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A Classical Introduction to Modern Number Theory

  • Kenneth Ireland
  • Michael Rosen

Part of the Graduate Texts in Mathematics book series (GTM, volume 84)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Kenneth Ireland, Michael Rosen
    Pages 1-16
  3. Kenneth Ireland, Michael Rosen
    Pages 17-27
  4. Kenneth Ireland, Michael Rosen
    Pages 28-38
  5. Kenneth Ireland, Michael Rosen
    Pages 39-49
  6. Kenneth Ireland, Michael Rosen
    Pages 50-65
  7. Kenneth Ireland, Michael Rosen
    Pages 66-78
  8. Kenneth Ireland, Michael Rosen
    Pages 79-87
  9. Kenneth Ireland, Michael Rosen
    Pages 88-107
  10. Kenneth Ireland, Michael Rosen
    Pages 108-137
  11. Kenneth Ireland, Michael Rosen
    Pages 138-150
  12. Kenneth Ireland, Michael Rosen
    Pages 151-171
  13. Kenneth Ireland, Michael Rosen
    Pages 172-187
  14. Kenneth Ireland, Michael Rosen
    Pages 188-202
  15. Kenneth Ireland, Michael Rosen
    Pages 203-227
  16. Kenneth Ireland, Michael Rosen
    Pages 228-248
  17. Kenneth Ireland, Michael Rosen
    Pages 249-268
  18. Kenneth Ireland, Michael Rosen
    Pages 269-296
  19. Kenneth Ireland, Michael Rosen
    Pages 297-318
  20. Back Matter
    Pages 319-344

About this book

Introduction

This book is a revised and greatly expanded version of our book Elements of Number Theory published in 1972. As with the first book the primary audience we envisage consists of upper level undergraduate mathematics majors and graduate students. We have assumed some familiarity with the material in a standard undergraduate course in abstract algebra. A large portion of Chapters 1-11 can be read even without such background with the aid of a small amount of supplementary reading. The later chapters assume some knowledge of Galois theory, and in Chapters 16 and 18 an acquaintance with the theory of complex variables is necessary. Number theory is an ancient subject and its content is vast. Any intro­ ductory book must, of necessity, make a very limited selection from the fascinat ing array of possible topics. Our focus is on topics which point in the direction of algebraic number theory and arithmetic algebraic geometry. By a careful selection of subject matter we have found it possible to exposit some rather advanced material without requiring very much in the way oftechnical background. Most of this material is classical in the sense that is was dis­ covered during the nineteenth century and earlier, but it is also modern because it is intimately related to important research going on at the present time.

Keywords

Zahlentheorie algebra algebraic number theory arithmetic diophantine equation elliptic curve finite field geometry number theory zeta function

Authors and affiliations

  • Kenneth Ireland
    • 1
  • Michael Rosen
    • 2
  1. 1.Department of MathematicsUniversity of New BrunswickFrederictonCanada
  2. 2.Department of MathematicsBrown UniversityProvidenceUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-1779-2
  • Copyright Information Springer-Verlag New York 1982
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-1781-5
  • Online ISBN 978-1-4757-1779-2
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site