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An Introduction to the Theory of Numbers

Sixth Edition

G. H. Hardy and E. M. Wright
Edited by Roger Heath-Brown, Joseph Silverman, and Andrew Wiles

31 July 2008

ISBN: 9780199219865

656 pages
Paperback
234x156mm

In Stock

Price: £46.49

The sixth edition of the classic undergraduate text in elementary number theory includes a new chapter on elliptic curves and their role in the proof of Fermat's Last Theorem, a foreword by Andrew Wiles and extensively revised and updated end-of-chapter notes.

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Description

The sixth edition of the classic undergraduate text in elementary number theory includes a new chapter on elliptic curves and their role in the proof of Fermat's Last Theorem, a foreword by Andrew Wiles and extensively revised and updated end-of-chapter notes.

  • Much-needed update of a classic text
  • Extensive end-of-chapter notes
  • Suggestions for further reading for the more avid reader
  • New chapter on one of the most important developments in number theory and its role in the proof of Fermat's Last Theorem

New to this edition

  • Revised end-of-chapter notes
  • New chapter on elliptic curves

About the Author(s)

G. H. Hardy, Formerly of the University of Cambridge, and E. M. Wright, Formerly of the University of Aberdeen

Edited by Roger Heath-Brown, Professor of Pure Mathematics, Oxford University, Joseph Silverman, and Andrew Wiles

Table of Contents

    Preface to the sixth edition, Andrew Wiles
    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 ø(n), µ(n), *d(n), *s(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, Joseph H. Silverman
    Appendix
    List of Books
    Index of Special Symbols and Words
    Index of Names
    General Index

Reviews

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

...an 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

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