that the following formula is valid:
 * For every $$n \in \mathbb N$$: $$0+1+2+3+4+...+n=\frac{n(n+1)}{2}$$

In this case we have $$P(n) \quad \equiv \quad 0+1+2+3+4+...+n=\frac{n(n+1)}{2}$$.
 * Base base of the induction: we have to prove the assertion $$P(n)$$ is true for $$n=0$$, and so, substituting, that $$0=\frac{0\cdot 1}2$$, and in effect there is very little work, one is talking of an elementary calculation;
 * Inductive step: we must show that for every n the implication $$P(n)\Rightarrow P(n+1)$$ is valid, that is, substituting:
 * $$0+1+2+3+4+...+n=\frac{n(n+1)}{2} \quad \Rightarrow \quad 0+1+2+3+4+...+n+(n+1)=\frac{(n+1)((n+1)+1)}{2}$$

Therefore we must assume as true
 * $$P(n) \quad \equiv \quad 0+1+2+3+4+...+n=\frac{n(n+1)}{2}$$,

working on this equality and concluding with the analogous equality for $$n+1$$: We could for example add $$n+1$$ to both sides of the equality P(n):
 * $$0+1+2+3+4+...+n+(n+1)=\frac{n(n+1)}{2}+(n+1)$$,

then we make some simple algebraic steps:
 * $$0+1+2+3+4+...+n+(n+1)=\frac{n(n+1)}{2}+\frac{2(n+1)}2$$,
 * $$0+1+2+3+4+...+n+(n+1)=\frac{(n+1)(n+2)}{2}$$,
 * $$0+1+2+3+4+...+n+(n+1)=\frac{(n+1)((n+1)+1)}{2}$$

and this final equality is exactly $$P(n+1)$$. This concludes the proof of the inductive step.

Having therefore proved the base of the induction and the inductive step we can conclude (from the principle of induction) that $$P(n)$$ must be true for every $$n\in \mathbb N$$.$$\square$$

Modular Arithmetic
Modular arithmetic (sometimes called clock arithmetic since the calculation of the hours in cycles of 12 or 24 is based on such principle) represents an important branch of mathematics. It finds applications in cryptography, in the theory of numbers (in particular in the research of prime numbers), and it is the basis of many of the most common arithmetical and algebraic operations. It deals with a system of integer arithmetic, in which the numbers "wrap round on themselves " every time that they reach multiples of a specific number n, called the modulo. Modular arithmetic was formally introduced by Carl Friedrich Gauss in his treatise Disquisitiones Arithmeticae, published in 1801. Modular arithmetic is based on the concept of congruence modulo n . Given three whole numbers a, b, n, with n≠0, we say that a and b are congruent modulo n if their difference (a−b) is a multiple of n. In this case we write

 * $$ a \equiv b \pmod{n} $$

and we say that a is congruent to b modulo n. For example, we can write

 * $$ 38 \equiv 14 \pmod{12} $$

since 38 − 14 = 24, which is a multiple of 12. In the case that both numbers are positive, one can also say that a and b are congruent modulo n if they have the same remainder from division by n. Therefore we can also say that 38 is congruent 14 modulo 12 since both 38 and 14 have remainder 2 after division by 12.

Properties of congruence
Congruence is a relationship of equivalence between integer numbers as one sees from the following properties:
 * Reflexive property: every number is congruent to itself modulo n, for every n different from fixed 0.

 * $$ a \equiv a \pmod{n} \qquad \forall a \in \mathbb{N},\forall n \in \mathbb{N}_0 $$

 * Proof: one has a - a = 0. But as is noted, every non-zero integer is a divisor of 0. Therefore n divides (a - a)

 * Symmetrical property: if a is congruent to b modulo n then b is congruent to a modulo n

 * $$ a \equiv b \pmod{n} \Rightarrow b \equiv a \pmod{n} \qquad \forall a,b \in \mathbb{N},\forall n \in \mathbb{N}_0 $$

 * Proof: if n divides (a - b), then n also divides the opposite (b - a) = - (a - b

 * Transitive property: if a is congruent to b modulo n and b is congruent to c modulo n then also a is congruent to c modulo n.

 * $$ a \equiv b \pmod{n} \quad\land\quad b \equiv c \pmod{n} \Rightarrow a \equiv c \pmod{n} \qquad \forall a,b,c \in \mathbb{N},\forall n \in \mathbb{N}_0 $$

 * Proof: if n divides (a - b) and n divides (a - c) then, because of the distributive property of the division with respect to the subtraction, n also divides [(a - c) - (a - b)]=[a - c - a + b] = (b - c).

Invariance with respect to arithmetical operations
Another important characteristic of the relationship of congruence is the fact of being preserved by the usual arithmetical operations between integers:

 * Invariance by addition: increasing or reducing two numbers congruent modulo n by the same quantity, the new numbers obtained are still congruent between themselves modulo n. More synthetically

 * $$ a \equiv b \pmod{n} \Leftrightarrow (a + c ) \equiv (b + c) \pmod{n} \qquad \forall a,b,c \in \mathbb{N},\forall n \in \mathbb{N}_0 $$

 * Proof: we write (a - b) = (a - b + c - c) = (a + c) - (b + c)

 * Invariance by multiplication: multiplying two numbers congruent modulo n by the same quantity, the new numbers obtained are still congruent between themselves modulo n.

 * $$ a \equiv b \pmod{n} \Rightarrow a\cdot c \equiv b \cdot c \pmod{n} \qquad \forall a,b,c \in \mathbb{N},\forall n \in \mathbb{N}_0 $$

 * Proof: if n divides (a - b) then n divides (a - b)×c
 * Note: One can only invert this property if n does not divide c, that is if c is not congruent to 0 (modulo n).

 * Invariance with respect to raising to a power: raising two numbers congruent modulo n to the same power k, the numbers obtained are still congruent between themselves modulo n.

 * $$ a \equiv b \pmod{n} \Rightarrow a^{k} \equiv b^{k} \pmod{n} \qquad \forall a,b,c \in \mathbb{N},\forall k \in \mathbb{N},\forall n \in \mathbb{N}_0 $$

 * Proof: if a ≡ b ≡ 0 (mod n) the proposition is banal. If a ≡ b (mod n) is non null, we suppose to know that $$a^{k-1}\equiv b^{k-1} \pmod{n}$$. Multiplying both the terms by a thanks to invariance by multiplication, we will have $$a^{k}\equiv b^{k-1}\cdot a \pmod{n}$$. We start now from the congruence a ≡ b (mod n) and we multiply both the members by $$ b^{k-1} \pmod{n}$$, thanks always to invariance by multiplication. We obtain:$$a\cdot b^{k-1}\equiv b^{k} \pmod{n}$$. Comparing the two expressions, and utilising the symmetrical and transitive properties, one deduces that $$a^{k}\equiv b^{k} \pmod{n}$$. Since the proposition is true for k = 1 and the fact that it may be true for k-1 implies that it is true for k, by the principle of induction the proposition is true for every k.

 * Note: This property can be inverted only if k is not 0.

title: Fermat's Last Theorem/Appendix


text:
User:Tannersf/A House

Formed Dublin, Ireland, 1985; disbanded 1997.

=History= The core of A House was the trio of Dave Couse, who wrote all the lyrics and sometimes played acoustic guitar, Fergal Bunbury (lead guitar) and Martin Healy (bass). Three other members – Dave Dawson (drums), David Morrissey (keyboards) and Susan Kavanagh (backing vocals) – recorded and toured with the band but were less involved in the group’s writing and development.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User:Tannersf/A House


text:
SwisTrack/Components/CalibrationLinear

Description
Calibration of the camera system with a second order linear system. The non-linear transformation from image pixels to world coordinates is approximated by a second-order, non-symmetric polynomial of the form

$$x = a_{11}u+a_{12}v+a_{13}+a_{14}u^2+a_{15}v^2+a_{16}uv$$

$$y = a_{21}u+a_{22}v+a_{23}+a_{24}u^2+a_{25}v^2+a_{26}uv$$

with u, v the image pixels, and x, y the coordinates in world space (meters). The twelve parameters of this-very simple model-are estimated in a least-square fashion from a sufficiently large number of coordinate pairs. Thus, the software has to be provided with a number of image points which positions in the real world are known -- for instance by using a pattern of known dimensions. Hereby, increasing the number of pairs used in the estimation process over the minimum of six moderates the effect of noisy measurements during calibration.

Also, one observes that the precision of the approximation and hence the precision of the prediction is higher in the neighborhood of the training points. By that, we are able to bias the region within the camera frame where we want to minimize the prediction area.

Input
Particles.

Output
Particles.

Calib. Points
Path the XML file containing the calibration points. The file must have the following format:

 0.3      0.9       9.8       10.3       34.1       7.9       44.3       25.9

More points can be added like the two in this example. A minimum of 6 non-collinear points is needed to compute the calibration.

title: SwisTrack/Components/CalibrationLinear


text:
Fermat's Last Theorem/Paul Wolfskehl

Paul Wolfskehl
The works of Kummer on the factorisation of complex numbers threw a general mistrust on the possibility of finding a proof of Fermat’s theorem in a reasonable time. The researches also halted because of the birth of new branches of mathematics that drew the studious away from the theory of numbers. Wolfskehl was a German industrialist from Darmstadt who came from a very rich family dedicated to patronage of the arts. Paul had studied at mathematical university and, although he had greater success in business than in mathematics, his contribution was decisive in reawakening interest in the theorem. Wolfskehl at that period was in love with a woman who refused his every attention. Driven by despondency Wolfskehl had decided to commit suicide at the stroke of midnight, but being a meticulous and precise person he had planned everything and had provided an adequate arrangement of his affairs and a salutation of his closest friends by means of letters. Wolfskehl had finished the preparations before midnight and in order to pass the time began to thumb through some texts on mathematics. In particular thumbing through the work of Kummer he noted an unproved assumption. If that assumption revealed itself in reality false perhaps it would have reopened the possibility of proving Fermat’s theorem with the method of Lamé or of Cauchy. Wolfskehl worked all night and finally succeeded in proving that the assumption was true and therefore the proof was correct. This was bad news for the mathematician but Wolfskehl was so happy to have been able to correct the great Kummer that he regained faith in himself. He abandoned the proposal of suicide and instead wrote a second will according to which he would have left a good part of his patrimony to whoever was able to prove Fermat’s theorem. The will became operative in 1908 and the Royal Society of Science of Göttingen became the organisation proposed for the verification of proofs that aspired to the prize. The prize was announced by all the European mathematical publications and thousands of aspiring mathematicians choked the university of Göttingen with presumed proofs of Fermat’s theorem. Unfortunately the prize did not attract many serious mathematicians, given that these were well aware of the extreme difficulty of the problem and therefore it did not produce a real turn-about in the field of mathematics, but it had the merit of rendering the problem of Fermat’s last theorem famous to the public at large.

