(last update 12/15, 2:40 pm)
I posted final exam solutions to the BBLearn page. Also please compare your BBLearn grades with your own records to make sure they agree. I hope to finish grading over the weekend and post final grades Monday.
Exam 3 takes place in class on Friday, 12/1. There is a review session Thursday, 11/30, in Room 162, from 4:30 until all questions are answered. The material to be covered on the exam is the material on rings and modules has been covered in class and on problem sets and exercises, since Exam 2 was distributed (October 28), and the material covered in Lectures 1 and 2 of Isaacs' videos (just up to the Exercises 2.1 and 2.2). (I hope you have studied further than that, but there won't be anything on the exam from beyond that point.) This includes most of Chapter 12 of Isaacs' book - anywhere you see the phrase "abelian X-group" replace it with "right R-module." (Also he writes a plus sign with a dot above it to denote direct sum.) Also I've uploaded Thomas Holtzworth's M.S. thesis, linked below - you will find that much of what we have done is treated in Chapter 1.
Also here is a pdf of Isaacs' Character Theory book. If you find it interesting reading, I encourage you to purchase an inexpensive copy: click here.
Isaacs' Character Theory
Other resources include these books:
- Character Theory, by L. Grove
- Noncommutative Rings, by I.N. Herstein
- any other graduate algebra text, such as Hungerford, Algebra
I've written up some supplementary notes to accompany Isaacs' video lectures - they include review material on rings from undergraduate abstract algebra, along with other background material to make the lectures more accessible, some of which has been discussed in class and some which will be over the coming lectures. I will re-post the notes as they develop - here is the first installment. I will add to these notes over the weekend.
Supplemental notes on rings, modules, and representations
Some comic relief, possibly amusing (produced by some grad students with too much time on their hands):
Finite simple group of order two
Here is a link to the first of the video lectures of Isaacs on representation theory and group characters:
Isaacs' Lecture 1
Links to the remaining lectures are on this page:
Our goal is to get through the proof of Burnside's paqb theorem, at the end of Chapter 5, which occurs in the third 75-minute lecture. We will attempt to get through one lecture per week, so you can start by watching the first part of Lecture 1. Here is a pdf of the slides, trimmed thanks to Jeffrey C, including only Chapters 1-5, which is what we hope to finish by December 8:
Isaacs' slides (trimmed)
Solutions to HW #5 are now available on the BBLearn page.
Here is a pdf with statements of Exercises assigned in class (including Exercises A-F):
Michael Falk's Home Page
Isaacs Chapter 1
Isaacs Chapter 2
Problem Sets and Solutions - see BBLearn page
Ch. 1 / 1.1, 1.5, 1.7. (Solutions: 1.1)
The exercises listed above from Chapter 1 are due Monday, 9/18.
Ch. 2 / 2.3, 2.4, 2.5, 2.6.
Solutions: 2.3, 2.4, 2.5 , 2.6
These exercises listed above from Chapter 2 are due Wednesday, 9/20.
Ch. 2 / 2.8, 2.9, 2.11, 2.12. (2.8 was included on HW #3.)
Ch. 2 / 2.13, 2.16, 2.18, 2.20, 2.21. ( 2.13(b) and 2.20 were done in class, and 2.13(c) is equivalent to Exam 1.5(c).); 2.19 and 2.22 were included, in modified form, on HW #2, 2.16 was on HW #3.)
Solutions: 2.18, 2.21
The exercises listed above from Chapter 2, along with in-class exercises A and B, are due Friday, 10/13.
Ch. 3 / 3.1, 3.3. (Both these problems were on HW #3.)
Ch. 3 / 3.2, 3.4, 3.5, 3.9, 3.11, 3.13, 3.14 (3.9 was done in class, as a corollary of HW #2.3)
The exercises listed above from Chapter 3 (except 3.1, 3.3, and 3.9), along with in-class exercises C and D, are due Wednesday, 10/25.
Ch. 4 / 4.1