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  • © 1990

A Classical Introduction to Modern Number Theory

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

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xiv
  2. Unique Factorization

    • Kenneth Ireland, Michael Rosen
    Pages 1-16
  3. Applications of Unique Factorization

    • Kenneth Ireland, Michael Rosen
    Pages 17-27
  4. Congruence

    • Kenneth Ireland, Michael Rosen
    Pages 28-38
  5. The Structure of U(ℤ/nℤ)

    • Kenneth Ireland, Michael Rosen
    Pages 39-49
  6. Quadratic Reciprocity

    • Kenneth Ireland, Michael Rosen
    Pages 50-65
  7. Quadratic Gauss Sums

    • Kenneth Ireland, Michael Rosen
    Pages 66-78
  8. Finite Fields

    • Kenneth Ireland, Michael Rosen
    Pages 79-87
  9. Gauss and Jacobi Sums

    • Kenneth Ireland, Michael Rosen
    Pages 88-107
  10. Cubic and Biquadratic Reciprocity

    • Kenneth Ireland, Michael Rosen
    Pages 108-137
  11. Equations over Finite Fields

    • Kenneth Ireland, Michael Rosen
    Pages 138-150
  12. The Zeta Function

    • Kenneth Ireland, Michael Rosen
    Pages 151-171
  13. Algebraic Number Theory

    • Kenneth Ireland, Michael Rosen
    Pages 172-187
  14. Quadratic and Cyclotomic Fields

    • Kenneth Ireland, Michael Rosen
    Pages 188-202
  15. The Stickelberger Relation and the Eisenstein Reciprocity Law

    • Kenneth Ireland, Michael Rosen
    Pages 203-227
  16. Bernoulli Numbers

    • Kenneth Ireland, Michael Rosen
    Pages 228-248
  17. Dirichlet L-functions

    • Kenneth Ireland, Michael Rosen
    Pages 249-268
  18. Diophantine Equations

    • Kenneth Ireland, Michael Rosen
    Pages 269-296
  19. Elliptic Curves

    • Kenneth Ireland, Michael Rosen
    Pages 297-318
  20. The Mordell-Weil Theorem

    • Kenneth Ireland, Michael Rosen
    Pages 319-338

About this book

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.

Reviews

From the reviews of the second edition:

K. Ireland and M. Rosen

A Classical Introduction to Modern Number Theory

"Many mathematicians of this generation have reached the frontiers of research without having a good sense of the history of their subject. In number theory this historical ignorance is being alleviated by a number of fine recent books. This work stands among them as a unique and valuable contribution."

— MATHEMATICAL REVIEWS

"This is a great book, one that does exactly what it proposes to do, and does it well. For me, this is the go-to book whenever a student wants to do an advanced independent study project in number theory. … for a student who wants to get started on the subject and has taken a basic course on elementary number theory and the standard abstract algebra course, this is perfect." (Fernando Q. Gouvêa, MathDL, January, 2006)

Authors and Affiliations

  • Department of Mathematics, Brown University, Providence, USA

    Michael Rosen

Bibliographic Information

  • Book Title: A Classical Introduction to Modern Number Theory

  • Authors: Kenneth Ireland, Michael Rosen

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-2103-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1990

  • Hardcover ISBN: 978-0-387-97329-6Published: 07 September 1990

  • Softcover ISBN: 978-1-4419-3094-1Published: 01 December 2010

  • eBook ISBN: 978-1-4757-2103-4Published: 17 April 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: XIV, 394

  • Topics: Number Theory

Buy it now

Buying options

eBook USD 69.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 94.95
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access