| Class Number |
Date |
Sections in Notes |
Brief Description |
| 1 |
Monday, 8/31 |
1.1 - 2.3 |
Introduction, Divisibility in the Integers, Division with Remainder |
| 2 |
Tuesday, 9/1 |
2.4 - 2.5 |
GCDs, Euclidean Algorithm, Primes, Fundamental Theorem of Arithmetic |
| 3 |
Thursday, 9/3 |
3.1 - 3.5 |
Equivalence Relations, Functions, Defining Functions on Equivalence Classes |
| 4 |
Friday, 9/4 |
3.6 - 4.3 |
Modular Arithmetic, The Group Axioms, Examples and Basic Results |
| 5 |
Monday, 9/7 |
4.4 - 4.5 |
The Groups Z/nZ, U(Z/nZ), and S_n |
| 6 |
Tuesday, 9/8 |
4.6 - 5.2 |
Orders of Elements, Direct Products, Subgroups |
| 7 |
Thursday, 9/10 |
5.2 - 5.3 |
Cyclic Groups, Inversions of Permutations, The Alternating Groups |
| 8 |
Friday, 9/11 |
5.4 - 5.7 |
Dihedral Groups, Center of a Group, Cosets |
| 9 |
Monday, 9/14 |
5.7 - 5.8 |
Cosets, Lagrange's Theorem |
| 10 |
Tuesday, 9/15 |
6.1 - 6.2 |
Quotients of Abelian Groups, Normal Subgroups |
| 11 |
Thursday, 9/17 |
6.2 - 6.3 |
Quotient Groups, Simple Groups, Isomorphisms |
| 12 |
Friday, 9/18 |
- |
First Exam |
| - |
Monday, 9/21 |
- |
Class Canceled |
| 13 |
Tuesday, 9/22 |
6.3 - 6.4 |
Isomorphisms, Internal Direct Products |
| 14 |
Thursday, 9/24 |
6.5 - 6.6 |
Classifying Groups up to Isomorphism, Homomorphisms |
| 15 |
Friday, 9/25 |
6.7, 8.1 |
First Isomorphism Theorem, Correspondence Theorem, Group Actions |
| 16 |
Monday, 9/28 |
8.1 - 8.3 |
Orbit-Stabilizer Theorem, Cayley's Theorem, The Conjugation Action |
| 17 |
Tuesday, 9/29 |
8.3 - 8.5 |
Class Equation, Cauchy's Theorem, Counting Orbits |
| 18 |
Thursday, 10/1 |
9.1 - 9.2 |
Rings, Units and Zero Divisors, Integral Domains and Fields |
| 19 |
Friday, 10/2 |
9.3 - 10.1 |
Polynomial Rings, More Ring Examples, Ideals |
| 20 |
Monday, 10/5 |
10.1 - 10.2 |
Ideals, Quotients, Ring Homomorphisms, Characteristic of a Ring |
| 21 |
Tuesday, 10/6 |
- |
Second Exam |
| 22 |
Thursday, 10/8 |
10.3 - 10.4 |
Roots of Polynomials, Lagrange Interpolation, Generating Subrings and Ideals |
| 23 |
Friday, 10/9 |
10.5 - 11.1 |
Prime and Maximal Ideals, Field of Fractions, Divisibility and Associates |
| 24 |
Monday, 10/12 |
11.2 - 11.3 |
Irreducible Elements, Irreducible Polynomials in Q[x] |
| 25 |
Tuesday, 10/13 |
11.4 - 11.5 |
Prime Elements, UFDs |
| 26 |
Thursday, 10/15 |
12.1 - 12.2 |
Euclidean Domains, PIDs |
| 27 |
Friday, 10/16 |
12.2 - 12.3 |
Quotients of F[x], Finite Fields |