Author Profile

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.

About The Book

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.

Table of Contents

Preface
Chapter 1. Foundations of Number Theory
Chapter 2. Congruences and Modular Arithmetic
Chapter 3. Diophantine Equations
Chapter 4. Arithmetic Functions
Chapter 5. Prime Numbers and Primality
Chapter 6. Fermat’s Theorems and Euler’s Theorem
Chapter 7. Quadratic Residues and Reciprocity
Chapter 8. Continued Fractions
Chapter 9. Algebraic Number Theory
Chapter 10. Transcendental Number Theory
Bibliography