03441cam a22004575i 4500 551 551 11318787 20190904111254.0 m d cr n 130321s1992 xxu| s |||| 0|eng d 9781475742527 9781441931016 (print) 10.1007/978-1-4757-4252-7 doi (WaSeSS)ssj0000899291 WaSeSS QA567.2 SIL 2010. PBMW bicssc MAT012010 bisacsh 516.35 23 Silverman, Joseph H. author. Rational Points on Elliptic Curves Rational Points on Elliptic Curves [electronic resource] / by Joseph H. Silverman, John Tate. x, 281 p.: ill.; Undergraduate Texts in Mathematics, 0172-6056 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. License restrictions may limit access. In 1961 the second author deliv1lred a series of lectures at Haverford Col lege on the subject of "Rational Points on Cubic Curves. " These lectures, intended for junior and senior mathematics majors, were recorded, tran scribed, and printed in mimeograph form. Since that time they have been widely distributed as photocopies of ever decreasing legibility, and por tions have appeared in various textbooks (Husemoller [1], Chahal [1]), but they have never appeared in their entirety. In view of the recent inter est in the theory of elliptic curves for subjects ranging from cryptogra phy (Lenstra [1], Koblitz [2]) to physics (Luck-Moussa-Waldschmidt [1]), as well as the tremendous purely mathematical activity in this area, it seems a propitious time to publish an expanded version of those original notes suitable for presentation to an advanced undergraduate audience. We have attempted to maintain much of the informality of the orig inal Haverford lectures. Our main goal in doing this has been to write a textbook in a technically difficult field which is "readable" by the average undergraduate mathematics major. We hope we have succeeded in this goal. The most obvious drawback to such an approach is that we have not been entirely rigorous in all of our proofs. In particular, much of the foundational material on elliptic curves presented in Chapter I is meant to explain and convince, rather than to rigorously prove. Mathematics. Geometry, algebraic. Mathematics. Algebraic Geometry. Tate, John. SpringerLink (Online service) Springer eBooks SpringerLink ebooks - Mathematics and Statistics (Archive) Printed edition: 9781441931016 Undergraduate Texts in Mathematics, http://www.columbia.edu/cgi-bin/cul/resolve?clio11318787 Full text available from SpringerLink ebooks - Mathematics and Statistics (Archive) Vendor-generated brief record lcc BK 0 0 lcc 0 0 MZUNILIB MZUNILIB 2016-03-17 0 QA 567.2 SIL 2010 MzULM-001324 2016-03-17 00:00:00 1324 2016-03-17 BK 0 0 lcc 0 0 MZUNILIB MZUNILIB 2016-03-17 0 QA 567.2 SIL 2010 MzULM-001323 2016-03-17 00:00:00 1323 2016-03-17 BK