| Date |
Sections(s) |
Topics covered |
| 22 Sep |
0.1 |
Equivalence Relations and Partitions |
| 24 Sep |
0.3 |
The definition of Z/nZ |
| 27 Sep |
1.1 |
Definition of groups; examples; begin dihedral group |
| 29 Sep |
1.2 - 1.3 |
The dihedral and symmetric groups |
| 1 Oct |
1.4 - 1.5, start 1.6 |
Matrix groups, Quaternions, isomorphism |
| 4 Oct |
1.6, 2.1 |
Homomorphisms and subgroups |
| 6 Oct |
2.1 |
Subgroups |
| 8 Oct |
2.3 |
Cyclic groups |
| 11 Oct |
2.4, 3.1 |
Subgroups generated by a set, cosets |
| 13 Oct |
3.1, 3.2 |
Cosets and homomorphisms |
| 15 Oct |
3.2 |
More on cosets and Lagrange's theorem |
| 18 Oct | 3.3, 3.5 | The first isomorphism theorem, and the
alternating group |
| 20 Oct |
1.7, 4.1, 4.2 |
Group Actions and Cayley's Theorem |
| 22 Oct | 4.3 | Groups acting by conjugation; the class equation |
| 25 Oct |
4.3, 4.5 |
Class equation, Sylow Theorems |
| 27 Oct |
5.4 |
Recognizing direct products, applications of Sylow theorems, and fundamental theorem of finite abelian groups
|
| 28 Oct |
7.1 |
Rings, basic definitions |
| 1 Nov |
7.2, 7.3 |
Polynomial Rings, homomorphisms
|
| 3 Nov |
7.3 |
Homomorphisms and quotient rings |
| 5 Nov |
7.4 |
Quotient rings and properties of ideals
|
| 8 Nov |
8.1, 9.1 |
Euclidean Domains, polynomial rings |
| 10 Nov |
8.2, 9.2 |
PIDs
|
| 12 Nov |
8.3 |
gcds, irreducibles, primes |
| 15 Nov |
8.3 |
Unique Factorization Domains
|
| 17 Nov |
9.3 |
Gauss's lemma and consequences (R UFD => R[x] UFD) |
| 19 Nov |
9.4 |
Irreducibility criteria
|
| 22 Nov |
9.4 |
Extension fields |
| 29 Nov |
|
Albegra in number theory and geometry
|
| 1 Dec |
|
Albegra in number theory and geometry |