title: Fermat's Last Theorem/Paul Wolfskehl


text:
Fermat's Last Theorem/Gabriel Lamé and Augustin Louis Cauchy

Gabriel Lamé and Augustin Louis Cauchy
Sophie Germain’s results appeared to many to be the turning point, and that the definitive solution of the enigma was close. The French Academy of Science offered a series of prizes to whoever succeeded in proving Fermat’s last theorem. In that epoch the offer of prizes for the solution of mathematical enigmas was a common practice followed by many academies, given that one was thus able to direct the research of many scientists into specific areas of knowledge. These prizes were used whether for research into the solutions of practical problems or for the solution of theoretical problems such as Fermat’s theorem. The mathematicians Gabriel Lamé and Augustin Luis Cauchy announced being on the point of proving the theorem utilising similar techniques. These mathematicians set the Parisian salons on fire with statements and extracts of their respective proofs but without ever publishing the complete proofs. This situation dragged on for the whole of the month of April 1847 until the mathematician Joseph Liouville read to the academy of science a letter from the mathematician Ernst Eduard Kummer. Kummer analysing the few pieces of evidence on the proofs of Cauchy and Lamé had become aware that the proofs followed the same reasoning and that they contained a logical error that rendered them fallacious. Kummer had become aware that the two mathematicians had based their proof on a property known as unique factorisation. This stated in substance that every integer number could be broken down into a single series of prime numbers. Known since the times of Euclid (fourth century B.C.) it was used in very many proofs and is so important that the theorem that enunciated it is called the fundamental theorem of arithmetic. The problem was that the proof of Cauchy and Lamé utilised complex numbers and, in the field of complex numbers, this property is not necessarily true. The lack of unique factorisation could have been worked round with some techniques but however there remained some recalcitrant numbers. These numbers could in theory have been faced singly, but being infinite that would not have resolved the problem. Lamé became aware of the impossibility of finding a general solution, while Cauchy held his implementation not so dependent on factorisation and worked for several weeks on the subject before giving up. Finally, in 1856, seeing that no correct solution had been presented to the academy, it decided to withdraw the prize. It still in fact lacked 138 years to the final solution.


text:
Logic for Computer Scientists/Predicate Logic/Semantics

Definition 4 (Semantics of predicate logic - Interpretation)
An interpretation is a pair $$\mathcal{I} = (U_\mathcal{I}, A_\mathcal{I})$$, where
 * $$U_\mathcal{I}$$ is an arbitrary nonempty set, called domain, or universe.
 * $$A_\mathcal{I}$$ is a mapping which associates to
 * a $$k$$-ary predicate symbol, a $$k$$-ary predicate over $$U_\mathcal{I}$$,
 * a $$k$$-ary function symbol, a $$k$$-ary function over $$U_\mathcal{I}$$, and
 * a variable an element from the domain.

Let $$F$$ be a formula and $$\mathcal{I} = (U_\mathcal{I}, A_\mathcal{I})$$ be an interpretation. We call $$\mathcal{I}$$ an interpretation for $$F$$, if $$\mathcal{A}_\mathcal{I}$$ is defined for every predicate and function symbol, and for every variable, that occurs free in $$F$$.

Example: Let $$F= \forall x p(x,f(x)) \land q(g(a,z))$$ and assume the varieties of the symbols as written down. In the following we give two interpretations for $$F$$: For a given interpretation $$\mathcal{I}= (U,A)$$ we write in the following $$p^\mathcal{I}$$ instead of $$A(p)$$; the same abbreviation will be used for the assignments for function symbols and variables.
 * $$\mathcal{I}_1 = (N_0,A_1)$$, such that
 * $$A_1(p) = \{ (m,n) \mid m,n \in N_0 \text{ and } m < n\}$$
 * $$A_1(q) = \{ n \in N_0 \mid n \text{ is prime} \}$$
 * $$A_1(f)(n) = n+1 \; \forall n \in N_0$$
 * $$A_1(g)(m,n) = m+n \; \forall n,m \in N_0$$
 * $$A_1(a) = 2$$
 * $$A_1(z) = 3$$
 * Under this interpretation the formula $$F$$ can be read as " Every natural number is smaller than its successor and the sum of $$2$$ and $$3$$ is a prime number."
 * $$\mathcal{I}_2 = (U_2,A_2)$$, such that
 * $$U_2= \{a, f(a), g(a,a), f(g(a,a)), g(f(a),f(a)), \cdots \}$$
 * $$A_2(f)(t) = f(t)$$ for $$t \in U_2$$
 * $$A_2(g)(t_1,t_2) = g(t_1,t_2)$$, if $$t_1,t_2 \in U_2$$
 * $$A_2(a) = a$$
 * $$A_2(z)= f(f(a))$$
 * $$A_2(p)=\{p(a,a), p(f(a),f(a)),p(f(f(a)),f(f(a)))\}$$
 * $$A_2(q)=\{g(t_1,t_2) \mid t_1,t_2 \in U_2\}$$

Definition 5 (Semantics of predicate logic - Evaluation of Formulae)
Let $$F$$ be a formula and $$\mathcal{I}$$ an interpretation for $$F$$. For terms $$t$$ which can be composed with symbols from $$F$$ the value $$\mathcal{I}(t)$$ is given by The value $$\mathcal{I}(F)$$ of a formula $$F$$ is given by \begin{cases} \;\;\,true & \text{ if } (\mathcal{I}(t_1), \cdots, \mathcal{I}(t_k))\in p^\mathcal{I} \\ \;\;\,false & \; otherwise \end{cases}$$
 * $$\mathcal{I}(x)= x^\mathcal{I}$$
 * $$\mathcal{I}(f(t_1, \cdots, t_k)) = f^\mathcal{I}(\mathcal{I}(t_1), \cdots , \mathcal{I}(t_k))$$, if $$t_1, \cdots, t_k$$ are terms and $$f$$ a $$k$$-ary function symbol. (This    holds for the case $$k=0$$ as well.)
 * $$ \mathcal{I}(p(t_1, \cdots, t_k)) =

\begin{cases} \;\;\,true & \text { if } \mathcal{I}(F) = true { and } \mathcal{I}(G) = true \\ \;\;\,false& otherwise \end{cases} $$ \begin{cases} \;\;\,true & \text { if } \mathcal{I}(F) = true { or } \mathcal{I}(G) = true \\ \;\;\, false& otherwise \end{cases} $$
 * $$ \mathcal{I}(F\land G)) =
 * $$ \mathcal{I}((F\lor G)) =

\;\;\,true & \text { if } \mathcal{I}(F) = false \\ \;\;\, false& otherwise \end{cases} $$ \;\;\,true & \text{ if for every } d\in U\; : \; \mathcal{I}_{[x/d]}(G) = true \\ \;\;\, false& otherwise \end{cases} $$ \;\;\,true & \text{ if there is a }    d\in U\; : \; \mathcal{I}_{[x/d]}(G) = true \\ \;\;\, false& otherwise \end{cases} $$
 * $$ \mathcal{I}(\lnot F) = \begin{cases}
 * $$\mathcal{I}(\forall G) = \begin{cases}
 * $$\mathcal{I}(\exists G) = \begin{cases}

where, $$ f_{[x/d]}(y) = \begin{cases} \;\;\, f(y)& \text{ if }  x \neq y \\ \;\;\, d  &  otherwise \end{cases} $$

The notions of satisfiable, valid, and $$\models $$ are defined according to the propositional case (Semantic (Propositional logic)).

Note that, predicate calculus is an extension of propositional calculus: Assume only $$0$$-ary predicate symbols and a formula which contains no variable, i.e. there can be no terms and no quantifier in a well-formed formula.

On the other hand, predicate calculus can be extended: If one allows for quantifications over predicate and function symbols, we arrive at a second order predicate calculus. E.g. $$ \forall p \exists f \; p(f(x))$$ Another example for a second order formula of is the induction principle from Induction.

Problem 1 (Predicate)
The interpretation $$\mathcal{I} = \text{ is given } (U_\mathcal{I}, A_\mathcal{I}) $$ as follows: $$ U_\mathcal{I} =  \N $$ $$ p^\mathcal{I} = { (m,n) \mid m < n } $$ $$ f^\mathcal{I}(m,n) =  m+n $$ $$ x^\mathcal{I} = 5 ;  y^\mathcal{I} = 7 $$ Determine the value of following terms and formulae:
 * 1) $$\mathcal{I}(f(f(x,x),y))$$
 * 2) $$\mathcal{I}(\forall x \forall y (p(x,y) \lor p(y,x))$$
 * 3) $$\mathcal{I}(p(x,x) \to p(y,x))$$
 * 4) $$\mathcal{I}(\exists x p(y,x))$$

$$\Box$$

Problem 2 (Predicate)
The interpretation $$\mathcal{I} = \text{ is given } (U_\mathcal{I},A_\mathcal{I})$$ as follows: $$ U_\mathcal{I} =  \R $$ $$ P^\mathcal{I} =  { z \mid z \geq 0 } $$ $$ f^\mathcal{I}(z) =  z^2  $$ $$ x^\mathcal{I} = \sqrt{2} $$ $$ E^\mathcal{I} =  { (x,y) \mid x=y } $$ $$ g^\mathcal{I}(x,y) =  x+y  $$ $$ y^\mathcal{I} =  -1 $$ Determine the value of following terms and formulae:

$$ 1. \mathcal{I}(g(f(x),f(y)))$$ $$ 2. \mathcal{I}(\forall x\,P(f(x)))$$ $$3. \mathcal{I}(\exists z \forall x \forall y\,E(g(x,y),z)) $$ $$ 4. \mathcal{I}(\forall y (E(f(x),y) \to P(g(x,y)))) $$

$$\Box$$

Problem 3 (Predicate)
The following formula is given: $$ F= \forall x \forall y \forall z\,R(h(h(x,y),z),h(x,h(y,z))) \ \land\ \exists x \exists y\,\lnot R(h(x,y),h(y,x)) $$ Indicate a structure $$\mathcal{A} $$, which is a model for $$F$$ and a structure $$\mathcal{B}$$ which is no model for $$F$$! $$\Box$$


text:
User talk:80.42.43.184

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. -- Herby talk thyme 17:17, 25 May 2007 (UTC)

title: User talk:80.42.43.184


text:
User talk:80.42.36.130

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. -- Herby talk thyme 17:33, 25 May 2007 (UTC)

title: User talk:80.42.36.130


text: A-level Chemistry/OCR (Salters)/Kevlar

title: A-level Chemistry/OCR (Salters)/Kevlar


text:
User talk:TexasGuy2009

Please do not add nonsense to wikibooks. It is considered as vandalism. Please use the sandbox instead. (or I'll personally throw you direct out of wikipedia! :( --Blueknight 19:41, 25 May 2007 (UTC)

