Elementary Number Theory 2nd Edition by Charles Vanden Eynden – Ebook PDF Instant Download/Delivery: 9781478639077 ,1478639075
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Product details:
ISBN 10: 1478639075
ISBN 13: 9781478639077
Author: Charles Vanden Eynden
This practical and versatile text evolved from the author’s years of teaching experience and the input of his students. Vanden Eynden strives to alleviate the anxiety that many students experience when approaching any proof-oriented area of mathematics, including number theory. His informal yet straightforward writing style explains the ideas behind the process of proof construction, showing that mathematicians develop theorems and proofs from trial and error and evolutionary improvement, not spontaneous insight. Furthermore, the book includes more computational problems than most other number theory texts to build students’ familiarity and confidence with the theory behind the material. The author has devised the content, organization, and writing style so that information is accessible, students can gain self-confidence with respect to mathematics, and the book can be used in a wide range of courses—from those that emphasize history and type A problems to those that are proof oriented.
Elementary Number Theory 2nd Edition Table of contents:
Chapter 0: What Is Number Theory?
Chapter 1: Divisibility
1.1 The Greatest Common Divisor and Least Common Multiple
1.2 The Division Algorithm
1.3 The Euclidean Algorithm
1.4 Linear Combinations
1.5 Congruences
1.6 Mathematical Induction
Chapter 2: Prime Numbers
2.1 Prime Factorization
2.2 The Fundamental Theorem of Arithmetic
2.3 The Importance of Unique Factorization
2.4 Prime Power Factorizations
2.5 The Set of Primes is Infinite
2.6 A Formula for T( n)
Chapter 3: Numerical Functions
3.1 The Sum of the Divisors
3.2 Multiplicative Functions
3.3 Perfect Numbers
3.4 Mersenne and Fermat Numbers
3.5 The Euler Phi Function
3.6 The Mobius Inversion Formula
Chapter 4: The Algebra of Congruence Classes
4.1 Solving Linear Congruences
4.2 The Chinese Remainder Theorem
4.3 The Theorems of Fermat and Euler
4.4 Primality Testing
4.5 Public-Key Cryptography
Chapter 5: Congruences of Higher Degree
5.1 Polynomial Congruences
5.2 Congruences with Prime Power Moduli
5.3 Quadratic Residues
5.4 Quadratic Reciprocity
5.5 Flipping a Coin over the Telephone
Chapter 6: The Number Theory of the Reals
6.1 Rational and Irrational Numbers
6.2 Finite Continued Fractions
6.3 Infinite Continued Fractions
6.4 Decimal Representation
6.5 Lagrange’s Theorem and Primitive Roots
Chapter 7: Diophantine Equations
7.1 Pythagorean Triples
7.2 Sums of Two Squares
7.3 Sums of Four Squares
7.4 Sums of Fourth Powers
7.5 Pell’s Equation
Index
List of Theorems
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