Math 5230 - Fall 2012
Algebraic Number Theory

Instructor Keith Conrad
Email kconrad at math dot uconn dot edu.
Office hours 4:30-5:30 M, 2:00-3:00 T, or by appointment in MSB  318.
Course info
Lecture MWF 2:00-2:50 in MSB 215.
 
Texts Algebraic Theory of Numbers by Pierre Samuel and Algebraic Number Theory by James Milne. (To get Milne's notes, at the link look in the left margin under Course Notes for the title).

Lecture notes on algebraic number theory by René Schoof (2003), Peter Stevenhagen (2004), and Tom Weston (1999) may be helpful, but are not required.

Course Handouts

The Gaussian Integers.

Examples of Mordell's equation.

Prime ideal factorization in quadratic fields.

The trace and norm for field extensions.

Review of separable field extensions, tensor products of modules, and tensor products of linear maps and algebras.

Separability and the trace map. (See Theorem 1.1)

Unique ideal factorization in rings of integers.

Factorization of ideals by Dedekind's method.

Discriminants and ramified primes.

Totally ramified extensions and Eisenstein polynomials

Orbits of SL2 and class numbers.

Matrix conjugation and class numbers.

PARI: an introduction and some commands specific to algebraic number theory.

Class Group Calculations.

Existence of Frobenius element.

Recent Announcements

8/27: First lecture.

Brief course description: This course is an introduction to algebraic number theory: rings of integers, applications to diophantine equations, ramification, Dirichlet unit theorem, ideal class group, and Frobenius elements in Galois groups. Further topics (e.g., local fields or zeta-functions) will be discussed if time permits.

Prerequisites: Math 5211.

Course grade:  This will be based on homeworks and a take-home final.

Homework: Homework assignments will be posted on the bottom of this web page.



Due Week of Homework Assignment
1. Aug. 26
2. Sept. 2
Set 1.
3. Sept. 9
4. Sept. 16
Set 2.
5. Sept. 23

6. Sept. 30 Set 3.
7. Oct. 7

8. Oct. 14
9. Oct. 21

Set 4.
10. Oct. 28

Set 5.
11. Nov. 4
12. Nov. 11
Set 6.
13. Nov. 18
None (it's Thanksgiving).
14. Nov. 25
15. Dec. 2

15. Dec. 9

15. Dec. 16

Set 7.