| Day | Topics | Preparation |
|---|---|---|
| Wed. 1/23 | Introduction, groups. Defintions and examples. |
Sec. 7.1-2 |
| Fri. 1/25 | Uniqueness of identity and inverse. Order of an element. See 7.2: #25, 29, 30, 31. |
Sec. 7.2 |
| Mon. 1/28 | Subgroups | Sec. 7.2-3 |
| Wed. 1/30 | Some important subgroups. | Sec. 7.3 |
| Fri. 2/1 | Homomorphisms and related subgroups. | Sec. 7.3-4 |
| Mon. 2/4 | Isomorphisms and automorphisms. | Sec. 7.4 |
| Wed. 2/6 | Cayley's theorem. | Sec. 7.5 |
| Fri. 2/8 | Congruence, Lagrange's theorem. Some exercises. |
Sec. 7.5 |
| Mon. 2/11 | Normal subgroups. | Sec. 7.6 |
| Wed. 2/13 | Quotient groups. | Sec. 7.7 |
| Fri. 2/15 | Some exercises on normal subgroups. | Sec. 7.6-8 |
| Mon. 2/18 | The three isomorphism theorems. | Sec. 7.6-8 |
| Wed. 2/20 | The groups D_n . | Sec. 7.6-8 |
| Fri. 2/22 | EXAM. | Sec. 7.1-8 |
| Mon. 2/25 | Classification of groups: some "easy" cases. | Thm. 8.32, 8.33 |
| Wed. 2/27 | Direct products of groups. | Sec. 8.1 |
| Fri. 2/29 | More on direct products. | Sec. 8.1 |
| Mon. 3/3 | Finite abelian groups factorization into p -groups. |
Sec. 8.2 |
| Wed. 3/5 | Fundamental Theorem of finite abelian groups. Factorization of p -groups. |
Sec. 8.2 |
| Fri. 3/7 | Invariant factor decomposition. | Sec. 8.2 |
| Mon. 3/10 | The symmetric group, S_n . | Sec. 7.9 |
| Wed. 3/12 | The alternating group, A_n . | Sec. 7.9 |
| Fri. 3/14 | Direct products, semi-direct products, extensions. | Sec. 8.3 |
| Mon. 3/17 | A_n is simple. | Sec. 7.10 |
| Wed. 3/19 | Sylow theorems. | Sec. 8.3 |
| Fri. 3/21 | Sylow theorems for classification. | Sec. 8.5 |
| Mon. 3/24 | Proof of Sylow theorems. | Sec. 8.4 |
| Wed. 3/26 | Questions?. | |
| Fri. 3/28 | EXAM. | Sec. 7.6-10, 8.1-5 |
| Mon. 4/7 | Field of quotients. | Sec. 9.4 |
| Wed. 4/9 | Vector Spaces. | Sec. 10.1 |
| Fri. 4/11 | Polynomial rings over a field.
Division and the GCD. Roots and remainders. |
Sec. 4.1-2, 4 |
| Mon. 4/14 | Polynomial rings over a field.
Irreducibles and unique factorization. |
Sec. 4.3-5. |
| Wed. 4/16 | F[x]/ p(x) for p(x)
irreducible. Adjoining roots. |
Ch. 5 |
| Fri. 4/18 | Extension fields. | Sec. 10.2 |
| Mon. 4/21 | Simple extensions. | Sec. 10.2 |
| Wed. 4/23 | Not so simple extension fields. | Sec. 10.2-3 |
| Fri. 4/25 | Splitting fields, the derivative. Freshman's rule for finite fields. |
Sec. 10.4,6 |
| Mon. 4/28 | Finite fields. | Sec. 10.6 |
| Wed. 4/30 | More on finite fields. | Sec. 10.6 |
| Fri. 5/2 | EXAM. | Ch. 10, Ch. 4-5. |
| Mon. 5/5 | Projects: discuss with me. | Ch. 10, Ch. 4-5. |
| Fri. 5/7 | Projects: discuss with me. | Ch. 10, Ch. 4-5. |
| Fri. 5/9 | Project Presentations. | Sheridan, Ben. |
| Fri. 5/16 | Project Presentations. | . |