Mathematics 5331 Abstract Algebra Schedule/Homework
Date 
Section/Topic 
Homework 
Tuesday 4/18 
§ 3.1 Rings 
Prove Propositions 15 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 1317 SPRING BREAK  
Tuesday 3/21 
§ 2.2 Finitely generated abelian groups 
Handout # 3 Problems in Group TheoryProblems # 13 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 TheoryProblems # 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 

Thursday 1/19 
§ 1.1 Groups 

Tuesday 1/24 
§ 1.2 Homomorphisms and subgroups 

Thursday 1/26 
§ 1.3 Cyclic groups 

Tuesday 1/31 
§ 1.4 Cosets 

Thursday 2/2 
§ 1.4 Counting 

Tuesday 2/7 
§ 1.5 Quotient groups and Isomorphism Theorems 

Thursday 2/9 
§ 1.5 Isomorphism Theorems 

Tuesday 2/14 
NO CLASS 

Thursday 2/16 
§ 1.6 Symmetric group 

Tuesday 2/21 
§ 1.6 Alternating groups; Cayley's Theorem 

Thursday 2/23 
Review Test # 1 

Tuesday 2/28 
Test # 1 
