Instructor: |
Monty (or William)
McGovern
Office: Padelford C-450 Phone: 206-543-1149 Email: mcgovern@math.washington.edu Grader email: wardm4.math.washington.edu Grader office: C114 Grader office hours: W 2:30-3:20, Th 9:30-10:20 Office Hours: drop in, or by appointment, Padelford C-450 |
Lectures: |
Monday, Wednesday & Friday, 9:30-10:20 a.m., Padelford Hall C-36 |
Required Text: |
Advanced Modern Algebra, by Rotman, (2d ed., AMS, 2010). |
Prerequisites: |
Math 504 or the equivalent. |
Grading: |
Your grade will be based on weekly homework, counting 50%, and a final exam, counting 50%. There will be five problems per week and *all* assigned problems will be graded this term. The final exam will be comprehensive. If you cannot complete a homework assignment on time, you can always turn it in by 4:00 on the day it is due to the grader's mailbox. PLEASE turn in WHATEVER YOU CAN rather than nothing. In the final you may use two letter-sized pages (one sheet front and back of notes in your own handwriting). class. |
Incompletes and Drops: |
The grade of Incomplete will be given ONLY if a student has been doing satisfactory work until the end of the quarter and then misses the final exam for a documented illness, religious reason, or family emergency. |
What to Expect: |
I will cover Galois theory and representation theory of finite groups this term, doing Chapter 3, a brief review of some of Chapter 4, and the last half of Chapter 7. Thus I will treat finite extensions over fields and their Galois groups, heading towards the Galois correspondence and Galois' Criterion for a polynomial over a field to be solvable by radicals. I will then cover the representation theory of finite groups, as a very nice application of the Artin-Wedderburn structure theory you have seen that is of considerable interest in its own right. I will try to broadly follow the book and at least indicate how it treats the material I am discussing, but I will feel free to omit certain topics, cover others in greater depth, and discuss still others that are not in the text at all. |
Due: | Problems: |
Jan 11/div> |
2.94,101,102, board problem: determine all fields lying
between Q and Q[{\sqrt{2,\sqrt{3}]: read 2.9, start 3.1 |
Jan 18 |
2.104; 3.6,12,16,17: read 3.2 |
Jan 25 |
13.6.13-17 of Dummit and Foote, passed out in class: finish
3.2, start 3.1 |
Feb 1
|
Dummit and Foote, 14.2.17,18,23,26,27, passed out in class:
finish 3.1, start 3.3 |
Feb 8 |
Dummit and Foote, 18.1.15-17, two board problems: show that the splitting field of x^{p^n} - x - 1 over F_p has degree np over F_p; show that F admits a normal basis if F/E is a cyclic Galois extension: review Artin-Wedderburn theory in Rotman (7.1-4) |
Feb 15 |
Dummit and Foote, 18.2.7,8; 18.3.12,20,22 :read D+F, 18.3 |
Feb 22 |
DF 19.1,5,8,9,17 [20 points] : read 19.1 |
Mar 1
|
17.1.2,3,9; 17.2.1,8 (correction to 17.2.1: \epsilon, not aug,
for augmentation map):read 19.2,17.1 |
Mar 8
|
17.2.2,3,9,11; 17.3.1: read 17.2,3 |
Mar 15
|
EXTRA CREDIT: pick any problems you like: read 17.4 |