Course text:

Notes on Algebraic Number Theory by J.S. Milne

Announcements:

• The final exam will be handed out in class on Tuesday, December 3 and will be due in class on Monday, December 9. Late exams will not be accepted.

Files available for downloading: (pdf format)

• Final examination
• Exposition of the paper "Primes is in P"

• Lecture 1 (8/20/02)
• Lecture 2 (8/22/02)
• Supplement to Lecture 2
• Lecture 3 (8/27/02)
• Lecture 4 (8/29/02)
• Lecture 5 (9/03/02)
• Lecture 6 (9/05/02)
• Lecture 7 (9/10/02)
• Lecture 8 (9/12/02)
• Lecture 9 (9/17/02)
• Lecture 10 (9/19/02)
• Lecture 11 (9/24/02)
• Lecture 12 (9/26/02)
• Lecture 13 (10/01/02)
• Lecture 14 (10/03/02)
• Lecture 15 (10/08/02)
• Lecture 16 (10/10/02)
• Lecture 17 (10/15/02)
• Lecture 18 (10/22/02)
• Lecture 19 (10/24/02)
• Lecture 20 (10/29/02)
• Lecture 21 (11/05/02)
• Lecture 22 (11/07/02)
• Lecture 23 (11/12/02)
• Lecture 24 (11/14/02)

• Homework Assignment #1
• Homework Assignment #2
• Homework Assignment #3
• Homework Assignment #4
• Homework Assignment #5
• Homework Assignment #6
• Homework Assignment #7
• Homework Assignment #8

• Solutions to Homework #1
• Solutions to Homework #2
• Solutions to Homework #3
• Solutions to Homework #4
• Solutions to Homework #5
• Solutions to Homework #6
• Solutions to Homework #7

Prerequisites:

Math 6000 and 6010 or equivalent, or permission of instructor.

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, and the interplay between local and global fields. We will put a particular emphasis on applications to diophantine equations.

We will roughly cover Chapters 2-5 of Milne's notes, as well as parts of Chapters 6-8. We will cover or refer to Chapter 1 (Preliminaries from Commutative Algebra) as needed. We may also discuss some additional topics, including zeta functions of number fields, p-adic analysis, and an introduction to Class Field Theory, as time permits.

Exams:

There will be an in-class midterm exam and a take-home final exam.

Homework:

Sesqui-weekly homework assignments will be assigned.

Collaboration:

On the homework sets, collaboration is not only allowed but encouraged. However, you must write up and understand your own individual homework solutions, and you may not share written solutions. If you learn how to solve a problem by talking to a classmate or looking it up in a book, you should cite the source in your homework write-up, just as you would reference your sources in a literature or history class. On the take-home final exam, collaboration is not permitted and, if detected, will result in a score of zero for that exam.

Miscellany:

If at any point during the semester you feel unsatisfied with some aspect of the course, please come talk to me. I don't give lectures to hear myself talk, I give them to help you learn Algebraic Number Theory! I *will* make adjustments if it is brought to my attention that I am going too fast or too slow, that the course is too easy or too hard, etc.