| Lecture |
Date |
Section |
Topic |
Homework |
| 1 |
8/25 |
1.2 |
Sets |
1.2# 1, 2, 4, 11, 20, 23 |
| 2 |
8/27 |
1.2 |
Equivalence Relations
|
1.2# 21, 24, 25, 28 |
| 3 |
8/30 |
2.1 |
Mathematical Induction
|
2.1# 2, 3, 5, 9 |
| 4 |
9/1 |
2.1 |
Mathematical Induction - con'd |
|
| 5 |
9/3 |
2.2 |
The Division Algorithm
|
2.1# 7*, 11, 19, 20, 23 |
| 6 |
9/6 |
3.1 |
The Integers mod n
|
Cht. 3# 1, 20, 23 and p. 47# 1(a,b,c,d) |
| 7 |
9/8 |
3.1 |
Symmetries
|
Cht. 3# 2, 3, 8, 13 |
| 8 |
9/10 |
3.2 |
Definition of a Group
|
Cht. 3# 16, 24, 26, 27, 29, 31 |
| 9 |
9/13 |
3.2 |
Examples
|
|
| 10 |
9/15 |
3.3 |
Subgroups
|
Cht 3# 40, 41 |
| 11 |
9/17 |
4.1 |
Cyclic Subgroups
|
Cht. 4# 2, 4ab, 5, 26, 31 |
| 12 |
9/20 |
4.2 |
The Group C* |
Cht. 4# 24, 26, 38* |
| 13 |
9/22 |
4.3 |
Method of Repeated Squares
|
|
| 14 |
9/24 |
5.1 |
Permutation Groups
|
Cht. 5# 1, 2(a,c,e), 3, 4, 17 |
| 15 |
9/27 |
5.1 |
Permutation Groups - con'd
|
Cht. 5# 14, 24 |
| 16 |
9/29 |
5.2 |
Dihedral Groups
|
Cht. 5# 8, 10, 13* |
| 17 |
10/1 |
6.1 |
Cosets
|
Cht. 6# 3, 4, 12, 18 |
| 18 |
10/4 |
6.2 |
Lagrange's Theorem
|
Cht. 6# 8 |
| 19 |
10/6 |
|
Review |
|
| 20 |
10/8 |
|
Midterm 1
|
|
| 21 |
10/11 |
|
|
|
| 22 |
10/13 |
6.3 |
Fermat's Little Theorem
|
Cht. 3# 6; Cht. 6# 5b, 7 |
| 23 |
10/15 |
6.3 |
Euler's Theorem
|
|
| 24 |
10/18 |
9.1 |
Isomorphisms
|
Cht. 9# 15, 16, 24, 25, 50 |
| 25 |
10/20 |
9.1 |
Cayley's Theorem
|
Cht. 9# 11, 48, 28* |
| 26 |
10/22 |
9.2 |
Direct Products
|
|
| 27 |
10/25 |
10.1 |
Factor Groups
|
Cht. 10# 1(a, c, d, e), 17, 21 |
| 28 |
10/27 |
10.1 |
Normal Subgroups
|
Cht. 10# 8, 12, 32 |
| 29 |
10/29 |
10.2 |
Group Homomorphisms
|
Cht. 10# 9, 13, 15 |
| 30 |
11/1 |
10.3 |
Simple Groups
|
Cht. 10# 23 (Hint), 26* |
| 31 |
11/3 |
15.1 |
Rings
|
Cht. 15# 1(a,b,c), 3(b,c,d) |
| 32 |
11/5 |
15.2 |
Integral Domains and Fields
|
Cht. 15# 11, 17 |
| 33 |
11/8 |
15.3 |
Ring Homomorphisms and Ideals
|
Cht. 15# 4(a,b,d), 28 |
| 34 |
11/10 |
15.4 |
Maximal and Prime Ideals
|
|
| 35 |
11/12 |
16.1 |
Polynomial Rings
|
Cht. 16# 1, 2(a,c,e), 3(a,b), 11, 23 |
| 36 |
11/15 |
16.2 |
Division Algorithm for Polynomials
|
|
| 37 |
11/17 |
|
Review |
|
| 38 |
11/19 |
|
Midterm 2 |
|
| 39 |
11/22 |
16.3 |
Irreducible Polynomials
|
|
| 40 |
11/24 |
|
|
|
| 41 |
11/26 |
|
|
|
| 42 |
11/29 |
13.1 |
Groups Acting on Sets
|
Cht. 13# 1, 4, 5, 20 |
| 43 |
12/1 |
13.2 |
The Class Equation
|
Cht. 13# 23 |
| 44 |
12/3 |
|
Presentations
|
|
| 45 |
12/6 |
|
Presentations
|
|