Mathematics 333ec - Topics in Abstract Algebra-Introduction to Eliptic Curves

When doing their favorite cyber activities, one is often relying— perhaps without realizing it—on elliptic curves to keep their personal information secure. In this course, students learn how to use Algebra, Geometry and Number Theory to study the arithmetic of Elliptic Curves. Fundamentally, the question is whether solutions for a given curve exist; and if one exists, what is the structure of the solution set? Discussions include, as time permits: Weierstrass normal form; geometry of elliptic curves and the group law; discriminants; the Nagell–Lutz and Mordell’s Theorems; elliptic curves over finite fields; applications to factorization and cryptography. MTH 233 and MTH 238 are helpful, but not required. Prerequisites: at least two proof-writing courses. (E)