This is your last warning. If you continue to vandalise Wikibooks, you WILL be blocked. --Blueknight 19:42, 25 May 2007 (UTC)

Can you PLEASE stop this bullshit before i knock you straight out of wikibooks!!? You are NOT funny. Get you a job, man!!! --Blueknight 19:48, 25 May 2007 (UTC)

Permanent Block
You have been permanently blocked from editing Wikibooks for apparent vandalism. There have been many cases of vandalism within the past hour and I believe you were a part of it but it's difficult to see at the moment from your edits if this is correct. Once all vandalism has been reverted and deleted I will fully check your contributions and unblock you if I believe I have made a mistake. Xania talk 20:10, 25 May 2007 (UTC)

title: User talk:TexasGuy2009


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User talk:Blueknight (Usurped)

You have been permanently blocked from editing Wikibooks. You have vandalised pages, moved pages to other locations and pretended to be other users and administrators from other projects. Xania talk 20:07, 25 May 2007 (UTC)

title: User talk:Blueknight (Usurped)


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User talk:3hitsallday

You have been permanently blocked from editing Wikibooks for mass vandalism of an offensive kind. Xania talk 20:08, 25 May 2007 (UTC)

title: User talk:3hitsallday


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Debate/Topics/Same-Sex Marriage

Same-sex marriage is a controversy that is part of the family values issue, and is related to homosexuality and marriage disputes.

Supporters: Those who believe that legal authorities should recognize the validity of marriages between two men or two women.

Opponents: Those who believe that legal authorities should only recognize the validity of marriages between one man and one woman.

Religion
Opponents: God has created the institution of marriage for the purpose of procreation. Same-sex couples are incapable of procreating.
 * This argument relies on the premise that God created marriage for the purpose of procreation.

This argument relies on the premise that God exists

Supporters: Not all couples procreate, some by choice and others because they are infertile. Nobody argues that infertile couples should not be allowed to marry.

Supporters: God desires that all people lead romantically and sexually fulfilling lives. The best way to do so is by committing to a monogamous relationship with a compatible person. For homosexuals, the most sexually and romantically compatible people are of the same sex.
 * This argument is part of the nature vs. nurture debate.

Supporters: Marriage is a religious institution defined by religious rules. In a country where there is separation between church and state marriage should not be recognized as an institution in law whatsoever.

Family Values
Opponents: Allowing same-sex marriage will contribute to the breakdown of the family unit in society. The end result will be more single-parent families and more instability in the lives of children.

 * This argument relies on claims regarding homosexuality and parenting.

Supporters: There is no evidence to indicate that same-sex couples are poorer parents then heterosexual couples. In addition, marriage will make families headed by homosexual couples more stable, not less so, and will have no impact on the parenting abilities of heterosexual couples.

 * This argument relies on claims regarding homosexuality and parenting.

Supporters: If things that weaken the family unit in society must be illegal, then divorce should by the same token be illegal, and it's not.

 * This argument assumes that the existence of divorce is accepted by all.
 * This argument assumes that the existence of one anti-family feature of our law can justify another anti-family feature.

Opponents: Critical court decisions in support of parental rights have been based on the structure of the traditional family in common law. If the definition of marriage were to change, these court decisions would be in jeopardy.
 * This argument assumes that the said court decision should be upheld.
 * This argument assumes that the said court decision could not be interpreted to include same-sex parents.

Opponents: Much of this battle is about financial and legal advantages given to families. While childless couples do benefit, the advantages have been fairly successful in improving the lives of children. These advantages apply to all of us, because even homosexuals start life as children.

Definition
Opponents: Marriage traditionally has meant the union of one man and one woman. Homosexual unions can be classed more or less with polygamy, in that advocates want to change the definition. And if the definition can be changed for homosexuals, why would any other limits be different?

 * This argument ignores the fact that there are documentations of historic same-sex marriages in Ancient Rome and some African tribes.
 * This argument can be considered an example of a Slippery Slope argument.
 * This argument is based on the assumption that multiple legal marriages should not exist.

Supporters: Gay marriage is unrelated to polygamous relationships. It is possible to logically examine the evidence and conclude that one is immoral and the other not.

 * This argument could well go either way. There are multiple cases of polygamy in the Bible. Thus, if we are to decide which type of marriage is immoral by examining evidence, we may conclude that same-sex marriage is immoral.
 * There are only hinted biblical reference to homosexuality in the story of Sodom and Gomorrah.
 * This con-argument assumes that the Bible is the one source from which moral laws should be taken.

Distinction
There is a distinction to be made between religious marriage and the government institution of marriage. Some religious institutions forbid same-sex marriage and some allow them. The question is whether or not the state should or should not recognize same-sex marriages.

Some people would break away from both camps on this debate and argue that the state institution of marriage should not exist altogether. They would argue that regardless of whether same-sex marriages are recognize by the state, the state institution of marriage amounts to the government determining how people are to live their lives by providing social and economic incentives to organize a particular model of family unit.

There are plenty of ways of organizing a family unit other than a heteronormative couple that are already in existence, and not all of these are based around two adults who are sexually and romantically attracted to each other. For instance collectives often raise children together. Regardless of whether the adult members are attracted to each other, this is a type of family unit that is held together by love. There is no reason, then, why members of a collective should be denied access to the privileges afforded heteronormative couples: for instance, hospital visitation rights.

title: Debate/Topics/Same-Sex Marriage


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User talk:Lewis 4762

Hello, welcome to Wikibooks!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be a good idea to add this page to your "watchlist" so that you can see when any new information is posted there. You can do that by clicking the tab labeled "watch" at the top of the page.

Good luck! Mattb112885 (talk) 21:08, 25 May 2007 (UTC)

title: User talk:Lewis 4762


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Cookbook:Ham and Cheese Crepes

Ingredients

 * 12 prepared crêpes
 * 1 ½ cups shredded cheddar cheese
 * 12 slices cooked, thinly sliced ham
 * 2 Tbsp finely-chopped green onion
 * ½ teaspoon salt
 * ⅛ teaspoon pepper
 * ½ cup sour cream
 * ½ teaspoon prepared mustard
 * ⅓ cup bread crumbs
 * 3 Tbsp melted butter

Procedure

 * 1) Preheat oven to 350°F.
 * 2) In small bowl, combine cheese, onion, salt, pepper, sour cream, and mustard.
 * 3) Lay one slice of ham on each crêpe.
 * 4) Spread about 1 tbsp of the mixture over each ham slice.
 * 5) Roll up crêpes, and arrange in 13x9-inch baking pan.
 * 6) Combine melted butter and bread crumbs, and sprinkle over crepes.
 * 7) Cover pan loosely with foil.
 * 8) Bake for 15–20 minutes at 350°F.

title: Cookbook:Ham and Cheese Crepes


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Iranian History

Iranian History

Ancient Iran

 * 1) Geography of Iran and Ethnological and Political Divisions
 * 2) Ancient pre-historic Iran
 * 3) The Elamites

The Achaemenids

 * 1) The Medes and the Early Achaemenids
 * 2) The Era of the three Dariuses
 * 3) Alexander's Campaign and the Macedonian Conquest of Persia
 * 4) The Seleucids

The Parthians

 * 1) The Early Arsacids 251 BC - 12 AD
 * 2) The Later Arsacids 12 AD - 226 AD

The Sassanians

 * 1) The Early Sassanians 226 - 379 AD
 * 2) The Middle Sassanian Period 379 - 488 AD
 * 3) Qobad I and the Two Khusros 488 - 629 AD
 * 4) Anarchy and Downfall of the Sassanian Empire
 * 5) Last Remnants of Sassanian Rule

Advent of Islam

 * 1) The Islamic Conquest of Iran
 * 2) The Umayyad Caliphate
 * 3) The Abbasid Caliphate
 * 4) /The Indigenous Dynasties: The Tahirids, the Samanids and the Saffarids
 * 5) Age of Literary Accomplishments

The Early Medieval Period

 * 1) Mahmud Ghaznavi
 * 2) The Later Ghaznavids and the Seljuqs
 * 3) The Empire of Khwarezm
 * 4) Origin of Sufism

The Mongols and the Ilkhanids

 * 1) The Invasion of Genghis Khan
 * 2) Halaku Khan and The Muslim Ilkhans
 * 3) Timur and the end of Mongol Rule

The Golden Age of Iranian Civilization

 * 1) The Early Safavids
 * 2) Abbas I or Shah Abbas
 * 3) The Later Saffavids

Nader Shah and the Qajars

 * 1) Nader Shah
 * 2) The Zand Dynasty
 * 3) The Rise of the Qajars
 * 4) The Great Game
 * 5) Modernity and The Rise of Islamic Fundamentalism
 * 6) The Iranian Constitional Revolution

Modern Iran

 * 1) The Pahlavis
 * 2) Ayatollah Khomeini and The Islamic Revolution
 * 3) /The Islamic Republic of Iran/

/Bibliography/

title: Iranian History


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User:Barak4wiki

Middle Eastern cuisine

 * Kibbeh
 * Hummus
 * Kebab
 * Tabouli
 * Fried cauliflower
 * Labneh
 * Mujaddara
 * Toum

Israeli cuisine

 * Israeli Salad
 * Shakshuka
 * Bagel toast
 * Bourekas
 * Chamin
 * Cholent
 * Couscous

Jewish traditional cuisine

 * Chicken soup
 * Cholent
 * Chamin
 * Sufganiyot
 * Hamentashen
 * Matzo balls
 * Matzah brei

Scandinavian cuisine

 * Swedish Meatballs
 * Luciabullar
 * Skolebrød

Italian cuisine

 * Pizza
 * Lasagne
 * Italian Meatballs

Chinese cuisine

 * Kung Pao Chicken
 * Noodle soup
 * Jiaozi

Hungarian cuisine

 * Goulash

Recepies I needa try

 * Baked Pork Chops
 * Midwestern Chicken Wings
 * Curry Chicken

Desserts

 * Cola Cake
 * Chokladboll

Easy Recepies

 * Pancake
 * French Toast

title: User:Barak4wiki


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Iranian History/Geography and Divisions

Iran forms a distinct parallelogram in the east part of the region most commonly known as the Middle East or West Asia. It is located between 32 00 N latitude and 53 00 E longitude. It has torrid plains, hot deserts and tall mountain peaks.Its history and culture is completely different from other countries of the Middle East, save Iraq which makes one wonder as to why it has been classified as a part of West Asia.

