Math 8803, Algebraic Number Theory

Fall 2006

• Instructor: Matt Baker
• Time and place: MWF 10:05 - 10:55, Skiles 246
• E-mail: mbaker@math.gatech.edu.
• Office: 263 Skiles
• Office Hours: Mondays 11-12 and Wednesdays 1-2

Course texts:

• "Algebraic Number Fields" (2nd edition) by Gerald J. Janusz (required)
• "A Brief Guide to Algebraic Number Theory" by H.P.F. Swinnerton-Dyer (recommended)

Files available for downloading: (pdf format)

• Course lecture notes (Last update: 12/27/06)

• Homework Assignment #1
• Homework Assignment #2
• Homework Assignment #3
• Homework Assignment #4
• Homework Assignment #5
• Homework Assignment #6
• Homework Assignment #7

Prerequisites:

Math 6121 or equivalent.

Course outline:

This course is intended to be an introduction to Algebraic Number Theory. The major topics to be covered include rings of integers, factorization in Dedekind domains, finiteness of the class group, Dirichlet's unit theorem, p-adic numbers and p-adic analysis, and the interplay between local and global fields. We will illustrate these concepts with applications to Diophantine equations and cryptography. As time permits, we will also discuss the analytic theory of Dedekind zeta functions and Dirichlet L-functions, and provide an introduction to Class Field Theory.

Exams:

There will be no exams in this class.

Homework:

Homework assignments will be assigned periodically throughout the course, and students are expected to turn in at least half of the assigned problems.

Grading Policy:

Students enrolled in the class will be encouraged to give a talk in an informal seminar accompanying the course, and will be required to complete a 6-10 page final paper on a topic which builds on material learned in the course. Some suggestions for final paper topics can be found here. Grades will be based on homework, class attendance, and the final paper.

Collaboration:

On the homework sets, collaboration is encouraged. However, you must write up your own solutions.