### Math 171 Syllabus

Prof.'s Dagan Karp and Mike Orrison
Fall 2008

## Syllabus

The following is a tentative syllabus for Math 171, Fall 2008. The actual topics covered will depend upon interest and pace.

## PART I: GROUPS

1. Groups and Subgroups (1.1, 2.1)
2. Dihedral Groups, Generators and Relations (1.2)
3. Symmetric, Matrix and Quaternion Groups (1.3-1.5)
4. Homomorphisms and Isomorphisms (1.6)
5. Quotient Groups and Homomorphisms (3.1)
6. More on Cosets and Lagrange's Theorem (3.2)
7. Subgroups Generated by Subsets, Lattice of Subgroups (2.3-2.5)
8. The Isomorphism Theorems (3.3)
9. EXAM I OUT (10/1)

## PART II: RINGS

10. Rings (7.1)
11. Polynomial Rings, Matrix Rings, and Group Rings (7.2)
12. Ring Homomorphisms and Quotient Rings (7.3)
13. Properties of Ideals (7.4)
:: FALL BREAK ::
14. Properties of Ideals (cont.) (7.4)
15. Euclidean Domains (8.1)
16. Principal Ideal Domains (8.2)
17. Unique Factorization Domains (8.3)
18. EXAM II OUT (11/5)

## PART III: SPECIAL TOPICS

19. Group Actions (1.7, 2.2, 4.1)
20. Groups Acting on Themselves (4.2-4.3)
21. Sylow Theorems (4.5)
22. Sylow Theorems (cont.) (4.5)
23. The Fundamental Theorem of Finitely Generated Abelian Groups (5.2)
:: THANKSGIVING ::
24. Modules over Polynomial Rings (10.1)
25. Modules over Groups Rings (18.1)
26. Applications of Abstract Algebra
27. Applications of Abstract Algebra