Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics) | 
 enlarge | Authors: Joseph H. Silverman, John Tate
Publisher: Springer
Category: Book
List Price: $44.95
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Rating:  4 reviews
Sales Rank: 127181
Media: Hardcover
Edition: Corrected
Pages: 281
Number Of Items: 1
Shipping Weight (lbs): 1.2
Dimensions (in): 9.3 x 6.5 x 0.8
ISBN: 0387978259
Dewey Decimal Number: 516.352
EAN: 9780387978253
Publication Date: November 18, 1994
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Condition: New Book. International Shipping Available
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Product Description
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. "Rational Points on Elliptic Curves" stresses this interplay as it develops the basic theory, thereby providing an opportunity for advance undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make "Rational Points on Elliptic Curves" an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry.
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| Customer Reviews:
Excellent Introduction to Elliptic Curves August 23, 1998
22 out of 22 found this review helpful
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.
Full of useful information and a great guide to intuition July 29, 2000
Dr. Lee D. Carlson (Saint Louis, Missouri USA)
10 out of 10 found this review helpful
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......
"It is possible to write endlessly on elliptic curves. (This is not a threat)" July 8, 2008
M_A_S (San Jose, CA)
0 out of 1 found this review helpful
This is great. I wish the prose in more "tougher" maths texts were written in similarly. The math can get so tough (for me) so quickly, but the authors are very gentle. Their conversational style really works.
This is a topic about which I knew almost nothing before-hand, apart from some basic stuff on elliptic curve cryptography (which is not covered here.) Now, at least, I start to see the tip of the iceburg on such a beautiful subject.
 Friendly, but probably not the best November 24, 2005
Viktor Blasjo
7 out of 9 found this review helpful
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.
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