### Math 171 Syllabus

Prof.'s Dagan Karp and Matt Davis
Fall 2010

## Syllabus

The following is a tentative syllabus for Math 171, Fall 2010. 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 (9/30)

## 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 (11/3)

## PART III: SPECIAL TOPICS

19. Category Theory: Definitions and Basic Examples
20. Category Theory: More Examples, Graphs
21. Category Theory: Monomorphisms and Epimorphisms
22. Functors: Definitions and Basic Examples
23. Functors: Natural Transformations
:: 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