Math 748, Algebraic Number Theory - Fall 2006

Rafe Jones

317 Van Vleck
Telephone: 263-5640
E-mail: jones [at] math [dot] wisc [dot] edu

Office Hours: MW 2:15-3:45 and by appointment

Links to articles on the Chebotarev density theorem:

The first is a short (5-page) description of how Chebotarev's Thm determines the statistics of factorization mod p of polynomials. It has some nice exercises at the end. The second is an expository article (18 pages) that contains good info on Chebotarev's life, some lovely applications of his theorem (including the mod p factorization statistics mentioned above), and a very comprehensible outline of his original proof.

The Chebotarev density theorem (Lenstra)
Chebotarev and his density theorem (Stevenhagen and Lenstra)

Homepage

Syllabus

Lecture: MWF 12:05-12:55, B223 Van Vleck

Text: Algebraic Number Theory by J.S. Milne. Available at http://www.jmilne.org/math/. You should print out one full copy. Another valuable text that will be a great reference during the course is Algebraic Number Theory by Jurgen Neukirch.

Course Description:

This course is an introduction to algebraic number theory, a beautiful theory that serves as the foundation for much of modern number theory. Topics will include rings of integers, Dedekind domains, factorization of prime ideals, finiteness of the class number, Dirichlet's unit theorem, cyclotomic extensions, and selected topics having to do with valuations, local fields, and global fields.

Homework:

Homework 1, due Monday, September 11

Homework 2, due Monday, September 18

Homework 3, due Wednesday, September 27

Homework 4 , due Wednesday, October 4

Homework 5, due Wednesday, October 11

Homework 6, due Wednesday, October 18

Homework 7, due Wednesday, October 25

Homework 8, due Monday, October 30

Homework 9, due Wednesday, November 8

Homework 10, due Wednesday, November 15

Homework 11, Part a, due Wednesday, November 29

Homework 11, Part b, due Wednesday, November 29

Homework 12, due Wednesday, December 6