‹ Return to the Contents

Geography

Most of the terrain is mountainous, with the Zagros chain extending from the north-west to the south-east and the Elburz Mountains extending all along the Caspian coastline in the north. Throughout history, the two mountain ranges have often acted as a physical barrier protecting the Iranian heartland from the marauding Turkish hordes of the north and the Arabs of the south. As a result, this region has been the one least affected by foreign invasions. Though Iran had been invaded by foreigners from time to time the evil effects of conquest were often felt only in the plains of the south while the north was relatively less influenced. The Elburz mountains have, in fact, sheltered innumerable revolutionaries, freedom-fighters and banditti and was a stronghold of a declining Zoroastrian religion well into the sixteenth century.

The two mountain ranges meet at Tabriz, beside Lake Urmia in the Iranian portion of Azerbaijan. Lake Urmia,situated at the head of the Zagros Range, is associated with numerous Persian legends and was a part of the original homeland of the Avestan people.

To the south of Azerbaijan, is the country of the Kurdish tribes (Pers. Kordestan).

To the south of Kurdistan, the Zagros range curves to the right and runs parallel to the sea enclosing a narrow tract of land between the mountains and the coastline. This province known as Khuzestan with its capital at Ahvaz is the region where most of Iran's 1.5 million Arabs live.

Southern Iran, historically known as Persia, comprises roughly the areas of modern-day Khuzestan, Fars and Kirman. This is a region of great antiquity known for its culture and civilization. This was the centre of the Achaemenid and Sassanian Empires with the ruins of a magnificent Persepolis adorning its scorched terrain. Now, it seems difficult for us to imagine that this was once the centre of a mighty empire which ruled most of the known world.

To the east of Fars, lies Hormuzgan province, which comprises the island of Hormuz or Qeshm and the adjacent coastline of southern Persia. This forms the easternmost limit of Persia proper.

Political Divisions
The Islamic Republic of Iran is divided into 31 provinces.

People
Forward to Ancient pre-historic Iran ›

title: Iranian History/Geography and Divisions


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Iranian History/The Elamites

Origins
The Elamites called their country Haltamti meaning 'highland' which the Akkadians rendered as Elam. was centered in the far west and the southwest of Khuzestan Province Kohgiluyeh and Boyer-Ahmad Province,Chaharmahal and Bakhtiari Province lurestan Province modern-day Iran, including a small part of southern Iraq.populated by Bakhtiari people Some people believe that the Elamites are the descendants of Elam, the eldest son of Shem of the Old Testament and hence the name.

Proto-Elamite
The period between 3200 and 2700BC when the Elamite civilization gradually evolved is known as proto-Elamite period. This was the period when the Jiroft and Zayandeh Rud civilizations flourished in Iran. Tappeh Sialk is one of the prominent monuments of this period.

The script of the proto-Elamite people is yet to be deciphered and bears a striking resemblance to the Indus script.

The Old Elamite Period 2700 - 1600BC
The Old Elamite period began in about 2700BC when King Peli commenced the Awan Dynasty of Elam. However around 2600BC, Elam was conquered by the legendary king Enmebargesi of Kish of whom we know from the Epic of Gilgamesh. Later, however, the Elamites established their independence and under the later Awans even controlled Sumer. But, there were also intermittent periods when Elam was on the decline and Sumerian rulers like Eannatum and Lugal-Ale-Mundu established their sovereignty over Elam.

The Sumerian king lists mention three successive kings who reigned collectively for a period of 356 years. In 2350BC, Sargon of Akkad inflicted a crushing defeat on the forces of the Avan king Luhi-Ishan and degraded them to the level of vassals. The capital city of Anshan was however not reached by the Akkadians and under Kutik-Inshushinak (or Puzur-Inshushinak) in 2240BC, the Awans not only regained their freedom but even established their control over Sumeria. Kutuk-Inshushinak is described as a blood thirsty monarch who destroyed 70 cities a day. However, he is also credited with having revived Elamite rule in Northern Mesopotamia, Sumer and Akkad, improved the administration of the Elamite kingdom and having extended a temple dedicated to Inshushinak.

A hundred years after the Awan restoration, Elam was attacked by Ur-Nammu and his son Shulgi of Ur who put an end to the Awan dynasty. However, Elam regained its freedom under the Shimashki Dynasty whose kings concluded marriage alliances with the rulers of Ur. In 2004BC, the Elamites allied with Susa and attacked Ur putting an end to the Third dynasty.

The Shimashkis were succeeded by the Eparti dynasty. Notable rulers of this dynasty include Sirukhdukh (c.1850BC),Siwe-Palar-Khuppak who was addressed as "Father" by Mesopotamian kings and Kudur-Nahhunte.

Middle Elamite Period 1500-1100BC
The Middle Elamite Period is characterized by the integration of Susa into the Elamite Empire and adoption of the Elamite language in place of Akkadian by Susiana.

During the Middle Elamite period, three dynasties ruled the kingdom one after the other. They are the Kidinuid,who used the titles 'King of Susa and Anshan' and 'servant of Kirwashir',the Igihalkid and Shutrukid dynasties. The Igihalkids intermarried with the Kassites. In around 1320BC, the Kassite king Kurigalzu II occupied Elam and the Elamite power wasnt restored until 1240BC when Khiddin-Kutran I of Elam repulsed the Kassites.

Under the Shutrukids (1210–1100BC), the Elamite empire reached the height of its power. Shutruk-Nakhkhunte who ruled from 1185BC to 1155BC was the greatest monarch of the Shutrukid dynasty. His three sons, Kutir-Nakhkhunte II, Shilhak-In-Shushinak, and Khutelutush-In-Shushinak were capable of frequent military campaigns into Kassite Mesopotamia, and at the same time were exhibiting vigorous construction activity -- building and restoring luxurious temples in Susa and across their Empire.

However, Shutruk-Nakhkhunte is famous today for the famous tablet inscription that he caused to be inscribed:

I am Shutruk Nahunte, King of Anshand and Susa, Sovereign of the land of Elam. I destroyed Sippar, took the stele of Naram-Sin, and brought it back to Elam, where I erected it as an offering to my god. Shutruk Nahunte - 1158 B.C.

In 1158BC, Shutru-Nakhkhunte defeated the Kassites of Babylon, killing their king and breaking their power permanently. Following the death of Shurtu-Nakhkhunte's son, Kutir-Nakhkhunte, Lgihalkid power began to decline rapidly.

The Neo-Elamite Period 1100 - 539 BC
The Neo-Elamite period is further subdivided into Neo-Elamite I(1100-770BC),Neo-Elamite II(770-646BC) and Neo-Elamite III periods (646-539BC)

Very little is known about the Neo-Elamite I period. During this period, there seems to have been constant wars between the Elamites and Babylonians on one side and the Assyrians on the other.

The Neo-Elamite II period witnessed the migration of the present-day Iranians into the Iranian plateau. The first historical references to the Medes (Mada) date to 835BC when they are mentioned in an inscription of ShalmanesserII, King of Assyria, who relates that after having subjugated the Zimri who held the Zagros Mountains he lead an expedition to Media and defeated the Medes. The Assyrian chronicles also mention the Parsu or the Persians living on the south-eastern shore of Lake Urmia in the year 844BC.

In the late 8th century BC, the Elamites allied with the Babylonian king Merodach-baladin against the Assyrians but were defeated by Shutruk-Nakhkhunte II (716-699BC) in 710BC. In 700BC, the Assyrian ruler Sennacherib dethroned Merodach-baladan and installed his own son on the Babylonian throne. Another battle was fought between the Babylonians and the Assyrians at Halule in 691BC which ended without either side achieving victory.

There was continuous warfare betweent the Elamites and the Assyrians during the reigns of Elamite monarchs Khumma-Kaldash I and Khumma-Kaldash II. Urtaku (674-664BC) maintained friendly relations with the Assyrians but during the end of his reign, the Elamites launched an invasion of Mespotamia and the Assyrian ruler Ashurbanipal responded by counter-attacking Elam and killing Urtaku's successor in 653BC. In this same year the Mede state to the north fell to the Scythians, immediately displacing the Parsu tribe to Anshan, which their king Teispes captured that same year. Civil war broke out in Elam and the government was rendered unstable. Perceiving his chance, Assurbanipal launched a massive invasion of Elam in 646BC and destroyed Susa altogether.In a tablet unearthed in 1854 by Henry Austin Layard, Ashurbanipal boasts of the destruction he had wrought: "Susa, the great holy city, abode of their Gods, seat of their mysteries, I conquered. I entered its palaces, I opened their treasuries where silver and gold, goods and wealth were amassed...I destroyed the ziggurat of Susa. I smashed its shining copper horns. I reduced the temples of Elam to naught; their gods and goddesses I scattered to the winds. The tombs of their ancient and recent kings I devastated, I exposed to the sun, and I carried away their bones toward the land of Ashur. I devastated the provinces of Elam and on their lands I sowed salt."

However, the destruction wrought wasnt so great as Assurbanipal claims in this inscription of his. The Elamites revived and ruled Susa till its conquest by Cyrus the Great in 539BC. This last period, when Elam was ruled by a set of weak kings is known as the Neo-Elamite III period.

title: Iranian History/The Elamites


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Iranian History/Ancient pre-historic Iran

Little is known about Iran prior to the rise of the Elamite power. This is so because there remains a treasure-trove of pre-historic artifacts and long-buried cities yet to be recovered. Only recently are Stone Age sites in Iran being excavated and observed. Therefore, our knowledge of pre-historic Iran is quite scarce and is almost entirely based on modern discoveries and findings of the last few decades.

