| 1 |
Monday, 1/23 |
1.1 - 1.3, 2.1 - 2.2 |
Introduction, Ideas and Goals of Abstract Algebra, Divisibility in the Integers |
| 2 |
Wednesday, 1/25 |
2.2 - 2.4 |
Divisibility in the Integers, Division with Remainder, GCDs, Euclidean Algorithm |
| 3 |
Friday, 1/27 |
2.4 - 2.5 |
Primes, The Fundamental Theorem of Arithmetic |
| 4 |
Monday, 1/30 |
3.1 - 3.3 |
Equivalence Relations, Functions, Composition |
| 5 |
Wednesday, 2/1 |
3.4 - 3.6 |
Left and Right Inverses of Functions, Defining Functions on Equivalence Classes, Modular Arithmetic |
| 6 |
Friday, 2/3 |
4.1 - 4.3 |
The Group Axioms, Examples |
| 7 |
Monday, 2/6 |
4.4 - 4.5 |
The Groups Z/nZ, U(Z/nZ), and S_n |
| 8 |
Wednesday, 2/8 |
4.5 - 4.6 |
Symmetric Groups, Orders of Elements |
| 9 |
Friday, 2/10 |
4.7 - 5.2 |
Direct Products, Subgroups |
| 10 |
Monday, 2/13 |
5.2 - 5.3 |
Cyclic Groups, Inversions of Permutations |
| 11 |
Wednesday, 2/15 |
5.3 - 5.4 |
The Alternating and Dihedral Groups |
| 12 |
Friday, 2/17 |
5.4 - 5.7 |
Dihedral Groups, Center of a Group, Cosets |
| 13 |
Monday, 2/20 |
5.7 - 5.8 |
Cosets, Lagrange's Theorem |
| 14 |
Wednesday, 2/22 |
5.8 - 6.1 |
Applications of Lagrange's Theorem, Quotients of Abelian Groups |
| 15 |
Friday, 2/24 |
6.2 |
Normal Subgroups, Quotient Groups |
| 16 |
Monday, 2/27 |
6.2 |
Quotient Groups, Simple Groups |
| 17 |
Wednesday, 3/1 |
6.3 |
Isomorphisms |
| 18 |
Friday, 3/3 |
6.4 - 6.5 |
Internal Direct Products, Classifying Groups up to Isomorphism |
| 19 |
Monday, 3/6 |
6.5 - 6.6 |
Classifying Groups up to Isomorphism, Homomorphisms |
| 20 |
Wednesday, 3/8 |
- |
First Exam |
| 21 |
Friday, 3/10 |
6.6 - 6.7 |
Homomorphisms, The First Isomorphism Theorem |
| 22 |
Monday, 3/13 |
6.7 - 7.1 |
The Correspondence Theorem, The Structure of Cyclic Groups |
| 23 |
Wednesday, 3/15 |
8.1 - 8.2 |
Group Actions, Orbits, Stabilizers |
| 24 |
Friday, 3/17 |
8.2 - 8.3 |
Cayley's Theorem, The Conjugation Action, The Class Equation |
| - |
- |
- |
Spring Break |
| 25 |
Monday, 4/3 |
8.3 - 8.4 |
The Class Equation, Cauchy's Theorem, Simplicity of A_5 |
| 26 |
Wednesday, 4/5 |
8.5 - 9.2 |
Counting Orbits, The Ring Axioms, Units and Zero Divisors |
| 27 |
Friday, 4/7 |
9.1 - 9.3 |
Rings, Integral Domains, Fields, Polynomial Rings |
| 28 |
Monday, 4/10 |
9.3 - 9.4 |
Division with Remainder in Polynomial Rings, Power Series, Matrix Rings, Rings of Functions |
| 29 |
Wednesday, 4/12 |
10.1 |
Ideals, Quotients, Ring Homomorphisms |
| 30 |
Friday, 4/14 |
10.2 - 10.3 |
Characteristic of a Ring, Polynomial Evaluation, Roots |
| 31 |
Monday, 4/17 |
10.3 - 10.4 |
Lagrange Interpolation, Generating Subrings and Ideals |
| 32 |
Wednesday, 4/19 |
10.5 - 10.6 |
Prime and Maximal Ideals, Field of Fractions |
| 33 |
Friday, 4/21 |
11.1 - 11.2 |
Divisibility and Associates, GCDs, Irreducible Elements |
| 34 |
Monday, 4/24 |
11.2 - 11.3 |
Irreducible Polynomials in Q[x] |
| - |
Wednesday, 4/26 |
- |
No Class |
| 35 |
Friday, 4/28 |
- |
Second Exam |
| 36 |
Monday, 5/1 |
11.4 - 11.5 |
Prime Elements, UFDs |
| 37 |
Wednesday, 5/3 |
11.5 - 12.1 |
UFDs, Euclidean Domains |
| 38 |
Friday, 5/5 |
12.1 - 12.2 |
Euclidean Domains, PIDs |
| 39 |
Monday, 5/8 |
12.2 - 12.3 |
PIDs and UFDs, Quotients of F[x] |
| 40 |
Wednesday, 5/10 |
- |
Linear Algebra, Finite Fields |
| 41 |
Friday, 5/12 |
- |
Where Does Abstract Algebra Go From Here? |