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© 1992

Rational Points on Elliptic Curves

Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-x
  2. Joseph H. Silverman, John Tate
    Pages 1-8
  3. Joseph H. Silverman, John Tate
    Pages 9-37
  4. Joseph H. Silverman, John Tate
    Pages 38-62
  5. Joseph H. Silverman, John Tate
    Pages 63-106
  6. Joseph H. Silverman, John Tate
    Pages 107-144
  7. Joseph H. Silverman, John Tate
    Pages 145-179
  8. Joseph H. Silverman, John Tate
    Pages 180-219
  9. Back Matter
    Pages 220-284

About this book

Introduction

In 1961 the second author deliv1lred a series of lectures at Haverford Col­ lege on the subject of "Rational Points on Cubic Curves. " These lectures, intended for junior and senior mathematics majors, were recorded, tran­ scribed, and printed in mimeograph form. Since that time they have been widely distributed as photocopies of ever decreasing legibility, and por­ tions have appeared in various textbooks (Husemoller [1], Chahal [1]), but they have never appeared in their entirety. In view of the recent inter­ est in the theory of elliptic curves for subjects ranging from cryptogra­ phy (Lenstra [1], Koblitz [2]) to physics (Luck-Moussa-Waldschmidt [1]), as well as the tremendous purely mathematical activity in this area, it seems a propitious time to publish an expanded version of those original notes suitable for presentation to an advanced undergraduate audience. We have attempted to maintain much of the informality of the orig­ inal Haverford lectures. Our main goal in doing this has been to write a textbook in a technically difficult field which is "readable" by the average undergraduate mathematics major. We hope we have succeeded in this goal. The most obvious drawback to such an approach is that we have not been entirely rigorous in all of our proofs. In particular, much of the foundational material on elliptic curves presented in Chapter I is meant to explain and convince, rather than to rigorously prove.

Keywords

Accessibility Area Grad Microsoft Access Multiplication algebra arithmetic field finite field group learning mathematics presentation theorem time

Authors and affiliations

  1. 1.Department of MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of MathematicsUniversity of Texas at AustinAustinUSA

Bibliographic information

  • Book Title Rational Points on Elliptic Curves
  • Authors Joseph H. Silverman
    John Tate
  • Series Title Undergraduate Texts in Mathematics
  • DOI https://doi.org/10.1007/978-1-4757-4252-7
  • Copyright Information Springer-Verlag New York 1992
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-97825-3
  • Softcover ISBN 978-1-4419-3101-6
  • eBook ISBN 978-1-4757-4252-7
  • Series ISSN 0172-6056
  • Edition Number 1
  • Number of Pages X, 281
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebraic Geometry
  • Buy this book on publisher's site
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Reviews

From the reviews:

"The authors' goal has been to write a textbook in a technically difficult field which is accessible to the average undergraduate mathematics major, and it seems that they have succeeded admirably..."--MATHEMATICAL REVIEWS

"This is a very leisurely introduction to the theory of elliptic curves, concentrating on an algebraic and number-theoretic viewpoint. It is pitched at an undergraduate level and simplifies the work by proving the main theorems with additional hypotheses or by only proving special cases. … The examples really pull together the material and make it clear. … a great book for a first introduction to the subject of elliptic curves. … very clearly written and you will understand a lot when you are done." (Allen Stenger, The Mathematical Association of America, August, 2008)