Math 620 -- Algebraic Number Theory I

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 dicussion 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 of the following week. 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.