Rational Points on Elliptic Curves

Author:   Joseph H. Silverman ,  John Tate
Publisher:   Springer-Verlag New York Inc.
Edition:   1st ed. 1992. Corr. 2nd printing 1994
ISBN:  

9780387978253


Pages:   281
Publication Date:   24 June 1992
Replaced By:   9783319185873
Format:   Hardback
Availability:   Awaiting stock   Availability explained
The supplier is currently out of stock of this item. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out for you.

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Rational Points on Elliptic Curves


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Overview

The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. ""Rational Points on Elliptic Curves"" streses 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.

Full Product Details

Author:   Joseph H. Silverman ,  John Tate
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1st ed. 1992. Corr. 2nd printing 1994
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   1.320kg
ISBN:  

9780387978253


ISBN 10:   0387978259
Pages:   281
Publication Date:   24 June 1992
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Replaced By:   9783319185873
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock   Availability explained
The supplier is currently out of stock of this item. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out for you.

Table of Contents

I Geometry and Arithmetic.- II Points of Finite Order.- III The Group of Rational Points.- IV Cubic Curves over Finite Fields.- V Integer Points on Cubic Curves.- VI Complex Multiplication.- Appendix A Projective Geometry.- 1. Homogeneous Coordinates and the Projective Plane.- 2. Curves in the Projective Plane.- 3. Intersections of Projective Curves.- 4. Intersection Multiplicities and a Proof of Bezout’s Theorem.- Exercises.- List of Notation.

Reviews

From the reviews: <p> 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 <p> 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. a ] The examples really pull together the material and make it clear. a ] a great book for a first introduction to the subject of elliptic curves. a ] very clearly written and you will understand a lot when you are done. (Allen Stenger, The Mathematical Association of America, August, 2008)


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)


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)


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