Math 371 Syllabus Outline
Fall 2004
- Week 1: Review of groups and linear algebra
(chap. 1, chap. 2, 3.1-3.3, 5.1)
- Weeks 2, 3: Group action, class equation (4.1-4.3)
- Week 4: Rings and ideals (chap. 7)
- Week 5: Euclidean domains, PID, UFD (chap. 8)
- Week 6: Polynomial rings (chap. 9)
- Week 7: Modules (chap. 10)
- Week 8: Dual vector spaces, determinant (chap. 11)
- Week 9: Modules over PID, application to abelian groups (12.1, 5.2)
- Week 10: Jordan forms (12.2, 12.3)
- Week 11: Sylow's theorems, semi-direct product (4.1, 5.4, 5.5)
- *Week 12, 13: Introduction to character theory of finite groups
(15.4, 16.1, if time permits)
We use Artin's book mostly as a reference;
the lectures will be logically self-contained.
Sometimes homework will be assigned from Artin.
You might have to read a theorem several times before you
understand the statement and the proof.
If you find Artin not to your liking, here are some alternatives:
- Dummit and Foote, Abstract Algebra
- Fraleigh, Abstract Algebra.
- Hoffman and Kunze, Linear Algebra.
- Herstein, Topics in Algebra.
Dummit and Foote has also been used in the past for Math 370 and
Math 371; it is very carefully written and contains a large number
of exercises.
Fraleigh has also been used before; it does not go as far as Artin or
Dummit/Foote.
The other two books have also been used before, sometimes
in conjunction with Artin.
Below are some other well-known general algebra texts:
- van der Waerdon, Modern Algebra. (a classic)
- Birkhoff and MacLane, A Survey of Modern Algebra.
- Herstein, Topics in Modern Algebra.
- Jacobson, Basic Algebra I, II (a graduate-level book).
- Lang, Undergraduate Algebra.
- Lang, Algebra (graduate level)