Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included. This book covers key concepts of number theory and could serve as a first course on the subject. It delves into more advanced topics and an exploration of related mathematics. It contains, for example, complete proofs of the Hasse–Minkowski theorem and the prime number theorem, as well as self-contained accounts of the character theory of finite groups and the theory of elliptic functions. Bridging the gap between elementary number theory and the systematic study of advanced topics, Modern Number Theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical development is stressed throughout, along with wide-ranging coverage of significant results with comparatively elementary proofs, some of them new.
Philip M. Maynard received his Bachelor of Arts (Honours) (1983) and his Certificate of Advanced Studies (Distinction) (1984) from Trinity College, Cambridge University. He received his PhD from Queen’s University in 1987 and was inducted into the Royal Society of Canada in 2006. He has been a faculty member at the Université de Montréal since 2002. Before moving to Montreal he was a mathematics professor at the University of Georgia (UGA) from 1991 until 2002. His work is mainly in number theory, in particular analytic number theory.
| Preface Chapter 1. Foundations of Number Theory Introduction to Number Theory Natural Numbers, Integers, and Rational Numbers Divisibility and the Division Algorithm Greatest Common Divisor and Euclidean Algorithm Prime Numbers and Their Properties Chapter 2. Congruences and Modular Arithmetic Definition of Congruences Properties of Congruences Linear Congruences Complete and Reduced Residue Systems Chinese Remainder Theorem Chapter 3. Diophantine Equations Introduction to Diophantine Equations Linear Diophantine Equations The Pythagorean Triples Diophantine analysis Pell’s Equation Chapter 4. Arithmetic Functions Euler’s Totient Function (φ-Function) Möbius Function and Möbius Inversion Divisor Function Sigma Function and Aliquot Sums Multiplicative Functions Chapter 5. Prime Numbers and Primality Prime Counting Function Prime Number Theorem Sieve of Eratosthenes Sieve of Sundaram and Sieve of Atkin Distribution of Primes |
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$280.00