Elliptic Tales: Curves, Counting, and Number Theory

Avner Ash · Robert Gross

Mar 2012 · Princeton University Press

About this ebook

A look at one of the most exciting unsolved problems in mathematics today

Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics—the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.

The key to the conjecture lies in elliptic curves, which may appear simple, but arise from some very deep—and often very mystifying—mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and, in the process, venture to the very frontiers of modern mathematics.

Ratings and reviews

I bought this book to familiarize myself with elliptic curves and their properties. While I have cursory understanding of math topics explored in the book, I am by no measure an expert, so I knew that there will be things in the book that I would not be able to understand without additional studies. However, somewhat surprisingly, I found this book accessible, challenging, and highly rewarding. It forced me to pull together my knowledge of number theory, modular arithmetic complex analysis, and a few other topics, and, as a result, I feel that I have improved my mathematical thinking. I now have other topics I want to explore. I strongly recommend this book to math enthusiasts who are ready to explore elliptic curves.

About the author

Avner Ash is professor of mathematics at Boston College. Robert Gross is associate professor of mathematics at Boston College. They are the coauthors of Fearless Symmetry: Exposing the Hidden Patterns of Numbers (Princeton).