# Introduction to Elliptic Curves and Modular Forms

• Neal Koblitz
Textbook

Part of the Graduate Texts in Mathematics book series (GTM, volume 97)

1. Front Matter
Pages i-viii
2. Neal Koblitz
Pages 1-50
3. Neal Koblitz
Pages 51-97
4. Neal Koblitz
Pages 98-175
5. Neal Koblitz
Pages 176-222
6. Back Matter
Pages 223-250

### Introduction

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.

### Keywords

Curves Grad Microsoft Access addition algebra algebraic geometry boundary element method elliptic curve form mathematics modular form number theory techniques time tool

#### Authors and affiliations

• Neal Koblitz
• 1
1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4684-0255-1
• Copyright Information Springer-Verlag New York 1984
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4684-0257-5
• Online ISBN 978-1-4684-0255-1
• Series Print ISSN 0072-5285
• Buy this book on publisher's site