Math 701-702, Abstract Algebra, University of South Carolina

Instructor: Frank Thorne, LeConte 317O, thorne [at] math [dot] sc [dot] edu.

Office hours: TBD.

Course objectives and learning outcomes:

In Math 701 and 702, successful students will:

Books:

In large part I will closely be following Dummit and Foote's Abstract Algebra. I encourage to obtain a copy of the book and follow along.

There are a number of other excellent books on algebra as well. Perhaps the most interesting is that by Lang. In my opinion Lang's book is not very good for the beginner, but is excellent for someone who has seen the material before and wants to review or see a different perspective. In particular, it is great to read when you are studying for quals.

Course Requirements:

There are other research seminars that may be of interest to you. These include algebraic geometry, number theory, combinatorics, and the department colloquium.

You should periodically go to these if a topic catches your interest. Even if you expect the seminar to go over your head, it's worthwhile to go anyway: in part, we learn mathematics the same way babies learn language. Here is Ravi Vakil's advice on how to go to a talk.

Exams: The exam questions will be similar to what will appear on the qualifying exam. Take-home and pledged, closed book/notes, 4 hours for the midterm, 6 hours for the final.

Special Accommodations:

If you have disability, or otherwise need special accommodations, please be in touch with me and I will do my best to accommodate your needs.

Grading Scale:

(Shamelessly stolen from Matt Ballard.)

Homework Assignments:

Lecture notes:

Rough schedule of topics:

This is for both 701 and 702, and is very much subject to change.

One innovation I'm trying out is a short unit on linear algebra at the very beginning of the term. This will showcase the themes of the course in a setting that will be very familiar, and yet possibly unfamiliar at the same time. (Matrices will be mentioned only briefly if at all, and they will certainly not be row reduced at the blackboard.)

For a more highbrow perspective, I recommend Lang's book. For a still more highbrow perspective, read this or this if you dare.

If there is additional time (wishful thinking?), we will cover additional topics such as homological algebra and group representation theory (see Ch. 17-19 of Dummit-Foote). Another option is to cover the basics of category theory, borrowing from Aluffi's Algebra: Chapter 0. Still another option is to do more noncommutative ring theory. If there are topics you would like to see covered, please be in touch! Other topics may be covered as well, depending on student interest.