Rational Points on Elliptic Curves

by Joseph H. Silverman, John Tate

Overview

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.

Product Details

ISBN-13:	9780387978253
Publisher:	Springer New York
Publication date:	06/24/1992
Series:	Undergraduate Texts in Mathematics
Edition description:	1992
Pages:	281
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

About the Author

Joseph H. Silverman is Professor of Mathematics at Brown University. He is the author of over 100 research articles and numerous books on elliptic curves, diophantine geometry, cryptography, and arithmetic dynamical systems.

John T. Tate is Professor Emeritus of Mathematics at The University of Texas at Austin and at Harvard University. For his seminal contributions to number theory, he was awarded the 2010 Abel Prize.

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.

Editorial 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)

From the Publisher

Based on a series of lectures for junior and senior mathematics majors. The theory of elliptic curves is used in a range of fields, from cryptography to physics. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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