E-mail: harryt@umd.edu
Course guide:
- Text: Helmut Koch,
Number Theory: Algebraic Numbers and Functions,
American Mathematical Society, 2000.
- Content:
- This is a graduate course in algebraic number theory. I
will assume that people taking this course have a working knowledge of
graduate level abstract algebra, especially rings, modules, and Galois
theory. Many of these concepts were developed in tandem with the
subject at hand, and indeed this course is highly recommended for all
students with an interest in algebra and its applications.
Our main goal is to understand the
structure of the ring of integers in an algebraic number field, and
explain the analogy between this picture and the corresponding one for
function fields. We will begin with Minkowski's theorem and Dirichlet's
unit theorem, and continue with the results of Dedekind on unique
factorization. After we cover the basic theory, there are several topics
to choose from, and I plan to include a discussion of function fields,
zeta functions and L-series.
- Homework:
- I plan to distribute some homework problems during the
course. The homework will be assigned on Thursday and is due in class on
the Thursday two weeks later. I encourage you to work on the
homework assignments; the only way to learn mathematics is to do
mathematics!
- READ
THIS:
- University
of Maryland course related policies. Includes a discussion of
academic integrity, the honor pledge, and accommodations for students
with disabilities.
- Office Hours:
- Feel free to come by my office
and talk at any time, either by chance or by appointment.
HOMEWORK
Assignment 1 (Due 9/12/24):
tex,
ps,
pdf
Assignment 2 (Due 9/26/24):
tex,
ps,
pdf
Assignment 3 (Due 10/10/24):
tex,
ps,
pdf
Assignment 4 (Due 10/24/24):
tex,
ps,
pdf
Assignment 5 (Due 11/7/24):
tex,
ps,
pdf
Assignment 6 (Due 12/3/24):
tex,
ps,
pdf