Paleolithic Period
By pre-historic Iran, we refer to the part of Iranian history from the date of Iran's oldest archaeological site discovered in Northern Iran and believed to be 800,000 years old up to the rise of the Elamites in around 3200BC when Iran becomes historical. The first part of Iran's pre-history would cover the Paleolithic Period or Stone Age. The earliest known evidence of hominin presence in Iran consist of a number of occurrences with surface collection of lithic tools that fall within Oldowan and Acheulian stone tool traditions. These sites are Kashafrud (Khorasan), Ladiz (Sistan and Baluchistan), Ganj Par and Darband Cave (Gilan), Shiwatoo (Mahabad), and few other sites in western Iran such as Amar Merdeg, Pal Barik and Gakia. Among these sites only Darband cave is dated radiometrically which indicate that the site was used by Lower Paleolithic hominins before 200.000 years ago. As recent as November 2006,a team of Iranian and Russian archaeologists excavating in northern provinces of Ardabil, Gilan, Mazenderan and Golestan discovered 50 pre-historic sites, 30 of them in Ardabil alone, which contained old Stone-Age implements dating to sometime between 800,000 and a million years ago. Another set of recent excavations by a joint Iranian-French team of archaeologists revealed Neanderthal sites in Iran, 40000 to 85000 years old. These recent discoveries have been made in Kermanshah province and in Mahabad in Western Azerbaijan as well as Niasar in Luristan province where caves inhabited by pre-historic Neanderthals were found. Remnants of Neolithic or New Stone Age settlements have been found at Ganj Dareh, Sarab, Mushki and tepe Chaxmaq. These have been dated to 7000 to 10,000BC.

Neolithic Age or early village period
The Neolithic Age is often associated with the growth of farming and irrigation as the temperature and rainfall of the time was found to be suitable for agriculture. The Neolithic Age in Iran began in about 8000BC and ended by about 5500BC. The Neolithic Age in Iran was characterized by the growth of small settlements having 50-100 inhabitants who lived either in houses built of unbaked brick or tents or brush-shelters.However excavations are yet to reveal the existence of class differences and temples or other special structures.

The Early Neolithic Period (8000-7300BC) preceded the use of pottery. The tools were mostly made up of flint,wood or fiber. Figurines of sheep,cattle,dogs, pigs and people made from clay have been found. With the introduction of agriculture and expansion of villages, people started uysing clay to make pottery. Bracelets and pendants were often worn by the inhabitants. Tools for harvesting crops, butchering, working hides, and other tasks were made from flint, while grinding stones, mortars, and pestles were made from limestone. Native pure copper from the central Iranian plateau was hammered into beads and pins.

Hajji Firuz, Abdul Hosein, Ali Kosh, Chogha Sefid, and Chogha Bonut are some of the prominent Neolithic Age sites that have been excavated.

The Rise of Mesopotamia
Iran was directly affected by the rise and evolution of city-states in neighbouring Mesopotamia as its South-Western provinces were under the Mesopotamian sphere of influence. Between 5300BC when the neolithic Eridu culture originated till 539BC when Cyrus the Great of Persia put an end to the last of the Mesapotamian kingdoms, the frontier regions of Khuzestan and Kordestan formed a part of the Greater Mesopotamian culture. In about 3200 BC, the Elamites, the first Iranian people of any significance, established a kingdom in south-western Iran and ruled this region, sometimes as vassals, for over two thousand years.

Uruk
The Samarra Culture first use irrigation in northern Mesopotamia at 5500BC. There was walls rounded the villages. The Chalcolithic Ubaid/Obeid or Eridu culture thrived from 5300 BC to 4000BC and pioneered farming and irrigation and the use of copper. Slowly villages grew into cities and Eridu civilization extended into Northern Mesopotamia. On late this period there was temples and some type chiefdoms. The Eridu period was followed by the Uruk period which extended from 4000 to 3100 BC. This period saw the rise of one of the world's oldest cities from which Mesopotamia's modern name Iraq could have originated. There was big cities in northern Mesopotamia before southern mesopotamia, tex. Tell Brak in Syria. Writing was invented and large temples was built. These city-states were remarkable for their excellent organization and governance. By 3000BC, the government of Uruk had become powerful enough to subdue other city-states and give rise to the Sumerian Empire.

Early dynastic Sumer
The Empire of Sumer began with the Dynasty of Kish in around 3000BC. At this time there were widespread conflicts between many city-states. One city conquered others, but soon was overthrown by another city. By 2700 BC, the focus seems to have shifted from Kish to Uruk. The Uruk and the Ur dynasties ruled from 2700BC to around 2500 BC when overlordship passed on to Lagash. In 2334 BC, the last of the Sumerian kings was overthrown by Sargon I of Akkad.

Akkad
Semitic Akkad established its supremacy over Mesopotamia and ruled the lands from 2334BC to around 2100BC. One of the early rulers of Akkad, Lugal-Zage-Si is credited with having established Akkadian supremacy over the Elamite kingdom based in south-west Iran. Sargon I, the first ruled after the conquest of Mesopotamia, is regarded as the greatest monarch of his dynasty. It is definitely possible that he might have exercised his authority over Iran proper as clay tablets belonging to his period makes references to copper being brought from Magan which most scholars believe, is modern Makran. Sargon's grandson Naram-Sin is credited with having led an expedition into Magan and having taken its monarch captive.

Gutians and Neo-Sumer
At around 2200BC, the Gutians invaded Mesopotamia from the Zagros Mountains. The first Guti kings had a barbaric manner to govern Sumer. They didn't repair irrigation canals those brought water to fields. Lagash rebelled and became independent. Gudea of Lagash was a strong king, but had only local significance. Gutians still ruled most of Sumer. But Utukhegal, the king of Uruk, drove the Gutians off, and Ur became overlord of Sumer under Ur-Nammu, who commenced the third dynasty of Ur. This dynasty ruled Mesopotamia over hundred years. Shulgi was most famous king of Ur III dynasty. This is known as the "Sumerian Renaissance" or Neo-Sumer. Temples were built and trade flourished. There were problems due the Amorite tribes on west.

But in Sumer there was a rebellion in the city of Lagash, that became independent. Soon after this Elam attacked till Sumer at 2004BC, and captured last king of Ur, Ibbi-Sin.

In Isin Ishbi-Erra-named semitic took power and drove the Elamites out from Sumer. Semitic Amorite tribes came to Sumer, and took power in many city states of Mesopotamia.

Old Babylonia
There was power struggle between Isin and Larsa at Southern Mesopotamia ca. 2000-1750BC. At 1750 BC the king of Babylon Hammurabi conquered most of present-day Iraq and made empire, that began collapse soon after his death.

The Kassites
The Kassites were a mountain tribe from Luristan who are believed to have migrated to the region from an obscure homeland sometime between 4000 and 3000 BC. It has often been thought that they were Indo-Europeans. But recent researches have established beyond doubt that their language was not Indo-European thereby disproving the theory that they were Indo-Europeans.

In 1595BC, they rose into prominence, taking hold of Northern Mesapotamia. Following their attendance to power, they ruled Babylon for four centuries. Some prominent Kassite rulers were Kurigalzu I (1400-1375 BC appx.), who built a town named after him called Dur-Kurigalzu, Kadashman Enlil I, and Burnaburiash II, who maintained correspondence with Amenhotep III and Akenaton (Amenhotep IV) of Egypt. The Kassites princes married Assyrian, Hittite and Elamite princesses. In the 12th century BC Kassite rule was brought to an end by the invasion of the Elamites who conquered Babylon and took the last Kassite ruler, Anllil-nadin-akhe, prisoner to Susa where he died.

Mittani and the Hittites
Mittani was a feudal kingdom established in Northern Mesopotamia (present-day Syria and Turkey) in the 14th century BC by fierce warriors believed to be of Aryan descent. This is one of the earliest instances when we hear of the Indo-European people who later founded the Persian kingdom. The connection of the Mittani with Indo-Aryan people was first proposed in 18 when inscriptions founded at Boghazkoy in Turkey spoke of a marriage alliance between the Mittani and the Hittites and invokes Vedic Gods like Indra, Varuna, Mitra and the Nasatyas to pour blessings upon the couple.The Aryan-origin theory of the Mittani is further strengthened by the records of the Mittani which mentions monarchs with Indo-Aryan names such as Kirta,Sutarna,Barattarna,Parshatatar,Artatama,Artashumara and Tushratta.

Mittani power began to decline after the 13th century BC and they gradually became vassals of the Assyrians.

Like the Mittani, the Hittites were speakers of an Indo-Aryan language who ruled over Central Anatolia. They rose to power in the 18th century BC and gradually expanded their dominions over the Levant and West Asia conquering Syria and clashing with the Mittani on the borders of Mesopotamia. In 1274BC, they clashed with Egyptian forces at Kadesh in Syria. However, after many days the battle came to a standstill with neither side able to vanquish the other. The rise of Assyria in Mesopotamia forced the Hittites to sign a treaty of peace with the Egyptians in 1258BC. However, their power did not survive for long and ended when Kaskas, Bryges and Luwian tribes burnt the Hittite capital Hattusa in 1180BC. A few centuries from the sack of Hattusa, the Hittites had completely disappeared.

Assyria and Neo-Babylonia
Assyria in Northern Mesopotamia seems to have come into prominence in the first half of the second millennium BC and to have conquered most of Mesopotamia on the defeat of the Hittites. The Assyrian Empire extended its authority over the Levant and parts of Iranian Kurdistan by the end of the millennium. However, frequent rebellions in Egypt taxed its resources and left Assyria badly weakened. When new peoples, the Persians and the Medes, migrated into modern Iran, they were able to attack and destroy the Assyrian civilization.The Assyrians ruled over Mesopotamia until 602BC, when Asur-uballit, the last ruler of Assyrians defeated by the Babylonians. The New Babylonians ruled much of Mesopotamia under kings like Nabopolassar and Nebuchadnezzar until 539BC when Cyrus conquered Babylon and put an end to Mesopotamian independence.

The Zayandeh-Rud Civilization

In the 5th millennium BC, just as city states were emerging in neighboring Mesopotamia the Zayendeh Rud civilization was flourishing along the banks of the river of the same name in Central Iran. Isfahan, Bakthiari and the Yazd provinces of the modern-day Iran lay at the heart of the Zayendeh-Rud civilization. Isfahan is, in many ways, regarded as one of the oldest cities in the world. Archaeological research has also revealed the remains of an ancient buried city, which according to local lore, were believed to have been destroyed by war and famine.

The site of Sialk or Sialk Tappeh in the central Iranian province of Isfahan is a typical example of Zayendeh-Rud settlement. Sialk also has the world's oldest Ziggurat, built by the successors of the Zayendeh-Rud people, the Elamites in about 2900BC.

The Cheshma culture of south-eastern Tehran and the Hesar culture are some other elements of the Zayendeh-Rud civilization.

