Math 335 Abstract Algebra I
Monday, Wednesday, and Friday 12:101:00pm
Hayes Hall 203
Textbook
A First Course in Abstract Algebra, Seventh Edition, by John B. Fraleigh.
Office Hours (Hayes 309A)
Monday 2:103:00pm
Tuesday
12:102:00pm
Thursday
10:10am12:00pm
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 

#3336 
9/4/2013 

2 
9/2/2013 
2 
Binary Operations 
#13, 4*, 5,
79, 10*, 17, 18*, 1921, 22*, 24, 28*, 33*, 34*, 37* 

9/6/2013 

#26, 3537 
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 14, Subgroups 
#15, 6*,
7abcdef*, 11, 1315, 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 
#59, 10*,
14*, 15, 17, 2021, 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 56, Permutation Groups 
#1, 5*, 6, 7*,
911, 13, 17, 18*, 21, 2329, 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 

Inclass
ODK I 
Takehome 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*, 2024, 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*, 2224, 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: 15, 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, 3942, 43*, 46, 50, 51 Worksheet: #5* 

10/28/2013 

#5254 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, 1921, 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*, 39,
10*, 1119, 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 

Inclass
ODK II 
Takehome ODK II 

11/18/2013 
29 
11/13/2013 

Conjugacy Classes 
GAP Exploring
Conjugation Worksheet: #18 (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 
FactorGroup Computations and Simple Groups 
#7, 9, 10, 11*,
14, 16*, 19, 22, 26, 30, 33*, 40*, 41* Worksheet:
#18, 3f*, 4b* Read Section
16. 
#3436 
11/22/2013 
32 
11/20/2013 
16 
Group Action on a Set 
#1, 2*, 3*,
46, 7*, 8, 10*, 11*, 12 11/22
worksheet: 13, 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 2^{nd}, not the 3^{rd}, 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
inclass 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,
413, 17, 19 
Section 37: #5, 6 
Due 12/13/2013, not to be collected. 