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Lecture 4. Pythagoras` Theorem and the Pythagoreans
Lecture 4. Pythagoras` Theorem and the Pythagoreans

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Primes and Greatest Common Divisors

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The Number of Topologies on a Finite Set

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On Rule Formats for Zero and Unit Elements

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Lecture notes

... We shall take the Basic Fact for granted. Essentially we shall be treating it as though it is a defining property of the integers (an ‘axiom’) and then proceed to deduce other information and theorems from it. There is an alternatve: we could construct the integers by some method and then prove that ...
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The representations of a quiver of type A n . A fast approach.

... Claus Michael Ringel It is well-known that a quiver Q of type An is representation-finite, and that its indecomposable representations are thin. By now, various methods of proof are known. The aim of this note is to provide a straight-forward arrangement of possible arguments in order to avoid indic ...
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Powers and Roots Student Notes

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3.3 | Power Functions and Polynomial Functions

... To describe the behavior as numbers become larger and larger, we use the idea of infinity. We use the symbol  ∞  for positive infinity and   − ∞  for negative infinity. When we say that “ x  approaches infinity,” which can be symbolically written as  x → ∞,   we are describing a behavior; we are say ...
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Sicherman Dice

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Lesson5 - Purdue Math

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Chapter 8: Roots and Radicals

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135. Some results on 4-cycle packings, Ars Combin. 93, 2009, 15-23.

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Linearly Independent Sets and Linearly

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Computing self-intersection curves of rational ruled surfaces

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final exam reviewb.tst

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2013 - Fermat - CEMC - University of Waterloo

arXiv:math/0407448v1 [math.NA] 27 Jul 2004
arXiv:math/0407448v1 [math.NA] 27 Jul 2004

http://www.ee.nmt.edu/~elosery/lectures/Quadrature_signals.pdf
http://www.ee.nmt.edu/~elosery/lectures/Quadrature_signals.pdf

... single sideband modulators, etc. ...
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THE COHOMOLOGY RING OF FREE LOOP SPACES 1. Introduction

Asymptotic Behavior of the Weyl Function for One
Asymptotic Behavior of the Weyl Function for One

... the variation of µ. The variation of a complex measure µ is always a positive finite measure and we have the inequality |µ|(A) ≤ |µ(A)| for A ∈ A. We want measures which are finite on all compact sets, thus we need the set on which our measure is operating equipped with a topology. Definition 1.3. L ...
< 1 ... 126 127 128 129 130 131 132 133 134 ... 480 >

Fundamental theorem of algebra

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with an imaginary part equal to zero.Equivalently (by definition), the theorem states that the field of complex numbers is algebraically closed.The theorem is also stated as follows: every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n roots. The equivalence of the two statements can be proven through the use of successive polynomial division.In spite of its name, there is no purely algebraic proof of the theorem, since any proof must use the completeness of the reals (or some other equivalent formulation of completeness), which is not an algebraic concept. Additionally, it is not fundamental for modern algebra; its name was given at a time when the study of algebra was mainly concerned with the solutions of polynomial equations with real or complex coefficients.
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