Mathematics 5331  Abstract Algebra Schedule/Homework

 

Date

Section/Topic

Homework

Tuesday 4/18

3.1 Rings

Prove Propositions 1-5 given in class.
Study the proof of Theorem 1.9
Problem # 6 on page 120.

Thursday 4/20

3.2 Ideals. The Isomorphism Theorems

HW # 9. Due Thursday 4/27
      
Page 120 # 3, 6, 7, 15

Tuesday 4/25

3.2 Prime and maximal ideals

Page 133 # 3, 4, 7a

Thursday 4/27

3.3 Factorization in commutative rings

HW # 10. Due Thursday 5/4
     
Page 133 # 3, 4, 7a, 10, 20

Tuesday 5/2

3.3 Unique factorization domains


    

Thursday 5/4

3.3 and Review

 

Tuesday 5/9

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

 

 

Date

Section/Topic

Homework

Thursday 3/2 2.1 Free abelian groups  

Tuesday 3/7

2.1 Basis of free abelian groups

Classwork handout

Thursday 3/9

2.1 Rank of free abelian groups

 
MARCH 13-17 SPRING BREAK

Tuesday 3/21

2.2 Finitely generated abelian groups

Handout # 3- Problems in Group Theory-Problems # 1-3
HW # 6
.
Due Tuesday 3/28
  Prove the two corollaries of  the Fundamental Theorem.
  Problem # 12 on page 82.

Thursday 3/23

2.4 Group actions

1. Prove the equivalent version of the class equation.
2.Complete the table of orbits and stabilizers.
3. Problems # 3, 9, 14 on page 92.

Tuesday 3/28

2.4 Cayley's theorem

HW # 7. Due Thursday 4/6
    
Proposition 4.8 and Corollary 4.10

Thursday 3/30

2.5 Sylow's Theorems

Problems # 1, 10, 11, 13 on page 96

Tuesday 4/4

2.5 Sylow's Theorems

1. Show that a group of order 36 is not simple.
2. Handout # 4- Problems on Group Theory-Problems # 1- 10
3. HW # 8. Due Tuesday 4/11
   
Problems # 1, 10, 11, 13 on page 96

Thursday 4/6

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

Tuesday 4/11

Review Test # 2

 

Thursday 4/13

Test # 2

 

 

 

Date

Section/Topic

Homework

Tuesday 1/17

1.1 Semigroups, monoids and groups

  1. Prove Proposition 1.3 on page 25.

  2. Problem 4, p.29. Give the Cayley table for the group of symmetries of the square.

  3. Prove Sn is non-abelian for n greater than 2.

  4. Problem 5, p.29. Prove the order of Sn is n!

  5. Problem 6 on page 29.

Thursday 1/19

1.1 Groups
1.2 Homomorphisms

  1. Prove Proposition 1.4 on page 25.

  2. Problem 15 on page 30.

Tuesday 1/24

1.2 Homomorphisms and subgroups

Pages 33-34 Problems # 1, 2, 6, 7, 9, 10, 11, 13, 17
HW # 1: Turn-in Problem # 6 on Tuesday January 31st.

Thursday 1/26

1.3 Cyclic groups

Pages 36-37 Problems # 1, 3, 4, 5, 6, 8, 9
HW # 2: Turn-in Problem # 3 on Tuesday February 7.

Tuesday 1/31

1.4 Cosets

Page 40 # 2, 3, 5

Thursday 2/2

1.4 Counting
1.5 Normality

Page 40 # 6
Page 45 # 1, 2, 6, 7

Tuesday 2/7

1.5 Quotient groups and Isomorphism Theorems

Page 45 # 5, 9a, 10, 11, 16
HW # 3: Turn-in Problems: # 6 page 40; # 1, 7, 11, 16 pages 45-46  on
Thursday 2/16.

Thursday 2/9

1.5 Isomorphism Theorems

Problems in group theory (Handouts I and II)
 HW # 4: Turn-in Problems # 4, 6, 7, 9, 10 from Handout II on  Tuesday 2/21.

Tuesday 2/14

NO CLASS

 

Thursday 2/16

1.6 Symmetric group

Study the proof of Corollary 6.4.

Tuesday 2/21

1.6 Alternating groups; Cayley's Theorem

Page 51 # 2, 3, 4, 5, 7, 8, 10
HW # 5: Turn-in Problems # 3, 10 on Tuesday February 28.

Thursday 2/23

Review Test # 1

 

Tuesday 2/28

Test # 1