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This semester's version of Math 125 is an introduction to algebraic number theory. Topics will include basic facts about algebraic number fields and integers, the Dirichlet unit theorem, discriminants of algebraic number fields, factorization of ideals in rings of integers, and p-adic fields. There are two primary objectives for this class: to prepare graduate students for a qualifying exam in algebraic number theory, and to prepare students to read about class field theory on their own.
Name: Andrew Yang
Office: Kemeny 316
Office Hours: By appointment
Unless otherwise specified, homework problems refer to questions in Neukirch.
Grading in this class will be based on homework assignments and in-class participation. Homework assignments will be provided from the text on a weekly basis. In-class participation will probably consist of presentation of selected homework problems, and some more extensive projects later in the class. This will either be presentations by people in the class on topics of their choosing, or some interactive activities using computational software (almost certainly using Sage).
The required book for this class is Algebraic Number Theory, by Jurgen Neukirch, ISBN 3540653996. The textbook is long, and we will only be covering something like 1/3 of it, but hopefully by the end of the class you will be equipped to read the rest of the book on your own. This book has more of an emphasis on drawing analogies with algebraic geometry than the typical algebraic number theory text.
There are many books written about algebraic number theory. The following is a list not meant to be all-inclusive, but if you are interested in learning about the subject from slightly different points of view consider reading the following books: