Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics) [Hardcover]

Joseph H. Silverman (Author), John Tate (Author)

Book Description

ISBN-10: 0387978259 | ISBN-13: 978-0387978253 | Publication Date: June 24, 1992 | Edition: Corrected

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.

Editorial Reviews

Review

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)

Product Details

• Hardcover: 281 pages
• Publisher: Springer; Corrected edition (June 24, 1992)
• Language: English
• ISBN-10: 0387978259
• ISBN-13: 978-0387978253
• Product Dimensions: 9.3 x 6.5 x 0.8 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.8 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #821,828 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

27 of 27 people found the following review helpful:

5.0 out of 5 stars Excellent Introduction to Elliptic Curves, August 23, 1998

By A Customer

This review is from: Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics) (Hardcover)

This wonderful book is an excellent introduction to elliptic curves over the rational numbers. It is self-contained and easily accessible, but still takes the reader quite far, thus giving an undergraduate reader some exciting glimpes of deeper mathematics. This book is ideally suited as a text book for an undergraduate course (I have myself enjoyed it as a course), but is written in a lively style that also makes it fun to read on one's own. It covers such topics as the Nagell-Lutz Theorem, Mordell's Theorem over rational numbers, elliptic curves over finite fields and reduction modulo p, Thue's Theorem and diophantine approximation, and even an introduction to complex multiplication. An appendix provides the reader with a basic background on projective geometry. This book is a must for any student wanting to see beyond the ordinary coursework, and at the same time provides a natural stepping stone to a more advanced treatment of the subject, such as "The Arithmetic of Elliptic Curves", also by Silverman, which has become pretty much the standard text on the subject.

13 of 13 people found the following review helpful:

5.0 out of 5 stars Full of useful information and a great guide to intuition, July 29, 2000

By 

Dr. Lee D. Carlson (Baltimore, Maryland USA) - See all my reviews
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This review is from: Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics) (Hardcover)

The authors do a fantastic job of introducing elliptic curves for individuals and students interested in this area. Because of the importance of elliptic curves to cryptography, in integrable models in statistical mechanics, in superstring theory in physics, in mirror symmetry in algebraic geometry, in mechanics in the solution of the spinning top, and even in financial engineering, this book will be useful in building intuition about these interesting objects. Be careful in reading this book though...the theory of elliptic curves is beautiful and addicting, and you will want no doubt to read more about them after finishing it. There are two other books by Silverman that will alleviate the monkey on your back for more knowledge about elliptic curves. Happy reading......

11 of 14 people found the following review helpful:

4.0 out of 5 stars Friendly, but probably not the best, November 24, 2005

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Viktor Blasjo - See all my reviews
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This review is from: Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics) (Hardcover)

The virtue of this book is its leisurely style; and the subject is very attractive as well. The idea that lies behind this whole theory is the way in which one imposes an arithmetic on the points of an elliptic curve. There is much to be said about this: the whole thing becomes a group, the rational points form a finitely generated group, etc. That's chapters 1-3. In chapters 4-5 we finally get to some number-theoretical applications. First applications to factorisation (and thus to cryptography). Then chapter 5 is on "integer points on cubic curves", which sounds nice and classical, but things quickly turn quite messy. And finally there is chapter 6, on complex multiplication and Kronecker's Jugendtraum, for those who are interested in this extension field business that everybody seems to love. One could certainly read chapter 1-3 as a very elementary and easy-going introduction to the basics of elliptic curve arithmetic. I think the applications are treated better elsewhere, in Koblitz's books for instance.