An Introduction to the Theory of Numbers

by G. H. Hardy, Edward M. Wright, Roger Heath-Brown (Editor), Joseph Silverman (Editor), Andrew Wiles

Overview

An Introduction to the Theory of Numbers by G. H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. Developed under the guidance of D. R. Heath-Brown, this Sixth Edition of An Introduction to the Theory of Numbers has been extensively revised and updated to guide today's students through the key milestones and developments in number theory.

Updates include a chapter by J. H. Silverman on one of the most important developments in number theory — modular elliptic curves and their role in the proof of Fermat's Last Theorem — a foreword by A. Wiles, and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid reader.

The text retains the style and clarity of previous editions making it highly suitable for undergraduates in mathematics from the first year upwards as well as an essential reference for all number theorists.

Product Details

ISBN-13:	9780199219858
Publisher:	Oxford University Press
Publication date:	09/15/2008
Series:	Oxford Mathematics
Edition description:	6th Revised ed.
Pages:	644
Product dimensions:	6.70(w) x 9.30(h) x 1.50(d)

About the Author

Roger Heath-Brown F.R.S. was born in 1952, and is currently Professor of
Pure Mathematics at Oxford University. He works in analytic number theory, and in particular on its applications to prime numbers and to
Diophantine equations.

Table of Contents

Preface to the sixth edition, Andrew WilesPreface to the fifth edition1. The Series of Primes (1)2. The Series of Primes (2)3. Farey Series and a Theorem of Minkowski4. Irrational Numbers5. Congruences and Residues6. Fermat's Theorem and its Consequences7. General Properties of Congruences8. Congruences to Composite Moduli9. The Representation of Numbers by Decimals10. Continued Fractions11. Approximation of Irrationals by Rationals12. The Fundamental Theorem of Arithmetic in k(l), k(i), and k(p)13. Some Diophantine Equations14. Quadratic Fields (1)15. Quadratic Fields (2)16. The Arithmetical Functions ø(n), μ(n), *d(n), *s(n), r(n)17. Generating Functions of Arithmetical Functions18. The Order of Magnitude of Arithmetical Functions19. Partitions20. The Representation of a Number by Two or Four Squares21. Representation by Cubes and Higher Powers22. The Series of Primes (3)23. Kronecker's Theorem24. Geometry of Numbers25. Elliptic Curves, Joseph H. SilvermanAppendixList of BooksIndex of Special Symbols and WordsIndex of NamesGeneral Index

Editorial Reviews

"A really good book!"—Fernando Gouvea, Colby College

From the Publisher