Math 31
Fall, 2005
The
following is a tentative syllabus for the
course. It is based on the 6th edition of Contemporary Abstract Algebra
by Joseph A. Gallian.
This page is a rough guide and will be updated irregularly. You can find an
exact weekly Syllabus in Homework.
|
Lectures |
Chapter |
Brief
Description |
|
Day 1: September 21, Wednesday |
Chapter 1 |
Course Administration. Introduction to Groups: Symmetries of the Square |
|
Day 2: September 23, Friday |
Chapter 2 |
Definitions and Examples of Groups |
|
Day 3: September 26, Monday |
Chapter 3 |
Exploring Basic Group Properties; Finite Groups |
|
September 27, Tuesday |
|
Last day to add a course without permission |
|
Day 4: September 28, Wednesday |
Chapter 3 |
Subgroups and Subgroup Tests; Some "special" subgroups |
|
Day 5: September 30, Friday |
Chapter 4 |
Cyclic Groups |
|
Day 6: October 3, Monday |
Chapter 5 |
Permutation Groups |
|
Day 7: October 5, Wednesday |
Chapter 5 |
Properties of Permutations |
|
Day 8: October 7, Friday |
Chapter 6, 8 |
Cayley’s Theorem; External Direct Products |
|
Day 9: October 10, Monday |
Chapter 7 |
Cosets and Lagrange’s Theorem |
|
Day 10: October 12, Wednesday |
Chapter 7 |
Consequences of Lagrange’s Theorem |
|
Day 11: October 14, Friday |
Chapter 9 |
Normal Subgroups and Factor Groups |
|
Day 12: October 17, Monday |
Chapter 9 |
More on Factor Groups |
|
Day 13: October 19, Wednesday |
Chapter 10 |
Group Homomorphisms |
|
Day 14: October 20, Thursday |
Chapter 10 |
X-hour: Fundamental Homomorphism Theorem and Isomorphism Theorems |
|
October 21, Friday |
|
Homecoming Weekend. Classes moved to the X-hour |
|
Day 15: October 24, Monday |
Chapter 12 |
Rings |
|
October 24, Monday |
|
Take Home Midterm begins. |
|
Day 16: October 26, Wednesday |
Chapter 13 |
Integral Domains |
|
October 28, Friday |
|
Take Home Midterm due at start of class. |
|
Day 17: October 28, Friday |
Chapter 13 |
Fields and the Characteristic of a Ring |
|
Day 18: October 31, Monday |
Chapter 14 |
Ideals and Factor Rings |
|
Day 19: November 2, Wednesday |
Chapter 14, 15 |
Prime and Maximal Ideals; Ring Homomorphisms |
|
Day 20: November 4, Friday |
Chapter 15 |
Ring Homemorphisms II |
|
Day 21: November 7, Monday |
Chapter 16 |
Polynomial Rings |
|
Day 22: November 9, Wednesday |
Chapter 17 |
Reducible and Irreducible Polynomials |
|
Day 23: November 11, Friday |
Chapter 17 |
Irreducibility Criterion |
|
November 11, Friday |
|
Last day to withdraw from a course |
|
Day 24: November 14, Monday |
Chapter 18 |
More Ring Types |
|
Day 25: November 16, Wednesday |
Chapter 19 |
Review of Vector Spaces |
|
Day 26: November 18, Friday |
Chapter 20 |
Field Extensions |
|
Day 27: November 21, Monday |
Chapter 20, 21 |
Zeros of Polynomials; Finite Field Extensions |
|
November 22 - 27 |
|
Thanksgiving Holiday |
|
Day 28: November 28, Monday |
Chapter 21 |
Algebraic Field Extensions |
|
Day 29: November 30, Wednesday |
Chapter 0 |
Review |
|
December 3 - 7 |
|
Final Examination Period |