000			02703cam a22002775i 4500
001			GB498
003			IN-BhIIT
005			20231123170513.0
008			130321s1992 xxu|||| o |||| 0|eng
020			_a9788181282699
040			_aIN-BhIIT
041			_aeng
082	0	4	_a516.352 _bSIL/R
100	1		_aSilverman, Joseph H, _eAuthor. _921609
245	1	0	_a Rational points on elliptic curves / _cby Joseph H. Silverman, John Tate.
260			_aNew Delhi : _bSpringer, _c1992.
300			_ax, 281 p. : _bill. ; _c24 cm
490	1		_aUndergraduate Texts in Mathematics,
504			_aIncluding bibliography and index.
505	0		_aI 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.
520			_aIn 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.
650		0	_aAlgebraic geometry. _920673
650	1	4	_aAlgebraic Geometry. _920673
700	1		_aTate, John, _eJoint author. _921610
942			_cGB
999			_c12918 _d12918