In December 2006, pottery and other decorated elements were found near the city of Bam in central Iran with unique motifs that bore a striking resemblance to those found in the artifacts found in Sialk Tappeh. This site which covers an area of over 300 hectares is believed to be the largest pre-historic archaeological site in Iran.


text:
SAT Study Guide/Part 4 - The Writing Section/The Essay

The First WELL of the Excellent Essay:

WELL-STRUCTURED

The Importance of Structure

·  Just starting to write as soon as you read the essay prompt is a BAD STRATEGY! Unfortunately, this is how many students approach the test. Why do they do this? Because most students do not realize that THE TEST GRADERS ARE EVALUATING YOUR EFFORTS BASED IN LARGE PART ON THE ORGANIZATION OF YOUR IDEAS.

·  Taking 2 minutes to OUTLINE YOUR ESSAY enables you to CREATE A ROADMAP for your essay.

·  Writing your essay without first creating a general outline is like taking a car trip without first having any sense of the directions you’ll need to follow in order to arrive at your destination.

·  Without a map travelers get lost. Without an outline, student essays ramble.

·  Take the two minutes to create a map of your essay – it is time very well spent. (And NOT, contrary to popular misconception, time wasted.)

 Success Secret for the Test

ESSAY GRADERS ARE LOOKING FOR

SOLID STRUCTURE

QUESTIONS ESSAY GRADERS WILL ASK THEMSELVES:

·  Is there a sensible progression of ideas?

·  Does the student logically move from Point A to Point B?

·  Does the essay have a Beginning, a Middle and an End?

KEY POINTS TO REMEMBER ABOUT OUTLINING:

·  It creates Focus.

·  It saves time. (Really, it does. When you know where you are going, it’s a lot easier to get there.)

·  It provides an intelligent Road Map that prevents rambling.

Reminder:  Those who outline tend to succeed in writing focused, well-structured essays. Those who do not, tend to ramble and run out of time.

What to do before you write your essay:

·  Understand what the essay prompt is asking of you.

·  THINK before you write. (Thinking is good – just writing is bad. Unfortunately, too many students do NOT think before they begin to write.)

·  TAKE TWO MINUTES TO OUTLINE YOUR THOUGHTS because outlining provides focus, structure, purposefulness and clarity – all of which are elements students will be evaluated on by the Test Graders.

How to Create an Outline:

The Four Paragraph SAT Essay of Excellence

NOTE:  Being that this is a timed test, students WILL NOT HAVE TIME to elaborate upon every possible aspect the question touches upon. Test Makers know this. Test Graders know this. Students who score well know this, too. By coherently and intelligently responding to the essay prompt in four well-written paragraphs students will enable themselves to earn an excellent score on the Essay Writing Section of the SAT.

There are Four Main Sections a student wants to outline before they begin to write their essay.

·  Paragraph 1  – The Main Idea (including a Thesis Statement)

·  Paragraph 2  – Supporting Paragraph #1 (Point A)

·  Paragraph 3  – Supporting Paragraph #2 (Point B)

·  Paragraph 4  – The Concrete Conclusion (re-connecting to the Thesis)

Outline these four Big Points in two minutes BEFORE YOU BEGIN!!

NOTE: Yes, this is a formula - a formula for success on the SAT. With only 25 minutes to complete a well-written essay, strategy is a HUGE factor for success on this test.

Put yourself in the shoes of a Test Grader.

If a Test Grader sees that you can write four well-structured paragraphs that progress from Point to Point, including a Thesis Statement and a Conclusion, you are on you way to an excellent score. Remember, all you need to do is write four paragraphs – there is no time for a 33 page doctoral thesis on the essay prompt - so do NOT try to write one.

PITFALLS: Watch out!

·  Avoid the temptation to skip the outline process.

·  Avoid the temptation to abandon the outline after taking the time to create it.

Samples Outlining Activities:

Sample #1

DIRECTIONS: Please explain the following quote and whether or not you agree or disagree with the statement.

Nothing great was ever achieved without enthusiasm. (Ralph Waldo Emerson)

 Two-Minute General Outline:

Paragraph 1 - You must care about something in order to really create greatness.

Paragraph 2 - I agree, being negative will never result in producing amazing results.

Paragraph 3 – Examples exist everywhere proving this point.

Paragraph 4 – Without genuine passion, excellence is unattainable.

Sample #2

DIRECTIONS: Please explain the following quote and whether or not you agree or disagree with the statement.

The person who lies for you will lie against you. (Harry Truman)

 Two-Minute General Outline:

Paragraph 1 – A liar is a liar.

Paragraph 2 – Betrayal will eventually happen.

Paragraph 3 – Honesty is a principle without exception.

Paragraph 4 – People who lie for you reveal their true character so beware.

Though these are only rough statements, one can see that these essays now have a clear sense of direction – and as a result they will be MUCH EASIER to write because a road map is now in place telling us where to go and what to accomplish.

TAKE TWO MINUTES TO CREATE AN OUTLINE!!

The Second WELL of the Excellent Essay:

WELL-SUPPORTED

The Importance of Support

·  Test Makers and Test Graders are looking for the strong, solid support of ideas in student essays.

·  An idea without strong, solid support is like a roof without a strong, solid foundation – it is going to collapse.

·  Many students will offer a strong, solid idea but not follow it up -- as a result, they do not earn excellent scores for their efforts.

How to Support: Know (and Use) The Umbrella Theory

Think of the four main points of your outline as if each of them were an umbrella.

·  Items properly placed under the umbrella are shielded from a storm of point subtraction.

·  Items not placed properly under the umbrella are at risk of being rained on by a storm of point subtraction.

·  Supporting ideas that are sensible and properly placed will fit nicely underneath the umbrellas of your outline.

·  Rambling statements that shoot off in all sorts of nutty directions will not fit under your umbrella.

What to support: Paragraph 1 - THE MAIN IDEA/THESIS STATEMENT

Each Well-Written Essay has a Thesis Statement that needs to be supported.

·  What is a Thesis Statement?

·   A Thesis statement expresses the MAIN IDEA OF THE ENTIRE ESSAY.

·  Why do you need a Thesis Statement?

·   You need a thesis statement because it controls the direction, focus and purpose of the essay.

·  How do you create a Thesis Statement?

·  A great way to create a thesis statement that will ensure you address the question you have been asked is to CONVERT THE QUESTION PROMPT INTO A THESIS STATEMENT.

How do you support a Thesis Statement?

·  The well-written thesis statement will be like an umbrella for your entire essay – everything will fit underneath its scope.

·  The TOPIC SENTENCES of Paragraphs 2, 3 and 4 will be the specific tent poles of support for your thesis by the time you are finished. (More on that in a bit.)

·  Remember, support for the thesis statement will be found throughout the entire essay. In one sense, the purpose of the entire essay is to support the thesis.

Don’t forget…

THE THESIS STATEMENT GUIDES YOUR ESSAY

 HOW TO CONVERT A QUESTION PROMPT INTO A THESIS STATEMENT

1.      Read the Question Prompt.

2.      Change the Prompt from a question into a firm statement.

Example:

Question Prompt: Why do you like vanilla ice cream?

Thesis: Many reasons exist for me to like vanilla ice cream.

Question Prompt: Do you agree that the United States should avoid raising taxes?

Thesis: I completely disagree with the idea that the United States should avoid raising taxes.

3.      Use this converted statement as the basis for your thesis.

More examples:

Question:  Considering that most teenage driving fatalities occur after dark, do you believe that teenage drivers should be banned from driving at night?

Converted to Thesis Statement: Because most teenage driving fatalities occur after dark, I believe teenagers should not be allowed to drive their cars after the sun sets.

Question:  If at the age of eighteen a person can join the military and die for their country, do you feel that they should then also be allowed to go into a bar and be served an alcoholic beverage?

Converted to Thesis Statement: If a person can join the military and die for their country, they should definitely be able to enter a bar and be served an alcoholic beverage.

Tips to Remember about Thesis Statements:

·  They need to be direct and focused.

·  They need to serve as an umbrella which can be used for the entire essay.

·  They must address a specific topic and put forth a clear main idea.

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What to support: Paragraph 2 - THE TOPIC SENTENCE

·  Paragraph 2 will begin with a TOPIC SENTENCE.

·  This topic sentence will have been generated from your outline.

·  This topic sentence will need to be supported by the paragraph that follows.

·  What is a Topic Sentence?

 The topic sentence will directly state the focus, direction and purpose of the paragraph.

·  Why do you need a Topic Sentence?

 A Topic Sentence is needed for two distinct reasons:

1.      So that the point of the paragraph is clear and precise.

2.      So that the thesis statement is provide with solid support.

·  How do you create a Topic Sentence?

 Since you will know what the focus and purpose of Paragraph 2 needs to be (because you did an outline that sketched out the main idea of this paragraph before you started writing this essay… remember section 1, Well-Structured?) you will know what you are going to be writing about and why. Take your topic sentence from your outline.

·  How do you support a Topic Sentence?

There are 3 Major Types of Support in the Excellent Essay:

1. Logical reasoning.

EX: If THIS happens, then THAT will be the result.

2. Personal Examples.

EX: Once, when I was younger, I learned THIS the hard way.

3.      Specific, vivid details.

EX: Green slime oozed from the nostril of the dead gazelle.

Remember, topic sentences are also like an umbrella.

·  Use logical reasoning, personal examples and specific, vivid details to support your topic sentences.

Students will want to include all three types of support for their topic sentences in order to score well on the SAT Essay Writing Section.

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What to support: Paragraph 3 - THE DIFFERENT/OPPOSITE PERSPECTIVE

·  Paragraph 3 will begin with a TOPIC SENTENCE.

·  This topic sentence will have been generated from your outline.

·  This topic sentence will need to be supported by the paragraph that follows.

 NOTE:  For an effective, excellent essay the topic sentence of Paragraph 3 will address A DIFFERENT/OPPOSITE PERSPECTIVE from the one addressed by Paragraph 2.

ESSAY GRADERS ARE LOOKING FOR A MULTIPLE OF PERSPECTIVES ON THE SAME ISSUE IN THE HIGH-SCORING SAT ESSAY.

 MAKE SURE THE PERSPECTIVE OF PARAGRAPH 3 IS DIFFERENT/OPPOSITE FROM THE PERSPECTIVE OF PARAGRAPH 2.

Students encounter problems when they do not address a different/opposite perspective in Paragraph 3:

·   Students who only look at the question from one perspective do not demonstrate the sophisticated thought process test graders like to see.

·   Students who only look at the question from one perspective tend to be repetitive in their thoughts and ideas.

