| Day | Topics | Reading |
|---|---|---|
| Tu. 8/25 | The Integers | [OS] Sec. 1.1,2 |
| Th. 8/27 | Exercises on properties of the integers. | [OS] Sec. 1.1,2 |
| Tu. 9/1 | Groups, subgroups and homomorphisms. | [OS] Sec. 2.1,2,3 |
| Th. 9/3 | Exercises on groups. | [OS] Sec. 1.2, 2.1,2,3 |
| Tu. 9/8 | Direct Products, Automorphism groups, permutation groups. The symmetric group. |
[OS] Sec. 2.3,4,5 |
| Th. 9/10 | Exercises: Lattices of subgroups, automorphism groups permutation groups. |
[OS] Sec. 2.3,4,5 |
| Tu. 9/15 | Parity of a permutation, the alternating group.
Cayley's theorem. Cosets and conjugates. |
[OS] Sec. 2.5, 2.7 |
| Th. 9/17 | Exercises: Alternating group, Cayley's theorem. Conjugation and inner automorphims. |
[OS] Sec. 2.5, 2.6, 2.7 |
| Tu. 9/22 | Normality and the first isomorphism/factor theorem. Matrix groups and other constructions. |
[OS] Sec. 2.6, 2.8, 2.9 |
| Th. 9/24 | Exercises: normal subgroups. Dicyclic groups on other groups, lattice diagrams. | [OS] Sec. 2.6, 2.8 |
| Tu. 9/29 | The third isomorphism theorem and correspondence theorem. Matrix groups Classfication of Finite Abelian Groups. Other abelian groups |
[OS] Sec 2.9, 2.10, 3.1. |
| Th. 10/1 | Exercises: matrix groups. Finite abelian groups. Other abelian groups. |
[OS] Sec. 2.9, 2.10, 3.1 |
| Tu. 10/6 | Other group constructions. Group actions. |
[OS] Sec. 2.9. |
| Th 10/8 | Test 1. Fundamentals of group theory. Abelian groups. |
[OS] Ch 2, 3.1. |
| Tu 10/13 | The second isomorphism theorem and semidirect product. Classification of finite groups. Simple groups. A_n is simple. |
[OS] Sec. 3.3. |
| Th 10/15 | Exercises: Semi-direct products Classification of groups. |
[OS] Sec. 2.9, 3.2, 3.3. |
| Tu 10/20 | Rings and homomorphisms. Units, zero divisors, nilpotents. F[x]. Direct products, polynomial rings. |
[OS] Sec. 4.1, 4.2, 4.3 |
| Th. 10/22 | Exercises: Homomorphisms, isomorphisms. Universal property of R[x]. Evaluation of a polynomial. |
[OS] Sec. 4.1, 4.2, 4.3 |
| Tu. 10/27 | Ideals and quotient rings. Isomorphism theorems. | [OS] Sec. 4.4, 4.5 |