A Comprehensive Course in Number Theory

by Alan Baker

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.

Genres: Mathematics, Number Theory

268 pages, Hardcover

First published August 23, 2012

About the author

Alan Baker was an English mathematician, known for his work on effective methods in Number theory, in particular those arising from transcendence theory. He was awarded the Fields Medal in 1970, at age 31. His academic career started as a student of Harold Davenport, at University College London and later at Cambridge. He was a visiting scholar at the Institute for Advanced Study in the fall of 1970. He is a fellow of Trinity College, Cambridge. His interests were in number theory, transcendence, logarithmic form, effective methods, Diophantine geometry and Diophantine analysis. In 2012 he became a fellow of the American Mathematical Society.

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Reviews

[Mark · Rating 5 out of 5]

The book is a wonderful, fairly advanced, overview of number theory as a whole. The proofs are unusual—terse and conversational in style, but one doesn’t read a book like this for all the details. It packs a lot of history in along the way, too,

[Mills College Library]

512.7 B1671 2012