# Syllabus for Math 581F (Fall 2007 at UW)

**Instructor:** William Stein (wstein@gmail.com; http://wstein.org)

**Course web page:** http://wiki.wstein.org/ant07

**Google group mailing list:** http://groups.google.com/group/uw-581f

**Office Hours:** Tuesday and Thursday 2-3pm

## Content

This course will have a strong mix of serious theory and algorithms. 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 the course textbook (or see this mirror). This book closely follows Swinnerton-Dyer and Cassels' classics.

### Course Topics

- Commutative algebra
- Dedekind domains
- Ideal class groups
- Unit groups
- Decomposition and inertia groups, ramification
- Galois representations
- The zeta function and the class number formula (statement only)
- Local fields
- Algebraic number theory computation using Sage

## Prerequisites

In addition to general mathematical maturity (you know what a proof is, and you've written some), this course assumes that you are familiar with the basics of:

- Finite groups
- Commutative rings, ideals, and quotient rings
- Elementary number theory
- Galois theory of fields
- Point set topology

## Your Grade

### Homework

There will be weekly homework assignments, worth 40% of your grade. Your lowest **two** homework grades will be dropped. No late homework will be accepted.

Homework will be assigned on Wednesday and **due on Wednesday**. On Wednesday, homework will be turned in, then *randomly redistributed to the other students in the class, who will grade it*. They will then turn in the graded homework. I will grade the result (and can change the grades however I want), and return the graded homework on Monday.

### Exams

There will be exactly one midterm take-home exam, which is worth 30% of your grade. It will be given on **Friday, November 2, 2007** and be due on **Monday, November 5, 2007**.

### Final Project

There will be a final project, which is worth 30% of your grade. It will be due **December 7, 2007**. Start thinking about your project... right now!