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A Classical Introduction to Modern Number Theory

  • Textbook
  • © 1990

Overview

Authors:
  1. Kenneth Ireland
    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Michael Rosen

    1. Department of Mathematics, Brown University, Providence, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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
    Download chapter PDF

  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
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Keywords

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

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