Information for Math 514a Algebraic Number Theory Fall 1995

Instructor: Doug Ulmer
Office: Math 716
Phone: 621-6861
Office Hours: Mondays and Wednesdays 2-3 in my office,

Wednesdays 1-2 in Math Annex, or by appointment

Class: 1-2 MWF, Math 501

Goals for the course: Our goal is to prove, and understand the significance of, the fundamental theorems on rings of algebraic integers: factorization of primes and ideals, finiteness of the ideal class group (which measures the failure of unique factorization), and the structure of the group of units in a number ring. (I will explain what some of these objects are in the first couple of days of class.) We will also discuss some analytic objects, like Dedekind zeta-functions and Dirichlet L-functions, and use them to prove algebraic facts, like the infinitude of primes in an arithmetic progression.

Prerequisites: (i) a graduate course in algebra, covering groups, rings, modules, and Galois theory; and (ii) basic knowledge of complex variables, including series expansions and analytic continuation.

Books: There are two required texts: “Number Fields” by D. Marcus, which is available at the university bookstore, and “Lectures on the Theory of Algebraic Numbers” by E. Hecke. This book is out of print, but you can buy a photocopy (for only $13.95) at Chedan Duplicating, 812 N. Tyndall.

Working together: Please do. You are free to organize yourselves into groups and discuss homework and lectures, work on projects, etc. Just make sure that any work you turn in is your own, i.e., that you have written things down in your own words. Plagiarism will be dealt with harshly.

Homework, exams, and grades: There will be a significant number of homework problems and these are essential to success in the course. There will also be some sort of midterm project and final project. Grades will be based 1/3 on homework and 1/3 on each of the two projects.