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-xiv
  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. Kenneth Ireland, Michael Rosen
    Pages 319-338

About this book

Introduction

Bridging the gap between elementary number theory and the systematic study of advanced topics, A Classical Introduction to Modern Number Theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical development is stressed throughout, along with wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. An extensive bibliography and many challenging exercises are also included. This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves.

Keywords

Zahlentheorie algebra finite field geometry number theory

Authors and affiliations

  • Kenneth Ireland
  • Michael Rosen
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-2103-4
  • Copyright Information Springer-Verlag New York 1990
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3094-1
  • Online ISBN 978-1-4757-2103-4
  • Series Print ISSN 0072-5285
  • About this book