An Introduction to the Theory of Numbers

An Introduction to the Theory of Numbers


By (author) Godfrey H. Hardy, By (author) Edward M. Wright, Volume editor Roger Heath-Brown, Volume editor Joseph H. Silverman

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  • Publisher: Oxford University Press
  • Format: Paperback | 656 pages
  • Dimensions: 155mm x 231mm x 36mm | 975g
  • Publication date: 1 October 2008
  • Publication City/Country: Oxford
  • ISBN 10: 0199219869
  • ISBN 13: 9780199219865
  • Edition: 6, Revised
  • Edition statement: 6th Revised edition
  • Illustrations note: 10 black and white line drawings
  • Sales rank: 116,693

Product description

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.

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Author information

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.

Review quote

Review from previous edition Mathematicians of all kinds will find the book pleasant and stimulating reading, and even experts on the theory of numbers will find that the authors have something new to say on many of the topics they have selected... Each chapter is a model of clear exposition, and the notes at the ends of the chapters, with the references and suggestions for further reading, are invaluable. Nature This fascinating book... gives a full, vivid and exciting account of its subject, as far as this can be done without using too much advanced theory. Mathematical Gazette important reference work... which is certain to continue its long and successful life... Mathematical Reviews ...remains invaluable as a first course on the subject, and as a source of food for thought for anyone wishing to strike out on his own. Matyc Journal

Table of contents

PREFACE TO THE SIXTH EDITION ; PREFACE TO THE FIFTH EDITION ; 1. The Series of Primes (1) ; 2. The Series of Primes (2) ; 3. Farey Series and a Theorem of Minkowski ; 4. Irrational Numbers ; 5. Congruences and Residues ; 6. Fermat's Theorem and its Consequences ; 7. General Properties of Congruences ; 8. Congruences to Composite Moduli ; 9. The Representation of Numbers by Decimals ; 10. Continued Fractions ; 11. Approximation of Irrationals by Rationals ; 12. The Fundamental Theorem of Arithmetic in k(l), k(i), and k(p) ; 13. Some Diophantine Equations ; 14. Quadratic Fields (1) ; 15. Quadratic Fields (2) ; 16. The Arithmetical Functions o(n), (n), *d(n), sigma(n), r(n) ; 17. Generating Functions of Arithmetical Functions ; 18. The Order of Magnitude of Arithmetical Functions ; 19. Partitions ; 20. The Representation of a Number by Two or Four Squares ; 21. Representation by Cubes and Higher Powers ; 22. The Series of Primes (3) ; 23. Kronecker's Theorem ; 24. Geometry of Numbers ; 25. Elliptic Curves ; APPENDIX ; LIST OF BOOKS ; INDEX OF SPECIAL SYMBOLS AND WORDS ; INDEX OF NAMES ; GENERAL INDEX