Elementary Number Theory 2nd Edition / Edition 2 available in Hardcover
- Pub. Date:
- McGraw-Hill Companies, The
This book is intended for an introductory course in number theory, primarily taken by mathematics majors. The author wrote the text with four main goals in mind. He wrote a book that is both easy to read and easy to teach from. The author also aims to ease students into using proofs, and to develop a self-confidence in mathematics surrounding the difficulty of mathematical proof. Although the main users of this text will be mathematics students, a large audience could easily use the book.
|Publisher:||McGraw-Hill Companies, The|
|Series:||International Series in Pure and Applied Mathematics|
|Product dimensions:||6.50(w) x 9.50(h) x 0.82(d)|
Table of ContentsCreditsPreface 0 What is Number Theory? 1 Divisibility 1.1 The GCD and LCM 1.2 The Division Algorithm 1.3 The Euclidean Algorithm 1.4 Linear Combinations 1.5 Congruences 1.6 Mathematical Induction 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 A Set of Primes is Infinite 2.6 A Formula for ¬(n) 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 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 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 6 The Number Theory of the Reals (and more...)