Math 581e: Algebraic Number Theory (Fall 2012) -- Syllabus

Basics

Course Webpage: http://wstein.org/edu/2012/ant/
Instructor: William Stein ([email protected])
Office Hours: Wednesday 12:30-2:00pm in Padelford C423

Content

This is a graduate-level course on algebraic number theory (though undergraduates are welcome!). This course will be mostly theoretical (we will prove a lot of results), augmented by tutorials about how to compute with the objects we encounter. We will give complete proofs of the two main theorems of algebraic number theory: finiteness of class groups and the unit theorem. You will also learn how to use Sage to compute with all of the objects discussed in the course. The course textbook is available online.

Main Course Topics

Commutative algebra
Dedekind domains
Ideal class groups
Unit groups
Decomposition and inertia groups, ramification
Algebraic number theory computation using Sage

Prerequisites

In addition to general mathematical maturity (you know what a proof is, and you've written some), I will assume that you are familiar with finite groups, linear algebra, commutative rings, ideals, elementary number theory, Galois theory of fields, topology of Rⁿ, and the Sage mathematics software.

Your Grade

Homework: There will be weekly homework assignments, worth 50% of your grade. Your lowest two homework grades will be dropped. No late homework will be accepted. Homework will typically be due on Fridays.
Final Projects: There will be a final project, which is worth 50% of your grade. It will be due December 7, 2012. Start thinking about your project now! Browse projects from 2007, 2005, 2004.