| Day | Topics | Reading |
|---|---|---|
| Mo. 8/26 | The Integers. | [OS] Sec. 1.1 |
| We. 8/28 | QR theorem, Euclidean algorithm unique factorization, modular arithmetic (group work) |
[OS] Sec. 1.1 |
| Fr. 8/30 | Groups, Rings, Fields Z/n and U_n |
[OS] Sec. 1.2, 2.1 |
| We. 9/4 | Basic properties of Groups (group work) | [OS] Sec. 1.2, 2.1 |
| Fr. 9/6 | Subgroups, Order, Lattice Diagrams | [OS] Sec. 2.1-2 |
| Mo. 9/9 | Homomorphisms, isomorphisms. Direct product. | [OS] Sec 2.3-4. |
| We. 9/11 | Lattice Diagrams and Automorphism groups (group work). | [OS] Sec 2.2, 2.3, 2.4. |
| Fr. 9/13 | Automorphism groups, direct products, |
[OS] Sec. 2.3,4 |
| Mo. 9/16 | Permutation groups. | [OS] Sec. 2.5 |
| We. 9/18 | .Permutation groups and Cayley's theorem (group work). | [OS] Sec. 2.5 |
| Fr. 9/20 | . The alternating group An
Cayley's theorem. Presentations of groups. |
[OS] Sec. 2.5, 6 |
| Mo. 9/23 | Cosets and Conjugates. Group presentations. | [OS] Sec. 2.6,7 |
| We. 9/25 | Normal subgroups. | [OS] Sec. 2.7 |
| Fr. 9/27 | Normal subgroups problems (group work). | [OS] Sec. 2.8 |
| Mo. 9/30 | Quotient groups 1st and 3rd isomorphism theorems. |
[OS] Sec. 2.8, 10 |
| We. 10/2 | Quotient groups and lattices correspondence theorem (group work). |
[OS] Sec. 2.8, 10 |
| Fr. 10/4 | Groups from rings and fields. Matrix groups. |
[OS] Sec. 2.9 |
| Mo. 10/7 | Test 1: Group fundamentals. | [OS] Ch. 2 |
| We. 10/9 | The second isomorphism theorem. | [OS] Sec. 3.1 |
| Fr. 10/11 | Semi-direct products (group work). | [OS] Sec.3.1 |
| Mo. 10/14 | Semi-direct products. Internal vs External |
[OS] Sec.3.1 |
| We. 10/16 | Finite abelian groups. | [OS] Sec. 3.2 |
| Fr. 10/18 | Finitely generated abelian groups (group work). | [OS] Sec. 3.2 |
| Mo. 10/21 | Simple groups and An. | [OS] Sec. 3.3 |
| We. 10/23 | Rings, units zero-divisors, nilpotents. | [OS] Sec. 4.1,2 |
| Fr. 10/25 | Ring problems (group work). | [OS] Sec. 4.1,2 |
| Mo. 10/28 | Ring homomorphisms and ring constructions. | [OS] Sec. 4.1-3 |
| We. 10/30 | Direct products, polynomial rings.
Universal properties. |
[OS] Sec. 4.4 |
| Fr. 11/1 | Ideals, homomorphisms (group work) | [OS] Sec. 4.2-4 |
| Mon. 11/4 | Quotient rings and the isomorphism theorems. | [OS] Sec. 4.4,5 |
| We. 11/6 | TEST #2 Group theory | [OS] Ch 2, 3 |
| Fr. 11/8 | Maximal, prime and radical ideals, and their quotient rings. |
[OS] Sec. 4.6 |
| We. 11/13 | Rings of fractions in Q (group work) HW 11. | [OS] Sec. 4.7 |
| Fr. 11/15 | Constructing rings of fractions. | [OS] Sec. 4.7 |
| Mo. 11/18 | Fields and field constructions. | [OS] Sec. 5.1-2 |
| We. 11/20 | Field extensions: adjoining a root. | [OS] Sec. 5.1-2 |
| Fr. 11/22 | A finite field and a number field (group work). | [OS] Sec. 5.3,4 |
| Mo. 11/25 | Complex numbers; Fundamental theorem of algebra. Gaussian numbers. | [OS] Sec. 1.2 |
| Mo. 12/2 | Finite Fields. | [OS] Sec. 5.1-2 |