| Day | Topics | Preparation |
|---|---|---|
| Fri. 1/23 | Introduction, groups. Defintions and first properties. |
Sec. 7.1-2 |
| Mon. 1/26 | Lots of examples of groups. D_n , S_n , (Z_n, +) , U_n Order of an element. |
Sec. 7.1-2 |
| Wed. 1/28 | Order of an element. See 7.2: #25, 29, 30, 31. Subgroups |
Sec. 7.2-3 |
| Fri. 1/30 | Examples of Groups and Subgroups | Sec. 7.3 |
| Mon. 2/2 | Homomorphisms and related subgroups. | Sec. 7.3-4 |
| Wed. 2/4 | Isomorphisms and automorphisms. | Sec. 7.4 |
| Fri. 2/6 | Isomorphisms and automorphisms. | Sec. 7.4 |
| Mon. 2/9 | Cayley's theorem. Cosets and Congruence |
Sec. 7.4 Sec. 7.5 |
| Wed. 2/11 | Lagrange's theorem. Classification of groups of order <8. |
Sec. 7.5 |
| Fri. 2/13 | Cosets. | Sec. 7.6 |
| Mon. 2/16 | Normal subgroups. | Sec. 7.6 |
| Wed. 2/18 | Quotient groups. | Sec. 7.7 |
| Fri. 2/20 | Some exercises on normal subgroups. | Sec. 7.6-8 |
| Mon. 2/23 | The three isomorphism theorems. | Sec. 7.6-8 |
| Wed. 2/25 | More on the isomorphism theorems. | Sec. 7.6-8 |
| Fri. 2/29 | Miscellaneous problems The groups D_n . |
Sec. 8.1 |
| Mon. 3/2 | EXAM. | Sec. 7.1-8 |
| Wed. 3/4 | Groups of order 2p Direct products. |
Sec. 8.1 |
| Fri. 3/6 | More on direct products Finite abelian groups, p -groups. |
Sec. 8.2 |
| Mon. 3/9 | Miscellaneous topics. Internal direct product theorem |
Sec. 7.7,8 Sec. 8.1 |
| Wed. 3/11 | Fundamental Theorem of finite abelian groups. Factorization of p -groups. |
Sec. 8.2 |
| Fri. 3/13 | Invariant factor decomposition. | Sec. 8.2 |
| Mon 3/16 | The symmetric group, S_n . | Sec. 7.9 |
| Wed. 3/18 | The alternating group, A_n . | Sec. 7.9 |
| Fri. 3/20 | A_n is simple. | Sec. 7.10 |
| Mon. 3/13 | Sylow theorems. | Sec. 8.3 |
| Wed. 3/25 | Sylow theorems for classification. | Sec. 8.5 |
| Fri. 3/27 | Proof of Sylow theorems. | Sec. 8.4 |
| Mon. 4/6 | The field of quotients of an integral domain. | Sec. 9.4 |
| Mon. 4/8 | Classification of groups, semi-direct products, extensions. Problems on groups. Bring questions. |
Sec. 8.5 Sec. 8.3 #1-7, |
| Fri. 4/10 | EXAM. | Sec. 7.6-10, 8.1-4 |
| Mon. 4/13 | Vector spaces over a field. | Sec. 10.1 |
| Wed. 4/15 | Polynomial rings over a field.
Division and the GCD. Roots and remainders. |
Sec. 4.1-2, 4 |
| Fri. 4/17 | Polynomial rings over a field.
Irreducibles and unique factorization. |
Sec. 4.3-4. |
| Mon. 4/20 | Irreduciblity in Q[x]. | Sec. 4.5. |
| Wed. 4/22 | F[x]/ p(x) for p(x)
irreducible. Adjoining roots. |
Ch. 5 |
| Fri. 4/24 | F_3[x]/ x^2+ 2x +2 in all its glory. | Ch. 5 |
| Mon. 4/27 | Algebraic, transcendental elements.
Extension fields. |
Sec. 10.2, 3 |
| Wed. 4/29 | Composition of extensions Splitting fields. |
Sec. 10.3-4 |
| Fri. 5/1 | Finite fields. | Sec. 10.6 |
| Mon. 5/4 | Questions?. | Ch. 10, Ch. 4-5. |
| Wed. 5/6 | EXAM. | Ch. 10, Ch. 4-5. |
| Fri. 5/8 | Projects: discuss with me. | . |
| Mon. 5/11 | Project Presentations. Tim, Bridget, Eric |
. |
| Wed. 5/13 | Project Presentations. | Sara/Andrea,. |
| Fri. 5/15 | Project Presentations. | Allison, Elizabeth, Juan/Katie, Melanie, Erin/Jim/Michelle. |