A Comprehensive Course in Number Theory

Alan Baker (University of Cambridge)

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English

Cambridge University Press
23 August 2012

Coding theory & cryptology; Mathematics & Sciences; Number theory

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.

By: Alan Baker (University of Cambridge)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 228mm, Width: 152mm, Spine: 15mm
Weight: 390g
ISBN: 9781107603790
ISBN 10: 110760379X
Pages: 264
Publication Date: 23 August 2012
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

Alan Baker is Emeritus Professor of Pure Mathematics in the University of Cambridge and Fellow of Trinity College, Cambridge. His many distinctions include the Fields Medal (1970) and the Adams Prize (1972).

Reviews for A Comprehensive Course in Number Theory

'[Baker] ... possesses ... powerful gifts for precision and concision ... [the book] never seems rushed or artificially compressed. Highly recommended.' D. V. Feldman, Choice Now the idea of a 250-page comprehensive introduction to number theory may seem audacious, but among mathematical writers, Baker manifestly possesses the powerful gifts for precision and concision that could even make it possible. Such a book surely demands very careful study, but amazingly never seems rushed or artificially compressed. Highly recommended. D.V. Feldman, University of New Hampshire for Choice Magazine Any competent instructor could use this as the starting point of a valuable course. Richard T. Bumby, Mathematical Reviews