LEADER 02449nam 22004095a 450 001 9910151938003321 005 20091109150325.0 010 $a3-03719-515-0 024 70$a10.4171/015 035 $a(CKB)3710000000953795 035 $a(CH-001817-3)35-091109 035 $a(PPN)178155071 035 $a(EXLCZ)993710000000953795 100 $a20091109j20060214 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOne Semester of Elliptic Curves$b[electronic resource] /$fTorsten Ekedahl 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2006 215 $a1 online resource (138 pages) 225 0 $aEMS Series of Lectures in Mathematics (ELM) ;$x2523-5176 330 $aThese lecture notes grew out of a one semester introductory course on elliptic curves given to an audience of computer science and mathematics students, and assume only minimal background knowledge. After having covered basic analytic and algebraic aspects, putting special emphasis on explaining the interplay between algebraic and analytic formulas, they go on to some more specialized topics. These include the j-function from an algebraic and analytic perspective, a discussion of elliptic curves over finite fields, derivation of recursion formulas for the division polynomials, the algebraic structure of the torsion points of an elliptic curve, complex multiplication, and modular forms. In an effort to motivate basic problems the book starts very slowly, but considers some aspects such as modular forms of higher level which are not usually treated. It presents more than 100 exercises and a Mathematica? notebook that treats a number of calculations involving elliptic curves. The book is aimed at students of mathematics with a general interest in elliptic curves but also at students of computer science interested in their cryptographic aspects. 606 $aAlgebraic geometry$2bicssc 606 $aConvex and discrete geometry$2msc 606 $aAlgebraic geometry$2msc 615 07$aAlgebraic geometry 615 07$aConvex and discrete geometry 615 07$aAlgebraic geometry 686 $a52-xx$a14-xx$2msc 700 $aEkedahl$b Torsten$0471656 801 0$bch0018173 906 $aBOOK 912 $a9910151938003321 996 $aOne semester of elliptic curves$9229439 997 $aUNINA