Rational Points on Elliptic Curves

by Joseph H. Silverman

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.

Genres: Mathematics, Number Theory, Nonfiction, Textbooks, Geometry, Algebra, Reference

291 pages, Kindle Edition

First published June 24, 1992

Reviews

[Dave Neary · Rating 4 out of 5]

Some dense math! I want to go back and review the exercises in chapters 3-6.

[Molidere · Rating 4 out of 5]

Solid undergrad level treatment of one of the more fashionable areas of mathematics. The majority of the book is comprehensible to someone entering their Second Year of University study (in the UK at least). Should even be approachable to sophisticated high-school students who have familiarised themselves with some Group Theory and the like. A little brisk at points but one is unlikely to find a better treatment at this level.

[azazo · Rating 4 out of 5]

Excellent beginner-friendly book on elliptic curves with a view towards solutions of Diophantine equations. While the last chapter on complex multiplication may feel sort of out of place, it's still a good introduction to a relatively complex (haha) topic. The exercises at the end of each chapter also help to consolidate the content. If you want to learn more about elliptic curves but are daunted by "The Arithmetic of Elliptic Curves" by the same author, this book is for you :)

[Rebekah Mercer · Rating 5 out of 5]

It was fun to be reminded of proofs of infinite descent, and proofs involving localisation (looking at an object wrt each prime, then piercing together what you learned at the primes to understand the object in a more general sense). The walkthrough of parts of the proof of Fermat's Last Theorem was a fun conclusion, and the explanation of projective coordinates was really the best i've seen :)

[Owen Levens · Rating 5 out of 5]

Came. Hard.