| Class Number |
Date |
Brief Description |
| 1 |
Friday, 8/27 |
Introduction, The Group Axioms, Examples |
| 2 |
Monday, 8/30 |
Properties of Groups, Induction, Well-Ordering, The Binomial Theorem |
| 3 |
Wednesday, 9/1 |
Divisibility in the Integers, Division with Remainder |
| 4 |
Friday, 9/3 |
Common Divisors, GCDs, The Euclidean Algorithm |
| 5 |
Monday, 9/6 |
Primes, The Fundamental Theorem of Arithmetic |
| 6 |
Wednesday, 9/8 |
Equivalence Relations, Defining Functions on Equivalence Classes,
Modular Arithmetic |
| 7 |
Friday, 9/10 |
Modular Arithmetic, The Groups Z/nZ and U(Z/nZ) |
| 8 |
Monday, 9/13 |
Orders, Subgroups |
| 9 |
Wednesday, 9/15 |
Subgroups, Cyclic Groups, Generating Subgroups |
| 10 |
Friday, 9/17 |
Functions, Symmetric Groups, Cycle Notation |
| - |
Monday, 9/20 |
Class Canceled |
| 11 |
Wednesday, 9/22 |
Alternating and Dihedral Groups |
| 12 |
Friday, 9/24 |
First Exam |
| 13 |
Monday, 9/27 |
Dihedral Groups, Cosets |
| 14 |
Wednesday, 9/29 |
Index of a Subgroup, Lagrange's Theorem and Applications |
| 15 |
Friday, 10/1 |
Direct Products, Quotients of Abelian Groups |
| 16 |
Monday, 10/4 |
Quotients of Abelian Groups, Normal Subgroups |
| 17 |
Wednesday, 10/6 |
Quotient Groups, Simple Groups |
| 18 |
Friday, 10/8 |
Isomorphisms |
| 19 |
Monday, 10/11 |
Cayley's Theorem, Internal Direct Products |
| 20 |
Wednesday, 10/13 |
Homomorphisms, The First Isomorphism Theorem |
| 21 |
Friday, 10/15 |
The Isomorphism and Correspondence Theorems |
| - |
Monday, 10/18 |
Fall Break |
| - |
Wednesday, 10/20 |
Fall Break |
| - |
Friday, 10/22 |
Fall Break |
| 22 |
Monday, 10/25 |
Group Actions, Orbits, Stabilizers |
| 23 |
Wednesday, 10/27 |
Conjugation, The Class Equation |
| 24 |
Friday, 10/29 |
Cauchy's Theorem, Counting Orbits |
| 25 |
Monday, 11/1 |
Using the Class Equation to find Normal Subgroups, Simplicity of A_5 |
| 26 |
Wednesday, 11/3 |
Rings, Units and Zero Divisors |
| 27 |
Friday, 11/5 |
Integral Domains, Fields, Polynomial Rings |
| 28 |
Monday, 11/8 |
Power Series Rings, Matrix Rings, Ideals, Quotients, Homomorphisms |
| 29 |
Wednesday, 11/10 |
Principal Ideals, Prime and Maximal Ideals |
| 30 |
Friday, 11/12 |
Characteristic of a Ring, Divisibility in Integral Domains |
| 31 |
Monday, 11/15 |
Polynomial Rings over Fields |
| 32 |
Wednesday, 11/17 |
Euclidean Domains, The Gaussian Integers |
| 33 |
Friday, 11/19 |
Principal Ideal Domains |
| 34 |
Monday, 11/22 |
UFDs, Roots of Polynomials |
| 35 |
Wednesday, 11/24 |
Gauss' Lemma, Eisenstein's Criterion |
| - |
Friday, 11/26 |
Thanksgiving Break |
| 36 |
Monday, 11/29 |
Quotients of F[x], Field of Fractions |
| 37 |
Wednesday, 12/1 |
Third Exam |
| 38 |
Friday, 12/3 |
Field of Fractions, Field Extensions |
| 39 |
Monday, 12/6 |
Algebraic Elements, Minimal Polynomials |
| 40 |
Wednesday, 12/8 |
Extensions by One Algebraic Element |
| 41 |
Friday, 12/10 |
Finite Extensions, Algebraically Closed Fields |