Mathematics 5331  Abstract Algebra I Schedule/Homework

Spring 2009

 

Date

Section/Topic

Homework

Tuesday 1/20

1.1 Semigroups, monoids and groups

  1.  Problem 4, p.29. Give the Cayley table for the group of symmetries of the square.
  2.  Problem 5, p.29. Prove the order of Sn is n!
  3.  Prove Sn is non-abelian for n greater than 2.
  4.  Problems 13, 14 pp. 30

Thursday 1/22

1.1 Properties of Groups
 

  1. Prove Proposition 1.3 on page 25.

  2. Problem 6 on page 29.

  3. Prove Proposition 1.4 on page 25.

  4. Problem 15 on page 30.

Tuesday 1/27

UTA CLOSED

Thursday 1/29

1.2 Homomorphisms and subgroups

Pages 33-34 Problems # 1, 2, 6, 7, 9, 10, 11, 13
HW # 1: Turn-in Problems # 6 and # 11  on Tuesday February 10th

Tuesday 2/3

1.3 Cyclic groups

Pages 36-37 Problems # 1, 3, 4, 6, 8,  9
HW # 2: Turn-in Problem # 3 on Thursday February 12.

Thursday 2/5

NO CLASS

 

Tuesday 2/10

1.4 Cosets and counting

Page 40 # 2, 3, 6

Thursday 2/12


1.5 Normality


Page 45 # 1, 2, 5, 6, 7, 9a
HW # 3: Turn-in Problems: # 6 page 40; # 1, 7 page 45  on Thursday 2/19.

Tuesday 2/17

1.5 Quotient groups

 

Problems in group theory (Handout I )

Thursday 2/19

Test # 1

 

Tuesday 2/24

1.5 Isomorphism Theorems

Pages 45-46 #  11, 16
HW # 4: Turn-in Problems: # 11, 16 pages 45-46  on Thursday 3/5.

Thursday 2/26

1.6 Symmetric group

Study the proof of Corollary 6.4.
Page 51 # 2, 3, 4

Tuesday 3/3

1.6 Alternating group.
Cayley's Theorem

Page 51 # 5, 8

HW # 5: Turn-in Problems pp. 51-52 # 3, 5 on Thursday 3/12

Thursday 3/5 1.8 Direct products.
2.2 Finitely generated abelian groups
Handout (Chapter 5) p. 156 # 1; p.165 # 1 a, b; 2 a, b, c
Handout problems on group Theory # 3-7
Tuesday 3/10 2.2 Invariant factors. Elementary divisors

Handout (Chapter 5)  p.165 # 3 a, b, c
Handout Problems on Group Theory # 21-25, 29

HW # 6: Turn-in Problem # 12 p.82  on Tuesday 3/24

Thursday 3/12 2.4 Group actions  
March 16-20 Spring break  
Tuesday 3/24 2.4 Group actions           Page 92 # 3, 9, 14
         Handout Problems in Group Theory II-All

Thursday 3/26

Test # 2

 

Tuesday 3/31

2.5 Sylow's Theorems
Problems # 1, 10, 11, 13 on page 96

Thursday 4/2

2.5 Sylow's Theorems
 
1. Show that a group of order 36 is not simple.
2. Handout - Problems on Group Theory-Problems # 1- 6
3. Handout-Problems on Sylow Theorems-# 1-10

 HW # 7. Turn in Problems # 1, 10, 11, 13 on page 96 on Thursday 4/9

Tuesday 4/7

2.6 Finite groups

Study the proof of Proposition 6.3 and Proposition 6.4
See link below for a listing of groups of small order.
http://www.math.usf.edu/~eclark/algctlg/small_groups.html
Pages 99-100  # 3, 4, 10
 HW # 8. Turn in Problems # 1,3, 5 from Handout Problems in Group Theory
and problems # 3, 4 from page 99 on Thursday 4/16

Thursday 4/9

2.7 Solvable groups.
Pages 106-107 # 2, 10, 14
Tuesday 4/14 2.7 Nilpotent groups  
Thursday 4/16 3.1 Rings and homomorphisms
HW # 9. Due Thursday 4/23
      
Page 120 # 3, 6,  7, 15
Tuesday 4/21

Review Test # 2

 
Thursday 4/23 Test # 2  
Tuesday 4/28 3.2 Ideals. The Isomorphism Theorems
Page 133 # 3, 4
Thursday 4/30 3.2 Quotient rings. The Isomorphism Theorems

HW # 10. Due Thursday 5/7
     
Page 133 # 3, 4, 7a, 10

Tuesday 5/5

3.2 Prime and maximal ideals
 

Page 134 # 20
Thursday 5/7

3.3 Factorization in commutative rings

Page 140 # 1

Tuesday 5/12

Final Examination
11:00 a.m.-1:30 p.m.