·   Students who only look at the question from only one angle tend to not score as high as those who view the question from a different/opposite perspective.

How to Create a Different/Opposite Perspective for Paragraph 3:

·   Think in terms of, “The Other Side of the Coin.”

·   Take the other side of the argument.

·   Play “Devil’s Advocate.”

·   Change sides for a minute to consider all angles.

For example…

·  If paragraph 2 is discussing the need for teenage drivers to stay off the road at night, paragraph 3 can address why teenage drivers might argue that they deserve to be able to drive on the road at night.

·  If paragraph 2 is arguing that being able to fight and die as a soldier in the military has nothing to do with being able to responsibly handle being served an alcoholic beverage in a bar, then paragraph 3 can talk about how silly it is that being served alcohol requires more maturity than being asked to handle a weapon in the army.

ADDRESSING A DIFFERENT/OPPOSITE PERSPECTIVE IN PARAGRAPH 3 ADDS DEPTH, SOPHISTICATION AND COMPLEXITY TO YOUR ESSAY IN AN EASY-TO-IMPLEMENT MANNER.

Good phrases to incorporate in Paragraph 3:

·   However…

·   On the other hand…

·   Another way of looking at this is…

·   Opponents might say…

·   While most may agree, there are others who feel…

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 What to support: THE CONCLUSION

Each Well-Written SAT Essay has a Concrete Conclusion!

 Paragraph 1 + Paragraph 2 + Paragraph 3 add up to Paragraph 4 (The Conclusion)

What is a Conclusion?

·   A conclusion is a definite ending whereby the reader of the essay will feel that the ideas are tied together and that the essay has been completed.

Why do you need a Conclusion?

·   Essays need endings. Including a conclusion shows the reader you understand the proper structure for the SAT essay and have implemented it successfully.

How do you create a conclusion?

·   Think of your essay as if it were a circle. You started at one point and now (in the conclusion) you need to bring everything back around again to complete the loop.

Techniques a student can use to craft a strong conclusion.

·   Restate and re-affirm your position.

·   Offer a solution to a problem.

·   Make a recommendation for a course of action.

·   Summarize your major points.

·  '' Restate your thesis. ''

Conclusion examples:

1)       In conclusion, teenage drivers are dangerous after dark and should be prohibited from taking the wheel at night. Too many pieces of evidence demonstrate that their general recklessness presents real peril after the sun has set. Stopping them from taking the road doesn’t just protect them, it protects all of us.

2)       Of all the crazy laws in our country, the one that says an eighteen year old can die for the American flag but not have a beer in a bar before doing so is the dumbest. Sure, people can argue about how the drinking age being set at twenty-one has some advantages but all in all, if I were thinking about serving my country, I’d find it ridiculous that Uncle Sam will permit me to shoot a man before sharing a glass of wine with him.

Keep in mind…

·   The conclusion is the final say.

·   The purpose of the conclusion is to hammer home an idea and make a point.

·   This is no time for wishy-washy language nor unclear positions. Take a side and assert your belief. Strength counts.

DO’s for the conclusion…

·   Tie up the major points of the essay.

·   Use strong, forceful language that MAKES A POINT.

·   Give the reader a sense that the essay is completely finished.

·   Hammer home an idea and let the reader know precisely the position the author of the essay has taken on the subject matter being discussed.

·   Draw a direct line to the thesis statement.

DON’T’s for the conclusion…

·   Start talking about new points and side issues that haven’t been mentioned in the essay prior to this paragraph.

·   Give the reader a sense that the essay might go on and may not be finished with yet.

·   Use weak, soft language that doesn’t really make a point about anything in particular.

·   Doesn’t leave an impression that the author of the essay has any particular belief about the subject matter being discussed.

·   Draws no connection to the thesis statement.

Remember…

·  Conclusions can be short (after all, this is a timed test and it might just come down to the last few nitty-gritty moments) but short conclusions can be effective.

·  Not writing a conclusion, however, is ineffective and will lower your score.

ALWAYS WRITE A CONCLUSION!!!

Two more Principles of the Well-Supported Essay you MUST use to Earn Higher Scores:

1. Use an example from your Personal Experience .

Test Graders are looking for you to support your essay with personal experience.

·  '' Your own life. ''

·   A friend’s life.

·   A family member’s life.

Test Graders want to see the generalities of the ideas you write about exemplified through concrete, real-life examples taken from your own personal experience.

If I were writing an essay about the need to keep teenagers off the road at night, I might want to tell the story about the neighborhood teenager who crashed his mother’s new car and ended up in a wheelchair three days after he first got his license. Why?

·   It’s got relevance.

·   It’s got juicy details.

·   It is unique. (Out of all the people taking the SAT in the entire country, I am probably the only one who can tell such a story because it really happened in my life.)

ALWAYS USE A PERSONAL EXAMPLE IN YOUR ESSAY!!

2. Be Specific, Use Details

Why be specific and use details?

 Test graders read lots and lots of papers. Lots of them are dull papers, too. Exciting language will stand out and capture their attention.

·   Bland language lays flat on the page.

·   Descriptive language leaps off the page.

·   General thoughts put readers to sleep.

·   Specific details make readers pay attention.

*In other words, VIVID LANGUAGE BRINGS WRITING TO LIFE.

Students MUST use descriptive language in order to achieve high scores!!

Never use the word GOOD!

 Use fantastic, amazing, incredible, tremendous, spectacular, extraordinary, unbelievable, phenomenal, stupendous, remarkable, astonishing, etc…

Never use the word BAD!

 Use horrible, disgusting, terrible, appalling, dreadful, horrifying, detestable, hideous, abominable, offensive, despicable, etc…

Enhance Your Descriptions by Tapping the Five Senses

·  Write about how the sunshine’s sizzle sounded like a Sunday morning omelet.

·  Write about how the old car smelled like a bad tuna fish sandwich.

·  Write about how the baby’s skin felt like the petal of an orchid.

·  Write about how the fresh rain tasted like an angel kissing your tongue.

·  Write about how the broken computer looked like a fallen soldier.

ALWAYS USE SPECIFIC DETAIL AND VIVID LANGUAGE IN YOUR ESSAY!!

PITFALLS: Watch out!

·  Not following your outline.

·  Making generalized statements that lack support.

·  Not including personal experience.

·  Using dull, non-descriptive language.

The Third WELL of the Excellent Essay:

Well-Reasoned

·  The Importance of Well-Reasoned: Simple, Strong and Straightforward.

With only 25 minutes to write an excellent SAT essay a student must know what they can and cannot accomplish. Almost all of the topics could lend themselves to 5 page typed papers if a student were given the time to write one.

 This is NOT what the Test Graders are looking for.

Test Graders are looking for students to demonstrate solid, strong proficiency in the area of essay writing when they only have a limited amount of time. The secret to successfully accomplishing this is found in the three S’s: SIMPLE, STRONG AND STRAIGHTFORWARD.

·  Make SIMPLE Arguments

 Being Simple does not mean being stupid, unsophisticated or unintelligent. Being simple means being; clear, precise and achievable.

Simple equals Clear.

·   On a timed test, the clarity of an argument adds to a student’s score. Some students try to tackle too much and get embroiled in convoluted thought processes that tangle them up more than they help them out. BEING CLEAR allows you to score higher.

Simple equals Precise.

·   On a timed test, the preciseness of an argument adds to a student’s score. Communicating a specific idea in a clear-cut manner allows a Test Grader to see evidence that the student can fashion a distinct, precise perspective in a limited amount of time, which allows you to score higher.

Simple equals Achievable.

·   On a timed test, completing one’s thoughts - and not leaving ideas or essays incomplete - adds to a student’s score. Many students begin elaborate, complicated patterns of logic that require 26 sentences to explain. This makes it very tough for them to finish the essay and opens the door up for them to make avoidable mistakes like constructing run-on sentences, engaging in convoluted logic or simply not finishing the essay because they have run out of time.

 *You do not want to run out of time. As discussed earlier, you need a strong conclusion to score well. If you try to tackle an overly complicated thought process, you might not finish in the allotted time frame. ACHIEVING COMPLETION OF YOUR ESSAY IN THE TIME ALLOWED IS A BIG PART OF SCORING WELL. Simplicity allows you to do this.

·  Make STRONG Arguments

 Break out the big guns right away! Find your biggest, most solid, most forceful, most dominant, #1 point and ADDRESS IT FIRST!!!

 Some students have 2 small points and then one really big one and they figure that they will save the biggest one for last and go with the smaller ones first. This is a bad strategy for the SAT essay!

 Remember, on a holistically graded test such as this, strong impressions count and the best way to make a really strong impression is by going with your number 1, biggest, strongest, most influential point first. Besides, there might not even be enough time to get to your #1 argument if you wait. (And wouldn’t that be a shame if you had saved your best for last but never got a chance to use your best due to time constraints?)

Remember…

·   Each paragraph should make a specific, solid point.

·   Each sentence should make a specific, solid point that relates to the overall, specific, solid point of the paragraph.

·  '' Use your best first. ''

·  Make STRAIGHTFORWARD Arguments

 Avoid over-complicated, intricate, sophisticated patterns of logic and reasoning. They suck up tons of time, open up the door for too many simple grammatical and punctuation mistakes to happen and they tend to cause students to ramble and go on straying tangents. Remember the Umbrella Theory? Arguments that stray from underneath the umbrella of the main point (either of the topic sentence or of the thesis statement) open up a student’s test to a rainstorm of point subtraction.

 Remember, a straightforward argument…

·   Creates an achievable goal because time is limited.

·   Prevents straying from the essential point.

·   Avoid Over-Extended logic patterns that create opportunities for missteps.

Something Else your Essay MUST HAVE to Earn Higher Scores:

A POINT OF VIEW (P.O.V.)

Test Graders want to see you take a clear position in your answer.

·   Test questions do not have right or wrong answers – they are subjective, interpretive, open-ended questions. Therefore, ASSERT YOUR OPINION.

·   You will not be penalized for the stance you take on a matter, nor on your beliefs. Your ideas are your ideas, however… YOU WILL NOT SCORE HIGH IF YOU DO NOT TAKE A STANCE OR PUT FORTH YOUR BELIEFS!

Remember…

HAVING A CLEAR POINT OF VIEW INCREASES YOUR ESSAY SCORE

 NOT HAVING AN OBVIOUS P.O.V. DETRACTS POINTS FROM YOUR SCORE.

·   Having an obvious P.O.V., countering with an opposing P.O.V. and then re-asserting an additional reason to support your own P.O.V. raises your scores into the upper echelons of the grading rubric.

