Syllabus
The following is a tentative syllabus for the course. This page will be updated irregularly. (Last update: 7/18)
| Lectures | Sections in Pinter | Brief Description |
|---|---|---|
| 6/27 | 1 | Why Abstract Algebra? |
| Appendix A | Set Theory | |
| 6/29 | 2 | Operations |
| 3 | The Definition of groups | |
| 6/30 (x-hour) | 4 | Elementary Properties of Groups |
| 7/4 | (No class, holiday) | |
| 7/6 | 5 | Subgroups |
| 6 | Functions | |
| 7/7 (x-hour) | 6 | Functions (cont.) |
| 7/11 | 7 | Groups of Permutations |
| 8 | Permutations of a Finite Set | |
| 7/13 | 8 | Permutations of a Finite Set (cont.) |
| 9 | Isomorphisms | |
| 7/18 | 10 | Order of Group Elements |
| 11 | Cyclic groups | |
| 7/19 | Midterm 1, 5:00-6:15 p.m. | |
| 7/20 | Appendix B | Integers |
| 12 | Partitians and equivalence relations | |
| 7/25 | 13 | Counting Cosets |
| 14 | Homomorphisms | |
| 7/27 | 14 | Homomorphisms (cont.) |
| 15 | Quotient Groups | |
| 8/1 | 16 | The Fundamental Homomorphism Theorem |
| 8/3 | 17 | Rings: Definitions and Elementary Properties |
| 18 | Ideals and Homomorphisms | |
| 8/8 | 18 | Ideals and Homomorphisms (cont.) |
| 19 | Quotient Rings | |
| 8/9 | Midterm 2, 5:00-6:15 p.m. | |
| 8/10 | 20 | Integral Domains |
| Appendix C | Induction | |
| 8/15 | 21 | The Integers |
| 22 | Factoring Into Primes | |
| 8/17 | 24 | Rings of Polynomials |
| 25 | Factoring Polynomials | |
| 8/22 | 26 | Substitution in Polynomials |
| Wrap-up | ||
| 8/28 | Final Exam, 8:00 a.m.-noon |