| Class Number |
Date |
Sections in Text |
Brief Description |
| 1 |
Friday, 8/28 |
0.1, 0.2 |
Introduction, Motivation, Operations on Sets |
| 2 |
Monday, 8/31 |
0.2 |
Relations, Functions, Injections, Surjections, Inverses |
| 3 |
Wednesday, 9/2 |
0.2 |
Equivalence Relations |
| 4 |
Friday, 9/4 |
1.1, 1.2 |
Mathematical Induction, Division, Greatest Common Divisors |
| 5 |
Monday, 9/7 |
1.2 |
GCDs, Euclidean Algorithm, Primes |
| 6 |
Wednesday, 9/9 |
1.2, 2.1, 2.2 |
Prime Factorization, Modular Arithmetic, Groups |
| 7 |
Friday, 9/11 |
2.2 |
Properties of Groups |
| 8 |
Monday, 9/14 |
2.3, 3.1 |
Subgroups, Cyclic Groups |
| 9 |
Wednesday, 9/16 |
3.1, 3.2 |
The Structure of Cyclic Groups, More Examples of Groups |
| 10 |
Friday, 9/18 |
4.1 |
The Symmetric Group, Permutation Groups, Cycle Notation |
| 11 |
Monday, 9/21 |
- |
First Exam |
| 12 |
Wednesday, 9/23 |
4.1, 4.2 |
Alternating and Dihedral Groups |
| 13 |
Friday, 9/25 |
5.1 |
Cosets |
| 14 |
Monday, 9/28 |
5.2, 5.3 |
Lagrange's Theorem and Applications |
| 15 |
Wednesday, 9/30 |
6.1 |
Primality Tests, Substitution Ciphers, Private Key Cryptography |
| 16 |
Friday, 10/2 |
6.2 |
Public Key Cryptography, RSA |
| 17 |
Monday, 10/5 |
8.1 |
Isomorphisms |
| 18 |
Wednesday, 10/7 |
8.1, 8.2 |
Cayley's Theorem, Direct Products of Groups |
| 19 |
Friday, 10/9 |
8.2, 9.1 |
Internal Direct Products, Motivating Quotient Groups |
| 20 |
Monday, 10/12 |
9.1 |
Normal Subgroups, Quotient Groups |
| 21 |
Wednesday, 10/14 |
- |
Second Exam |
| 22 |
Friday, 10/16 |
9.2 |
Examples of Quotient Groups, Group Homomorphisms |
| - |
Monday, 10/19 |
- |
Fall Break |
| - |
Wednesday, 10/21 |
- |
Fall Break |
| - |
Friday, 10/23 |
- |
Fall Break |
| 23 |
Monday, 10/26 |
9.2, 9.3 |
Group Homomorphisms, Simple Groups, The First Isomorphism Theorem |
| 24 |
Wednesday, 10/28 |
9.3 |
The Isomorphism and Correspondence Theorems |
| 25 |
Friday, 10/30 |
10.1, 11.1 |
The Orthogonal Group, Finite Abelian Groups |
| 26 |
Monday, 11/2 |
11.1, 12.1 |
Fundamental Theorem of Finitely Generated Abelian Groups, Group Actions |
| 27 |
Wednesday, 11/4 |
12.1, 12.2 |
Orbits, Stabilizers, The Class Equation |
| - |
Friday, 11/6 |
- |
Class Canceled |
| 28 |
Monday, 11/9 |
12.2 |
Conjugation, Consequences of the Class Equation |
| 29 |
Wednesday, 11/11 |
12.3 |
Burnside's Lemma, Counting Orbits |
| 30 |
Friday, 11/13 |
14.1, 14.2 |
Introduction to Rings |
| 31 |
Monday, 11/16 |
14.2, 14.3 |
Integral Domains, Fields, Ideals |
| 32 |
Wednesday, 11/18 |
- |
Third Exam |
| 33 |
Friday, 11/20 |
14.3, 14.4 |
Quotients, Maximal and Prime Ideals |
| 34 |
Monday, 11/23 |
15.1, 15.2 |
Polynomial Rings, Division |
| 35 |
Wednesday, 11/25 |
15.2, 15.3 |
Roots, GCDs in Polynomial Rings, Irreducibles |
| - |
Friday, 11/27 |
- |
Thanksgiving Break |
| 36 |
Monday, 11/30 |
15.3 |
Gauss' Lemma, Irreducibility Criteria |
| 37 |
Wednesday, 12/2 |
15.3, 16.1 |
Quotients of F[x], Fields of Fractions |
| 38 |
Friday, 12/4 |
16.2 |
Factorizations, PIDs, UFDs |
| 39 |
Monday, 12/7 |
16.2 |
PIDs are UFDs, Noetherian Rings |
| 40 |
Wednesday, 12/9 |
16.2, 18.1 |
Euclidean Domains, Vector Spaces |
| 41 |
Friday, 12/11 |
- |
Algebraic and Transcendental Numbers, Fundamental Theorem of Algebra |