Also remember…

You will not be marked down by a scorer because they disagree with your argument. You will be marked down by a scorer if you do not take a position and make an argument.

 SPECIAL SECTION:   Do NOT B.S.

·   Trying to impress scorers by using big vocabulary words you are not sure how to use properly detracts from – not adds to – your score.

·   Trying to impress scorers by sounding artificially sophisticated when you do not know what you are talking about detracts from – not adds to –your score.

·   Writing simply for the sake of writing (i.e. aimless, wandering, & imprecise sentences written just to fill space on the page) detracts from – not adds to - your overall score.

Remember…

Test Graders are masters at detecting B.S. so don’t even try it.

·  '' Make real points. ''

·   Take a definite P.O.V.

·   Implement the proper, 4 paragraph structure.

·   Use specific details and vivid language.

·   Include a personal example from your own, unique life.

 *If you do all of this, there is no need to B.S. – you will be in good shape.

The Fourth WELL of the Excellent Essay:

Well-Executed

The Importance of Execution

 Time is limited. MAKING A STRONG IMPRESSION in this limited amount of time is a key ingredient to success.

 The best way to make a strong impression is to prove that you can write well.

 The way you prove that you write well is through the use of proper grammar, spelling and punctuation.

No matter how brilliant your ideas are, if you do not know how to write a PROPERLY PUNCTUATED essay that USES CORRECT GRAMMAR and is ALMOST ENTIRELY FREE OF SPELLING ERRORS, you will not earn an excellent score.

And the truth is, you do not deserve one, either. These are the basic tools of the writer’s trade… KNOW THEM!!!

Remember…

A student does NOT have to be perfect to earn an excellent score.

·   Small mistakes such as misplaced commas will not ruin you.

·   Too many simple errors will definitely hurt your score.

But Spelling, Punctuation and Grammar Count!

Simple Tools to Ensure a Higher Score

 Proofread Your Work.

·   It always amazes me to watch students who finishes their essay with 2 minutes to spare and fold their paper over and stare into space as if they have nothing to do.

·   What they NEED to do is PROOFREAD their work!

·   On timed tests when students are working quickly and efficiently, test takers often forget a word in a sentence, omit a period or question mark and misspell easy words they know how to spell. Finding even one of these small mistakes might be the last little thing you need to inch your score up a notch and move you into a higher echelon in the Test Grader’s eyes.

·   PROOFREAD!!! If you have the time and you really care about earning the best score you can, there will not be a wasted moment of time on the SAT Essay writing section. Students who have the time but do not bother to check over their work are not students who traditionally perform excellently well on the test. Proofread! It matters.

 Avoid Carelessness.

·   Pay attention to details.

·   Make it a point to do away with sloppiness.

·   If you practice NOT BEING SLOPPY during your practice essays, you will find that your performance will tend not to be sloppy as well.

 Be legible.

·   Students will NOT be marked down for their handwriting HOWEVER, without being legible, scores might suffer. (If I can’t read it, I can’t evaluate it.)

 Remember, the Essay is Graded Holistically

 Students get one score (on a scale from 1-6).

·   Simple, proper execution can raise scores.

·   A lack of simple execution can lower them.

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·   Excellently Execute your Essay:  Use Proper Grammar

 I’ll say it again, these are the basic tools of the writer’s trade and this is the foundation for what your score will be based upon. KNOW THIS MATERIAL!!!

 Subject/Verb Agreement

 All subjects and verbs need to agree.

·   Writing things like, “They is going to the store” is the same as begging for a low score.

·   Basic subject/verb agreement is a fifth grade Language Arts skill strong essay writers need to have mastered.

 Commas

 Make sure you properly use commas where they are needed.

·   One or two misplaced commas will not kill you.

·   An entire essay riddled with misplaced commas will definitely hurt.

·   If you are not sure how to properly use a comma, seek help.

 Apostrophes

 Possessives, contractions, plurals – hey, they need apostrophes (sometimes).

·   Proper apostrophe use is a fairly simple skill to know.

·   Students who forget apostrophes are sending a secret signal to the Test Grader that they are really not a solid, competent writer.

·   Forgotten apostrophes are usually due to sloppiness, laziness or a lack of attention to detail. REMEMBER THEM!

 Parallel Sentence Structure

 Smooth, clear writing has parallel sentence structure.

·   Use the same grammatical form to express equal, or parallel ideas.

·   Pair a noun with a noun.

·   Pair a phrase with a phrase.

·   Pair a clause with a clause.

·   Pair an infinitive with an infinitive.

 Pronouns

·   A Pronoun by itself has no definite meaning.

·   A Pronoun is only clear when the reader knows what the pronoun refers to.

·   Be sure that the references you utilize pronouns for are clear.

 Colons and Semicolons

 In general, I recommend students AVOID USING COLONS AND SEMICOLONS.

·   Students do not gain extra points for using colons and semicolons properly.

·   Students can lose points for using colons and semicolons improperly.

·   If there is really nothing to be gained but something to be lost, why bother getting involved in the first place?

 NOTE:  Many students love to try and impress the Test Graders by showing off their vast use of sophisticated punctuation when they really do not have an excellent grasp of how to use the punctuation properly.

This is NOT necessary - avoid doing it yourself. You’re only creating potential potholes on the road you’ll be travelling.

''' Capitalize! '''

·   All proper nouns must begin with a capital letter.

·   All sentences must begin with a capital letter.

·   Capitalization is easy – try not to shoot yourself in the foot.

 Indent your paragraphs

·   You will be writing 4 paragraphs.

·   Indent all 4 Paragraphs.

·   Again, this is very simple stuff that low scoring students do not do.

 Use Proper Spelling

·   If you are not sure how to spell a word, use a different word. The English language is very flexible.

·   Remember, synonyms you do know how to spell are better than enriched vocabulary words you do not know how to spell.

·   Test score do not rely on any one word so do not feel the need to force things.

 NOTE:  Do NOT use vocabulary words with which you are not familiar to impress test graders. It’s a BAD IDEA.

·   Trying to impress Test Graders by using 14 letter vocabulary words that you are not sure about how to use properly is a sure sign of an amateur test taker.  Remember, using words incorrectly can do more harm than good.

 Use Proper Punctuation

 All sentences require punctuation. Use it properly. Keep it simple.

·  '' The period. ''

·   It’s a silly mistake to forget these at the end of sentences.

·  '' The question mark. ''

·   It’s a silly mistake to forget these at the end of questions.

·   The exclamation point.

·   A great tool – but not if used every other sentence. Be judicial!

·  '' Quotation marks. ''

·   Knowing how to use them correctly impresses Test Graders.

 The Rule on Slang

 This is a test to see how well you use formal, written English – so use formal, written English. In general, AVOID SLANG!!!

·   However, slang can be effectively used to make a point – particularly inside a line of dialogue a student might be quoting.

·   For Example: If you are telling a story to make a certain point about how crime is rampant in your own neighborhood, you might make reference to the time when a guy crept up behind you, put a weapon in your lower back and said in a very menacing tone, “Dude, gimme your wallet.”

·   This would be an acceptable use of slang.

·   However, when writing an essay about how rampant crime is in your neighborhood, you should not write a sentence that reads, “There are a multitude of dudes who only want me to give ‘em my wallet which I ain’t gonna do.”

·   This is a poor use of slang. Know the difference!

 THE BASIC 4 PARAGRAPH FORMULA FOR AN EXCELLENT SAT ESSAY

Yes, this is a formula - a formula for success on the SAT. With only 25 minutes to complete a well-written essay, students need a strategy to succeed. This is it.

Achieve this and you will have done well.

Paragraph 1    Main Idea

Includes a Thesis Statement

Paragraph 2    Topic Sentence – Point A

 Supported by Vivid Details and/or a Personal example

Paragraph 3    Topic Sentence – Point B – Opposite/Different Perspective from Point A

 Supported by Vivid Details and/or a Personal example

Paragraph 4    Strong Conclusion

 Connects back to the Thesis Statement

Plus, you have…

·  Addressed what the question has asked you to address.

·  Used a uniquely personal example from your own life to illustrate an idea.

·  Used vivid language and specific sensory details.

·  Made simple, strong and straightforward points.

·  Shown a clear Point of View in your essay.

·  Avoided B.S.

·  Properly punctuated your essay.

·  Used proper grammar throughout your essay.

·  Done a solid job of spelling almost all words correctly.

·  Capitalized and Indented.

·  Tried to write legibly.

·  Avoided slang.

·  Proofread your work.


text:
The Cold War/Yalta

In 1945, the leaders of the three allies (the USA, Britain and the USSR) met twice to decide the fate of the Axis countries after the War. The first meeting was at Yalta, near the Crimea, in the USSR, in February, between Roosevelt, Stalin and Churchill. It is important to notice that this was before the War was over. Hence, the subject of the conference was to decide what would would happen once Germany had been defeated, so plans were only in brief. The following things were decided at Yalta:

Redivision of Land in Europe
The allies agreed that post-War Germany would be divided into four zones, and that each of the allies would be given a zone to occupy. The remaining zone, it was agreed, would be given to France. Also, a portion of eastern Germany would be given to Poland, although a portion of eastern Poland would be given to the USSR. This created the "Iron Curtain", splitting Europe in two, and increasing tension between the superpowers.

Free Elections
Stalin also agreed at Yalta that he would allow "free elections" in Soviet-occupied eastern Europe. However, the Soviet Union and the other allies appear to have been working to different definitions of the word "free". The Soviet constitution officially allowed "free elections". However, in the Soviet Union, to quote George Orwell,:

All animals are equal, but some animals are more equal than others.

This definition of "free" was not acceptable to the West, and was the beginning of Cold War tensions between the superpowers. However, they were able to agree that "free" elections would be allowed in Eastern Europe.

Japan
The allies also agreed that, three months after VE Day, the USSR would declare war on Japan. This caused problems, once the Truman Doctrine had been instituted, because the USA was not willing to allow further expansion of Communism into Japan, and hence had to use the atomic bomb on Hiroshima and Nagasaki in order to prevent Soviet involvement in the final stages of the War.

The allies met again at Potsdam, later that year.

title: The Cold War/Yalta


text:
User:Timlee90

Hey there, my name's Tim and I live in Singapore...yeah, that's about it, nothing special about me. To get a better picture of me, see my Wikipedia userboxes :-D

Links
I'd recommend a visit to the following pages, these links are not advertising (all non-profit):

 * My Work Blog!
 * My Church Web, dutifully maintained by myself ;-)

title: User:Timlee90