| Class Number |
Date |
Sections in Notes |
Brief Description |
| 1 |
Monday, 1/20 |
1.1 - 1.4, 2.1 |
Introduction, Ideas and Goals of Abstract Algebra, Induction |
| 2 |
Wednesday, 1/22 |
2.2 - 2.4 |
Divisibility in the Integers, Division with Remainder, GCDs,
Euclidean Algorithm |
| 3 |
Friday, 1/24 |
2.4 - 2.5 |
Primes, The Fundamental Theorem of Arithmetic |
| 4 |
Monday, 1/27 |
3.1 - 3.3 |
Equivalence Relations, Functions |
| 5 |
Wednesday, 1/29 |
3.4 - 3.6 |
Left and Right Inverses of Functions, Defining Functions on
Equivalence Classes, Modular Arithmetic |
| 6 |
Friday, 1/31 |
4.1 - 4.3 |
The Group Axioms, Examples |
| 7 |
Monday, 2/3 |
4.4 - 4.5 |
The Groups Z/nZ, U(Z/nZ), and S_n |
| 8 |
Wednesday, 2/5 |
4.6 |
Orders of Elements |
| 9 |
Friday, 2/7 |
4.7, 5.1 - 5.2 |
Direct Products, Subgroups, Cyclic Groups |
| 10 |
Monday, 2/10 |
5.2 - 5.3 |
Generating Subgroups, The Alternating Groups |
| 11 |
Wednesday, 2/12 |
5.3 - 5.4 |
The Alternating and Dihedral Groups |
| 12 |
Friday, 2/14 |
5.5 - 5.7 |
The Quaternion Group, The Center of a Group, Cosets |
| 13 |
Monday, 2/17 |
5.7 - 5.8 |
Cosets, Lagrange's Theorem |
| 14 |
Wednesday, 2/19 |
5.8, 6.1 |
Applications of Lagrange's Theorem, Quotients of Abelian Groups |
| 15 |
Friday, 2/21 |
6.1 - 6.2 |
Normal Subgroups, Quotient Groups |
| 16 |
Monday, 2/24 |
6.2 |
Quotient Groups, Simple Groups |
| 17 |
Wednesday, 2/26 |
6.3 |
Isomorphisms |
| 18 |
Friday, 2/28 |
- |
First Exam |
| 19 |
Monday, 3/3 |
6.4 - 6.5 |
Internal Direct Products, Classifying Groups up to Isomorphism |
| 20 |
Wednesday, 3/5 |
6.5 - 6.6 |
Classifying Groups up to Isomorphism, Homomorphisms |
| 21 |
Friday, 3/7 |
6.6 - 6.7 |
The Isomorphism and Correpsondence Theorems |
| 22 |
Monday, 3/10 |
7.1 - 7.2 |
Group Actions, Orbits, Stabilizers |
| 23 |
Wednesday, 3/12 |
7.2 - 7.3 |
Cayley's Theorem, The Conjugation Action |
| 24 |
Friday, 3/14 |
7.3 - 7.4 |
The Class Equation, Cauchy's Theorem, Simplicity of A_5 |
| - |
- |
- |
Spring Break |
| 25 |
Monday, 3/31 |
7.5, 8.1 |
Counting Orbits, Structure of Cyclic Groups |
| 26 |
Wednesday, 4/2 |
9.1 - 9.2 |
The Ring Axioms, Units and Zero Divisors |
| 27 |
Friday, 4/4 |
9.2 - 9.3 |
Integral Domains, Fields, Polynomial Rings |
| 28 |
Monday, 4/7 |
9.3 - 9.4 |
Division with Remainder in Polynomial Rings, Power Series, Matrix
Rings, Rings of Functions |
| 29 |
Wednesday, 4/9 |
10.1 |
Ideals, Quotients, Ring Homomorphisms |
| 30 |
Friday, 4/11 |
10.2 - 10.3 |
Characteristic of a Ring, Polynomial Evaluation, Roots |
| 31 |
Monday, 4/14 |
10.3 - 10.5 |
Lagrange Interpolation, Generating Subrings and Ideals, Prime and
Maximal Ideals |
| 32 |
Wednesday, 4/16 |
10.5, 11.1 |
Prime and Maximal Ideals, Divisibility and Associates |
| 33 |
Friday, 4/18 |
11.1 - 11.2 |
Greatest Common Divisors, Irreducible and Prime Elements |
| 34 |
Monday, 4/21 |
11.3 |
Irreducible Polynomials in Q[x] |
| 35 |
Wednesday, 4/23 |
- |
Second Exam |
| 36 |
Friday, 4/25 |
- |
Guest Speaker |
| 37 |
Monday, 4/28 |
11.4 |
Unique Factorization Domains |
| 38 |
Wednesday, 4/30 |
12.1 |
Euclidean Domains |
| 39 |
Friday, 5/2 |
12.2 |
Principal Ideal Domains |
| 40 |
Monday, 5/5 |
12.2 - 12.3 |
Ideals and Quotients of PIDs |
| 41 |
Wednesday, 5/7 |
12.3 - 12.4 |
Quotients of F[x], Field of Fractions |
| 42 |
Friday, 5/9 |
- |
Linear Algebra |