Math 485: Representation Theory
Spring 2017

The syllabus for Math 485 is linked.  Much of that information is repeated bellow (but not all of it, so read the syllabus!)

Instructor
Rebecca E. Field
fieldre@math.jmu.edu
(540) 568-4962
Office: Roop 114
Office Hours: MWF 2:20-3:20pm, Tu 12:00-2:00pm
Also by appointment
(I can make appointments for Tuesdays, but am not available on Thursdays)

Algebra by Michael Artin (1991)

Course summary:
This is a special topics course on a topic in abstract algebra that is usually not taught to undergraduates, but is useful, fascinating, and accessible, so why not?  Also, you'll definitely see it in grad school, and since large portions of mathematics are secretly linear algebra, it ends up being very important.  Representation Theory is about all of the various ways to write a group as a subgroup of a (in our case, finite dimensional) matrix group over a field (in our case, often, though not always, $ℂ$).

Here is my most important piece of advise about this course:     DO NOT FALL BEHIND!!  This includes things like DO NOT MISS CLASS!!  (If you must miss a class, get notes from one of your classmates and read them before the next class.)  It also includes things like DO YOUR HOMEWORK!!  It is not possible to actually learn this material without doing problems.  You might be able to convince yourself you understand, but if you can't do problems, you aren't at the level of understanding required to pass the class.  In fact, if the class seems too easy at any point, do extra problems!

Exams:
Big Quiz 1: Wednesday February 15, during class time
Midterm: week of March 22, evening
Big Quiz 2: Wednesday, April 12, during class time
Final: Wednesday, May 3, 10:30am-12:30pm

Homework:
Problem sets will be posted here as they are assigned.
Homework 1 (short, 3 easy proofs, 3 examples) due Monday, January 23 (weekly quiz 1 is also Monday, January 23)
Homework 2 (more group actions) due Wednesday, February 1
Homework 3 (bilinear forms) due Friday, February 10
Homework 4 (representations, hermitian forms, and Haar measure) due Monday, February 20
Homework 5 (characters), due Wednesday, March 29
Homework 6 (finite and infinite groups), due with the final exam

LaTeX:
I'm requiring that students type set their assignments using LaTeX.  Here is a link to a LaTeX Setup and Tutorial along with a sample document and its source code.

Extra Help:
Please come by my office hours or make an appointment if you need extra help!

Topics we will cover are roughly as follows:

Chapters 5&6: Group Actions on a Set
Chapters 4,7,&8: Linear Algebra Review
Chapter 9: Representation Theory of Finite Groups
Chapters 8&9: Lie Groups/Lie Algebras