Math 335 Abstract Algebra I
Monday, Wednesday, and Friday 12:10-1:00pm
Hayes Hall 203
Textbook
A First Course in Abstract Algebra, Seventh Edition, by John B. Fraleigh.
Office Hours (Hayes 309-A)
Monday 2:10-3:00pm
Tuesday
12:10-2:00pm
Thursday
10:10am-12:00pm
Homework – Turn in asterisked problems.
|
Lesson |
Date |
Section |
Topic |
Homework |
Presentation Problems |
Due |
|
1 |
8/30/2013 |
1 |
Introduction
and Examples |
#4, 7, 8*, 10,
16, 18*, 20, 22, 24, 26*, 32*, 37*, 38 |
|
9/2/2013 |
|
|
#33-36 |
9/4/2013 |
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|
2 |
9/2/2013 |
2 |
Binary Operations |
#1-3, 4*, 5,
7-9, 10*, 17, 18*, 19-21, 22*, 24, 28*, 33*, 34*, 37* |
|
9/6/2013 |
|
|
#26, 35-37 |
9/4/2013 |
||||
|
3 |
9/4/2013 |
1, 2 |
|
Student
Presentations |
|
|
|
4 |
9/6/2013 |
3 |
Isomorphic Binary Structures |
#2*, 3, 6*, 7,
15, 16*, 21, 23*, 27*, 28, 29*, Section 3
Worksheet |
|
9/9/2013 |
|
#31, 32 |
9/11/2013 |
|||||
|
5 |
9/9/2013 |
4 |
Groups! |
#2, 3, 5, 6*,
8, 9*, 19, 21, 23, 24*, 27*, 28*, 29* |
|
9/13/2013 |
|
#33, 34, 36,
41 |
9/11/2013 |
|||||
|
6 |
9/11/2013 |
3, 4 |
|
Student
Presentations |
|
|
|
7 |
9/13/2013 |
5 |
odk: Sections 1-4, Subgroups |
#1-5, 6*,
7abcdef*, 11, 13-15, 18*, 20, 22, 24, 26*, 27, 28*, 29, 36*, 39, 40, 42*, 51,
54* |
|
9/18/2013 |
|
#46, 57 |
9/20/2013 |
|||||
|
8 |
9/16/2013 |
6 |
Cyclic Groups |
#5-9, 10*,
14*, 15, 17, 20-21, 22*, 24, 27*, 29, 32, 33, 34*, 35, 36*, 37, 45*, 49* Worksheet (day
2): 5, 7*, 9* |
|
9/23/2013 |
|
#50, 51, 52 |
9/20/2013 |
|||||
|
9 |
9/18/2013 |
6 |
Cyclic Groups |
|
|
|
|
10 |
9/20/2013 |
5, 6 |
|
Student
Presentations |
|
|
|
11 |
9/23/2013 |
8 |
odk: Sections 5-6, Permutation Groups |
#1, 5*, 6, 7*,
9-11, 13, 17, 18*, 21, 23-29, 32, 35, 46* |
|
Due 9/27/2013, not to be collected. |
|
12 |
9/25/2013 |
8 |
Permutation Groups |
|
|
|
|
13 |
9/27/2013 |
9 |
Orbits, Cycles, and the Alternating Groups |
|
|
|
|
14 |
9/30/2013 |
|
In-class
ODK I |
Take-home ODK I |
10/4/2013 |
|
|
15 |
10/2/2013 |
|
Intro to GAP |
Worksheet |
|
|
|
16 |
10/4/2013 |
9 |
Orbits, Cycles, and the Alternating Groups |
#2, 3, 6*, 8*,
11, 12*, 14, 15, 17*, 20-24, 25*, 26, 29*, 33*, 34 |
|
10/9/2013 |
|
Group 1: #27a, 30 Group 2: #27b, 31 Group 3: #27c, 32 |
10/14/2013 |
|||||
|
17 |
10/7/2013, 10/9/2013 |
10 |
Cosets and Lagrange’s Theorem |
#1, 2*, 3, 4,
12*, 19, 20, 21*, 22-24, 25*, 28*, 29*, 32, 34* Worksheet 1:
#4*, 5, 6* |
|
10/18/2013 |
|
|
#27, 35, 36, 39, 40, coset
properties |
10/16/2013 |
||||
|
18 |
10/14/2013 |
9 |
|
Student
Presentations |
|
|
|
19 |
