Math 5230 - Fall 2008
Algebraic Number Theory

Links:    Recent Announcements     Homework     Grade information    
Instructor Keith Conrad
Email kconrad at math dot uconn dot edu.
Office hours Wed. 2—3:30 in MSB  318.
Course info
Lecture MWF 1:00-1:50, MSB 307.
 
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. More online lecture notes on algebraic number theory are listed here.

Course Handouts

The Gaussian Integers.

Examples of Mordell's equation.

Prime ideal factorization in quadratic fields.

The trace and norm for field extension.

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.

A non-free integral extension.

Discriminants and ramified primes.

Totally ramified extensions and Eisenstein polynomials

Orbits of SL2 and class numbers.

Matrix conjugation and class numbers.

Ostrowski's theorem for number fields.

Exterior powers and base extensions.

Primitive Vectors and SLn.

Class Group Calculations.

Dirichlet's Unit Theorem.

PARI: an introduction and a reference card.

Lucy and Lily, an algebraic number theory game. (For the website to play the game, go here. A lower-dimensional version of the same idea is here.)

Frobenius' proof of the existence of Frobenius elements (an application of localization)

Recent Announcements

8/25: First lecture, first problem set posted.

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. 25
2. Sept. 1
Avg: 90/100 		Set 1.
3. Sept. 8
4. Sept. 15

5. Sept. 22
Avg: 81/100 		Set 2.
6. Sept. 29
7. Oct. 6
Avg: 87/100 		Set 3.
8. Oct. 13
9. Oct. 20
Avg: 78/100
Set 4.
10. Oct. 27
Avg: 85/100
Set 5.
11. Nov. 3
12. Nov. 10
13. Nov. 17
Avg: 76/100
Set 6.
14. Nov. 24
None (it's Thanksgiving).
15. Dec. 1

Set 7.
Credit: I respectfully stole the code for much of this page from Glenn Tesler. Thanks, Glenn!