The second edition of this text includes an updated bibliography indicating the latest, dramatic changes in the direction of proving the Birch and Swinnerton conjecture. It also discusses the current state of knowledge of elliptic curves. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Swinnerton-Dyer.

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Bibliographic Details

Title: Introduction to Elliptic Curves and Modular Forms
Publisher: Springer-Verlag New York Inc.
Publication Date: 2012
Language: English
ISBN 10: 1461269423
ISBN 13: 9781461269427
Binding: Paperback
Edition: 2nd Edition
Condition: Good

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Synopsis

This textbook covers the basic properties of elliptic curves and modular forms, with emphasis on certain connections with number theory. The ancient "congruent number problem" is the central motivating example for most of the book. My purpose is to make the subject accessible to those who find it hard to read more advanced or more algebraically oriented treatments. At the same time I want to introduce topics which are at the forefront of current research. Down-to-earth examples are given in the text and exercises, with the aim of making the material readable and interesting to mathematicians in fields far removed from the subject of the book. With numerous exercises (and answers) included, the textbook is also intended for graduate students who have completed the standard first-year courses in real and complex analysis and algebra. Such students would learn applications of techniques from those courses. thereby solidifying their under� standing of some basic tools used throughout mathematics. Graduate stu� dents wanting to work in number theory or algebraic geometry would get a motivational, example-oriented introduction. In addition, advanced under� graduates could use the book for independent study projects, senior theses, and seminar work.

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