A Comprehensive Course in Number Theory

The author's classic concise introduction now fully updated and developed to suit courses extending from primers to introductions to research.

Alan Baker (Author)

9781107019010, Cambridge University Press

Hardback, published 23 August 2012

268 pages, 7 b/w illus. 195 exercises
22.9 x 15.2 x 1.9 cm, 0.57 kg

'[Baker] … possesses … powerful gifts for precision and concision … [the book] never seems rushed or artificially compressed. Highly recommended.' D. V. Feldman, Choice

Developed from the author's popular text, A Concise Introduction to the Theory of Numbers, this book provides a comprehensive initiation to all the major branches of number theory. Beginning with the rudiments of the subject, the author proceeds to more advanced topics, including elements of cryptography and primality testing, an account of number fields in the classical vein including properties of their units, ideals and ideal classes, aspects of analytic number theory including studies of the Riemann zeta-function, the prime-number theorem and primes in arithmetical progressions, a description of the Hardy–Littlewood and sieve methods from respectively additive and multiplicative number theory and an exposition of the arithmetic of elliptic curves. The book includes many worked examples, exercises and further reading. Its wider coverage and versatility make this book suitable for courses extending from the elementary to beginning graduate studies.

Preface
Introduction
1. Divisibility
2. Arithmetical functions
3. Congruences
4. Quadratic residues
5. Quadratic forms
6. Diophantine approximation
7. Quadratic fields
8. Diophantine equations
9. Factorization and primality testing
10. Number fields
11. Ideals
12. Units and ideal classes
13. Analytic number theory
14. On the zeros of the zeta-function
15. On the distribution of the primes
16. The sieve and circle methods
17. Elliptic curves
Bibliography
Index.

Subject Areas: Computer science [UY], Number theory [PBH], Mathematics [PB], Coding theory & cryptology [GPJ]