10/16/2013 |
10 |
|
Student
Presentations |
|
|
|
20 |
10/18/2013 |
8, 9 |
Rubik’s Cube |
GAP Rubik’s
Worksheet: 1-5, 6*, 7*. Study coset
material for odk. |
10/21/2013 |
|
|
21 |
10/21/2013 |
|
odk, Discussion of ODK I |
Read Section
11. |
|
10/23/2013 |
|
22 |
10/23/2013 |
11 |
Direct Products and Finitely Generated Abelian Groups |
#1, 6, 7*, 8*,
10, 13, 14, 15*, 16*, 19, 20, 24*, 25, 29*, 32, 36, 39-42, 43*, 46, 50, 51 Worksheet: #5* |
|
10/28/2013 |
|
|
#52-54 Worksheet: #4, 7 |
10/25/2013 |
||||
|
23 |
10/25/2013 |
11 |
|
Student
Presentations |
11/8/2013 |
|
|
24 |
10/28/2013 |
11 |
Direct Product Homework Discussion |
Read Section
13. |
|
10/30/2013 |
|
25 |
10/30/2013 |
13 |
Homomorphisms |
#2, 4, 5, 8*,
9, 15, 16, 19-21, 25, 26*, 29*, 32, 33, 36, 38, 40, 44*, 45*, 50, 52* Worksheet:
#3.4, 4*, 6* |
|
11/4/2013 |
|
26 |
11/1/2013, 11/4/2013, 11/6/2013 |
14 |
odk, Factor Groups |
#1, 2*, 3-9,
10*, 11-19, 22, 23, 24*, 25*, 27, 29, 34*, 38 Worksheet:
#2g, 4* Read Section
14. |
|
Due 11/8/2013, not to be collected |
|
27 |
11/8/2013 |
|
Review for ODK II |
Study! |
|
|
|
28 |
11/11/2013 |
|
In-class
ODK II |
Take-home ODK II |
|
11/18/2013 |
|
29 |
11/13/2013 |
|
Conjugacy Classes |
GAP Exploring
Conjugation Worksheet: #1-8 (recommended only) |
|
11/20/2013 |
|
30 |
11/15/2013 |
|
Conjugacy Classes |
Turn outline
of proof into proof.* Read Section
15. |
|
11/20/2013 |
|
31 |
11/18/2013 |
15 |
Factor-Group Computations and Simple Groups |
#7, 9, 10, 11*,
14, 16*, 19, 22, 26, 30, 33*, 40*, 41* Worksheet:
#1-8, 3f*, 4b* Read Section
16. |
#34-36 |
11/22/2013 |
|
32 |
11/20/2013 |
16 |
Group Action on a Set |
#1, 2*, 3*,
4-6, 7*, 8, 10*, 11*, 12 11/22
worksheet: 1-3, 4*, 5* |
|
12/4/2013 |
|
33 |
11/22/2013 |
15 |
|
Student
Presentations, start homework
worksheet. |
|
|
|
34 |
12/2/2013 |
34 Wow! – Good thing we skipped ahead! |
The Isomorphism Theorems |
Worksheet:
#2e*, 3g*, 4*, 5*, 6* (Note that #6 should be an application of the 2nd, not the 3rd, isomorphism thm). Section 34:
#2, 4, 8* Read Section
34. |
|
12/6/2013 |
|
|
#7, 9 |
12/6/2013 |
||||
|
35 |
12/4/2013, 12/6/2013 |
36 |
The Sylow Theorems |
Read Section
36. Finish the
in-class worksheet. Study for odk
Monday (Sections 15, 16, 34). *Prove the
First Sylow Theorem in your own words; explain each step. |
|
12/9/2013 |
|
36 |
12/9/2013 |
36! |
The Sylow Theorems |
Study for odk
Wednesday (State Sylow Theorems). Finish
worksheet problems 1 and 2, think about 3. |
|
12/11/2013 |
|
Section 36: #2,
4-13, 17, 19 |
Section 37: #5, 6 |
Due 12/13/2013, not to be collected. |