Algebra Seminar - MA841 - Fall
2015 |

Course Home Page |

Course: MA845

Instructor: Jared Weinstein

Lectures: MWF 12-1 in PSY B36

Office Hour: F 3-4 in MCS 227

This course is an introduction to the arithmetic theory of elliptic curves. We'll cover some basic algebraic geometry and the theory of algebraic curves. Then we'll discuss elliptic curves over the complex field, finite fields, and p-adic fields. The goal will be to show that the Mordell-Weil rank of an elliptic curve is finite. Time permitting, we may discuss the relationship to modular forms.

*The Arithmetic of Elliptic Curves*, by Joseph Silverman

Weekly assignments account for 100% of your grade in this course. Assignments will appear on this page. I won't be collecting them, but each Friday (starting 9/11), we'll spend some time going over the assignments. All students should be prepared to present the solutions they've worked out.

#1, due Sept. 19: 1.1, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.10, 1.12(b), 2.1, 2.5, 2.6, 2.8, 2.14.

#2, due Sept. 26: 3.3, 3.5, 3.6, 3.10, 3.12.

#3, due Oct. 3: 3.14, 3.15, 3.16, 3.18, 3.24.

#4, due Oct. 23: 5.1, 5.2, 5.3, 5.4, 5.6, 5.8.

#5, due Oct. 30: 5.9, 5.11, 5.12, 6.1, 6.2, 6.3.

#6, due Nov. 6: 7.3, 7.5, 7.6, 7.8, 7.9, 7.10.

#7, due Nov. 20: 8.1, 8.2, 8.3, 8.13a, 8.19.

#8, due Dec. 4: 10.2, 10.6, 10.7, 10.8, 10.12c.

MA843 Home Page | Jared Weinstein | Department of Mathematics | Boston University |