Rational Points on Elliptic Curves

Rational Points on Elliptic Curves

Hardback Undergraduate Texts in Mathematics

By (author) Joseph H. Silverman, By (author) John T. Tate

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  • Publisher: Springer-Verlag New York Inc.
  • Format: Hardback | 281 pages
  • Dimensions: 165mm x 236mm x 20mm | 544g
  • Publication date: 18 November 1994
  • Publication City/Country: New York, NY
  • ISBN 10: 0387978259
  • ISBN 13: 9780387978253
  • Edition: 4
  • Edition statement: 1st ed. 1992. Corr. 2nd printing 1994
  • Illustrations note: biography
  • Sales rank: 536,850

Product description

The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book's accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.

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Review quote

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)

Table of contents

I Geometry and Arithmetic.- II Points of Finite Order.- III The Group of Rational Points.- IV Cubic Curves over Finite Fields.- V Integer Points on Cubic Curves.- VI Complex Multiplication.- Appendix A Projective Geometry.- 1. Homogeneous Coordinates and the Projective Plane.- 2. Curves in the Projective Plane.- 3. Intersections of Projective Curves.- 4. Intersection Multiplicities and a Proof of Bezout's Theorem.- Exercises.- List of Notation.