LEADER 03765nam 22005415 450 001 9910481019203321 005 20200702154855.0 010 $a1-4757-4252-5 024 7 $a10.1007/978-1-4757-4252-7 035 $a(CKB)2660000000022214 035 $a(SSID)ssj0000899291 035 $a(PQKBManifestationID)11533562 035 $a(PQKBTitleCode)TC0000899291 035 $a(PQKBWorkID)10923719 035 $a(PQKB)11404902 035 $a(DE-He213)978-1-4757-4252-7 035 $a(MiAaPQ)EBC3085867 035 $a(PPN)238039552 035 $a(EXLCZ)992660000000022214 100 $a20130321d1992 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aRational Points on Elliptic Curves$b[electronic resource] /$fby Joseph H. Silverman, John Tate 205 $a1st ed. 1992. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1992. 215 $a1 online resource (X, 281 p.) 225 1 $aUndergraduate Texts in Mathematics,$x0172-6056 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-97825-9 311 $a1-4419-3101-5 320 $aIncludes bibliographical references and index. 327 $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. 330 $aIn 1961 the second author deliv1lred a series of lectures at Haverford Col­ lege on the subject of "Rational Points on Cubic Curves. " These lectures, intended for junior and senior mathematics majors, were recorded, tran­ scribed, and printed in mimeograph form. Since that time they have been widely distributed as photocopies of ever decreasing legibility, and por­ tions have appeared in various textbooks (Husemoller [1], Chahal [1]), but they have never appeared in their entirety. In view of the recent inter­ est in the theory of elliptic curves for subjects ranging from cryptogra­ phy (Lenstra [1], Koblitz [2]) to physics (Luck-Moussa-Waldschmidt [1]), as well as the tremendous purely mathematical activity in this area, it seems a propitious time to publish an expanded version of those original notes suitable for presentation to an advanced undergraduate audience. We have attempted to maintain much of the informality of the orig­ inal Haverford lectures. Our main goal in doing this has been to write a textbook in a technically difficult field which is "readable" by the average undergraduate mathematics major. We hope we have succeeded in this goal. The most obvious drawback to such an approach is that we have not been entirely rigorous in all of our proofs. In particular, much of the foundational material on elliptic curves presented in Chapter I is meant to explain and convince, rather than to rigorously prove. 410 0$aUndergraduate Texts in Mathematics,$x0172-6056 606 $aAlgebraic geometry 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 615 0$aAlgebraic geometry. 615 14$aAlgebraic Geometry. 676 $a516.35 700 $aSilverman$b Joseph H$4aut$4http://id.loc.gov/vocabulary/relators/aut$057147 702 $aTate$b John$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910481019203321 996 $aRational Points on Elliptic Curves$9382657 997 $aUNINA