| Week | Tuesday | Wednesday | Thursday |
|---|---|---|---|
| 1 (Jan 2-4) | no class | Introduction, the dihedral group (Chapter 1) In class: 1-(2,3,11), 0-22 |
Groups (Chapter 2), Order of a Group (Chapter 3) In class: 2-(3,8,26,25) |
| 2 (Jan 7-11) | Subgroups, Cyclic groups (Chapter 3) In class: 2-(9,29), 3-1 |
Cyclic Groups (Chapter 4) In class: 3-(2,3) |
Fundamental Theorem of Cyclic Groups, Euler Phi Function (Chapter 4) In class: 3-51, 4-(3,4,5) |
| 3 (Jan 14-18) | Introduction to Permutations (Chapter 5) In class: 5-(1,2,3,4) |
Odd and Even Permutations (Chapter 5) In class: 4-(17,21) |
Permutations, Isomorphisms (Chapter 5-6) In class: P.90-(1,4) |
| 4 (Jan 21-25) | Isomorphisms, Automorphisms (Chapter 6) In class: D_4 is isomorphic to a group of permutations |
Cosets (Chapter 7) In class: Aut(G) and Inn(G) are groups, 7-1 |
Lagrange's Theorem (Chapter 7) In class: Converse of Lagrange's Theorem is not true, D_4 is not isomorphic to the quaternion group |
| 5 (Jan 28-Feb 1) | External Direct Product (Chapter 8) In class: Stabilizer and Orbit |
External Direct Product, Normal Subgroup (Chapter 9) In class: Orbit-Stabilizer Theorem |
Factor Groups (Chapter 9) In class: 3-14, 6-23, 7-16 |
| 6 (Feb 4-8) | Internal Direct Product (Chapter 9), Group Homomorphisms (Chapter 10) In class: 8-7,25, 9-1 |
Review, Group Homomorphisms (Chapter 10) In class: 8-26, 9-6 |
Test 1 |
| 7 (Feb 11-15) | First Isomorphism Theorem (Chapter 10) In class: Proofs of 10.2, 10.3 |
Fundamental Theorem of Finite Abelian Groups (Chapter 11), Rings
(Chapter 12) In class: Presentation of proofs |
Properties of Rings (Chapter 12), Intergral Domains and Fields
(Chapter 13) In class: Thm 12.1, 12-3 |
| 8 (Feb 18-22) | Integral Domains, Fields, Characteristic (Chapter 13) In class: 12-6,19,38 |
Ideals, Factor Rings (Chapter 14) In class: Example 11 |
Prime and Maximal Ideals, Ring Homomorphisms (Chapters 14, 15) In class: 13-16, 18, 19, 20, 50 |
| 9 (Feb 25-29) | Ring Homomorphisms, First Isomorphism Theorem for Rings, Field of
Quotients (Chapter 15) In class: Theorem 15.1 |
Polynomial Rings, Division Algorithm for F[x], Remainder Theorem,
Factor Theorem (Chapter 16) In class: Presentations |
Principal Ideal Domain, Irreducible Polynomials (Chapters 16-17) In class: Homework 9 |
| 10 (Mar 3-7) | Review, SOCI | Test 2 | Mod p irreducibility test, Eisenstein's Criterion, Unique Factorization in Z[x] (Chapter 17) |
| 11 (Mar 10-11) | Review | Exam Period | Exam Period |