01849nam a2200205Ia 4500 CTU_134093 210402s9999 xx 000 0 und d 1477000 516.352 E10 Ekedahl, Torsten One Semester of Elliptic curves Torsten Ekedahl Germany European Mathematical Society 2006 These 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 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 TM 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. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Curves, Elliptic,Đường cong, Elip Trọng Hải Trung tâm Học liệu Trường Đại học Cần Thơ