Undergraduate Seminar (Fall 2015): Elliptic Curves

Organizer

Daniel Gulotta

Email

dgulotta .at. math.columbia.edu

Prerequisites

Experience with proofs and elementary number theory is recommended.

Location and time

Monday and Wednesday 4:10-5:10 PM in 622 Math.

Office Hours

I will be in the help room (406 Math) on Mondays from 1-2pm, Tuesdays from 3-4pm, and Fridays from 12-1pm. Let me know if you want to meet at some other time.

Resources

The main reference for the couse will be:

• Rational Points on Elliptic Curves by Joseph Silverman and John Tate.
  Columbia students can get a free PDF copy and reduced price softcover copy here.

The following reference isn't required, but you may want to take a look at it to get a different perspective on the material.

• Elliptic Curves: Number Theory and Cryptography by Lawrence Washington.
  Columbia students can get a free PDF copy here. (The PDF of chapter 2 is unreadable in some places, but the other chapters seem to be okay.)

Requirements

Each student will give two 50-minute lectures and write a paper (approximately 10 pages) on a topic related to the course. A third lecture is optional.

The goal of the paper assignment is to learn something new about a topic related to the class, and then write an article to introducing the topic to other undergraduate mathematics majors. Here is a list of suggested topics for the paper. If you want some ideas on how to structure your paper, you can look at some examples here, or ask me. The first draft will be due before Thanksgiving break, and the final version will be due on the last day of classes.

I recommend that you use LaTeX to typeset your paper. A good reference for LaTeX is The Not So Short Introduction to LaTeX2e. Detexify is useful for looking up LaTeX symbols.

Some useful mathematical writing resources:

• Writing a Phase Two Math Paper by Steven Kleiman. The first page and a half refers to an old MIT writing requirement, but the rest is still useful.
• Mathematical Writing by Donald Knuth, Tracy Larrabee, and Paul Roberts.

Schedule of talks

All references are to Silverman and Tate unless otherwise noted. [IR] refers to A Classical Introduction to Modern Number Theory by Ireland and Rosen.