Math 254A - Number Theory

Instructor: Brian Osserman

Lectures: MWF 11:00-12:00pm, Room 65 Evans

Course Control Number: 55182

Office: 767 Evans, e-mail:

Office Hours: M 3:00-4:00pm, W 1:00-2:00pm, F 2:00-3:00pm

Prerequisites: Math 250A required, 115 and 250B recommended

Required Text: Lang, Algebraic Number Theory

Recommended Reading: Cox, Primes of the form x^2+ny^2

Syllabus: Roughly, we will cover algebraic number theory from scratch, using Lang's book with examples and motivation from other sources. Advanced topics such as class field theory and Tchebotarev density will be discussed with an emphasis on the statements and applications, so proofs of these will be omitted, and they will be treated in the classical language of ideals rather than ideles and group cohomology.

Grading: Homework: 2/3rds of grade, final paper: 1/3rd of grade.

Homework: Homework will be assigned weekly, on Mondays, except that they will be assigned the previous Friday when Mondays are holidays.


Final paper guidelines

The purpose of the final paper is twofold: to learn in detail about a topic not covered in class, and to practice mathematical writing. As such, it will be graded as much on clarity of writing as on any other factors.

Guidelines:

Lecture notes

I will attempt to type up and post lecture notes. If I have not prepared notes for a lecture, I will give advance warning. Actual problem sets are posted below, so feel free to ignore exercises mentioned in the lecture notes.

Problem sets