| Day | Topics | Reading |
|---|---|---|
| Tu. 8/23 | The Integers | [OS] Sec. 1.1 |
| Th. 8/25 | Groups and their subgroups. | [OS] Sec. 2.1,2 |
| Tu. 8/30 | Homorphisms, isomorphisms, automorphisms. | [OS ] Sec 2.3,4 |
| Th. 9/1 | Direct Products, intersections of subgroups. | [OS ] Sec 2.3,4 |
| Tu. 9/6 | Some exercises. The symmetric group. |
[OS] Sec 2.5. |
| Th. 9/8 | Automorphism groups. Products of transpositions. | [OS] Sec. 2.5 |
| Tu. 9/13 | Parity of a permutation, the alternating group. Cayley's theorem. | [OS] Sec. 2.5 |
| Th. 9/15 | Generators and Relations Cosets and Conjugates. |
[OS] Sec. 2.6, 2.7 |
| Tu. 9/20 | Normality and the first isomorphism theorem. | [OS] Sec. 2.8 |
| Th. 9/22 | Correspondence Theorem. Some problems with normal subgroups. |
[OS] Sec. 2.8 |
| Tu. 9/27 | The third isomorphism theorem and correspondence theorem. Matrix groups and other examples of groups. |
[OS] Sec 2.9, 2.10. |
| Th. 9/29 | Matrix group problems. Metabelian groups.
The second isomorphism theorem. |
[OS] Sec. 2.9, 3.1 |
| Tu. 10/4 | The second isomorphism theorem and semi-direct products. | [OS] Sec. 3.1. |
| Th 10/6 | Problems: semi-direct products. | [OS] Sec. 3.1. |
| Th 10/11 | Classfication of Finite Abelian Groups. | [OS] Sec. 3.2. |
| Th 10/13 | Simple groups. A_n is simple. | [OS] Sec. 3.3. |
| Tu 10/18 | Rings and homomorphisms. Units, zero divisors, nilpotents. F[x]. Direct products, polynomial rings. |
[OS] Sec. 4.1,3 |
| Th. 10/20 | Homomorphisms, isomorphisms. Universal property of R[x]. Evaluation of a polynomial. |
[OS] Sec. 4.1-3 |
| Tu. 10/25 | Ideals and quotient rings. Isomorphism theorems. | [OS] Sec. 4.4 |
| Th. 10/27 | Operations and properties of ideals and quotient rings. | [OS] Sec. 4.5 |
| Th. 11/1 | Tidying up: ideals, quotient rings, isomorphism theorems. Polynomial rings in 2+ variables. |
[OS] Sec. 4.5 |
| Th. 11/3 | TEST: group theory. | [OS] Ch. 3,4. |
| Tu. 11/8 | Formation of Fractions. | [OS] Sec. 4.6 |
| Th. 11/10 | More fractions. | [Ash] Sec. 4.1 |
| Th. 11/15 | Fields and field extensions. | [OS] Sec. 5.1,2. |
| Th. 11/17 | Finite fields. | [OS] Sec. 5.3. |
| Tu. 11/22 | More on fields and finite fields. | [OS] Sec. 5.1-3. |
| Tu. 11/29 | Splitting fields, field automorphisms. | [OS] Sec. 5.4. |
| Th. 12/1 | Number fields | [OS] Sec. 5.5. |
| Tu. 12/6 | Algebraic closure, function fields. | [OS] Sec. 5.6. |
| Th. 12/8 | Tidying up. | [OS] Sec. 4. |
| Th. 12/15 | TEST: Rings, Fields. | [OS] Ch, 4,5. |