Math 594, Algebra II
t=Winter 2005, MWF 2pm-3pm,
(x,y,z)=3088 East Hall
FINAL EXAM, THURSDAY APRIL 20, 1:30-3:30, 3088EH on Field and
All problem sets are in pdf
-format. Let me know if
that does not work for you. I can make other formats if necessary.
- Problem Set 1, due 1/20/06,
- Problem Set 2, due 1/30/06
- Problem Set 3, due 2/8/06
- Problem Set 4, due 2/15/06
- Midterm on Monday February 20 (in class)
- Problem Set 5, due 3/8/06
- Problem Set 6, due 3/20/06
- Problem Set 7, due 3/29/06
- Problem Set 8, due 4/10/06
- Problem Set 9, NOT TO BE HANDED IN
- final exam
||3067 East Hall
||(734) 763 2309
||MW 1-2pm, F 3-4pm.
||David S. Dummit, Richard M. Foote, Abstract Algebra, third edition, John Wiley & Sons, Inc., 2004.
The course consists of two parts, Group Theory
and Field/Galois Theory
Topics in Group Theory include:
- group actions on sets and permutation representations
- the Sylow theorems
- the Jordan-Hölder theorem
- simplicity of the alternating group An
for n at least 5
- nilpotent groups and solvable groups
Topics in Field/Galois theory include:
- field extensions
- splitting fields, algebraic closures
- separable and inseparable extensions
- cyclotomic polymomials
- finite fields
- the Galois correspondence
- solving equations by radicals, insolvability of the quintic
We will cover roughly Chapters 4,6,13,14 of Dummit-Foote. (Parts of Chapter 3,5
may also be covered.)
You should be
already familiar with the topics in Chapter 1-3, the structure
theorem for finitely generated abelian groups (5.2). You also should
have a sturdy knowledge of linear algebra.
Other resources are:
- Lang, Algebra.
- Artin, Algebra.
- MacLane, Birkhoff, Algebra.
- Van der Waerden, Modern Algebra, vol I.
- Hungerford, Algebra.
- Jacobson, Basic Algebra.
Homework/Exams: Yes, both. About 10 homework
assignments and 2 or 3 exams are planned.