A Comprehensive Course in Number Theory [NOOK Book]

Overview

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 ...
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A Comprehensive Course in Number Theory

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Overview

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.
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Editorial Reviews

From the Publisher
"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

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Product Details

  • ISBN-13: 9781139564458
  • Publisher: Cambridge University Press
  • Publication date: 7/26/2012
  • Sold by: Barnes & Noble
  • Format: eBook
  • Sales rank: 1,247,404
  • File size: 6 MB

Meet the Author

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).

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Table of Contents

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.

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