2016-17 Academic Catalog

Introduction to the geometry and arithmetic of elliptic curves, with selected advanced topics. Introductory topics include the geometry of cubics, the group law on an elliptic curve, points of finite order, the group of rational points, heights and the Mordell-Weil theorem. Students will have the opportunity to explore through group projects advanced topics such as: integral points on elliptic curves; elliptic curves over finite fields; elliptic curves with complex multiplication; and Galois representations on torsion points. Prerequisite: Mathematics 342, an equivalent Budapest or Moscow Semester in Mathematics course or instructor permission