**MA 842 (Explicit methods for elliptic and hyperelliptic curves)**

Instructor: Jennifer Balakrishnan

Time: MW 12:20 - 1:35PM in KCB 201

Office hours: MW 2:30 - 4:00PM
**Course overview**

This course will serve as an introduction to the theory of elliptic
and hyperelliptic curves, and in particular, will explore how explicit
computation can aid in our understanding of several open questions and
conjectures in number theory. We will begin with an overview of elliptic and
hyperelliptic curves; further topics will include algorithms for zeta
and *L*-functions, arithmetic statistics and databases of curves,
finding rational points on curves, and computations motivated by the
Birch and Swinnerton-Dyer conjecture. Throughout, we will make use of various computational packages, such as those available in Sage and Magma. We will also try our hand at a few new large-scale
computations using SageMathCloud or Google Compute Engine.
**Evaluation**

There will be homework assignments (60%) and a final project (40%).
Problem set 1, due February 1

Problem set 2, due February 8

Problem set 3, due February 20

Problem set 4, due March 3

Problem set 5, due March 29

Problem set 6, due April 19