A Comprehensive Course in Number Theory
1st Edition
Published on 11. September 2012
978-1-139-55837-2 (ISBN)
Description
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.
Reviews / Votes
'[Baker] ... possesses ... powerful gifts for precision and concision ... [the book] never seems rushed or artificially compressed. Highly recommended.' D. V. Feldman, ChoiceMore details
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
College/higher education
Professional and scholarly
Illustrations
Worked examples or Exercises; 7 Line drawings, unspecified
File size
2107,36 MB
ISBN-13
978-1-139-55837-2 (9781139558372)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Alan Baker
A Comprehensive Course in Number Theory
Book
08/2012
1st Edition
Cambridge University Press
€149.20
Shipment within 15-20 days
Alan Baker
A Comprehensive Course in Number Theory
Book
08/2012
1st Edition
Cambridge University Press
€55.60
Shipment within 15-20 days
Person
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).
Content
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.
