Professor: Dr.
Janet Vassilev
Office: SMLC 324
Office Hours: MWF 10:20 am10:50 am and 2 pm2:30 pm and by
appointment.
Telephone: (505) 2772214
email: jvassil@math.unm.edu
webpage: http://www.math.unm.edu/~jvassil
Date 
Section 
Topic 
Homework 
8/21 
1.11.5 
Groups and Examples 

8/23 
1.62.1 
Subgroups, Homomorphisms and Actions 
1.1 9, 20, 22, 24, 25, 31 1.2 6 1.3 11, 16, 18 
8/25 
2.2 
Subgroup Examples 

8/28 
2.3 
Cyclic groups  
8/30 
2.4, 3.1 
Subgroups generated by a subset, Cosets and Quotient Groups  1.4 10, 11 1.6 3, 17, 18 1.7 16, 18 2.1 6 2.3 16, 19 
9/1 
3.2 
Lagrange's Theorem 

9/6 
3.3 
Isomorphism Theorems, Composition Series 
2.4 3, 13 3.1 3, 5, 11, 22, 36 3.2 10, 11, 18 
9/8 
3.4, 3.5 
Holder's Theorem 

9/11 
3.5 
The Alternating Group 

9/13 
4.1 
Groups Actions and Representations of Permutations  3.2 19, 20 3.3 3, 4 3.4 1, 7, 11 3.5 2, 4, 12 
9/15 
4.2 
Cayley's Theorem 

9/18 
4.3, 4.4 
Class Equation, Automorphisms 

9/20 
4.5 
Sylow's Theorems 
4.1 2, 7, 9 4.2 9, 14 4.3 23, 24, 27 4.4 7, 8 
9/22 
4.5  Sylow's Theorems 

9/25 
4.5  Sylow's Theorems  
9/27 
4.5  _{}Sylow's Theorem Examples  4.4 18 4.5 13, 16, 18, 24, 30, 38 
9/29 
Review  
10/2 
_{ }Midterm 1  
10/4 
4.6 
Simplicity of A_{n} 
Homework 
10/6 
5.15.2, 5.4  Direct products of groups and the , Recognizing Direct Products  
10/9 
5.2 
Fundamental Theorem of Finitely Generated Abeliean Groups  
10/11 
5.2 
Fundamental Theorem of Finitely Generated Abeliean Groups  5.1 1, 2, 4, 14 5.2 4, 7 5.4 7, 11 
10/16 
5.2 
Fundamental Theorem of Finitely Generated Abeliean Groups  
10/18 
5.5 
Semidirect Products  4.4 3, 5 5.5 6, 11, 12, 18 
10/20 
5.5 
Semidirect Products continued  
10/23 
6.1 
Nilpotent Groups  
10/25 
6.1 
More on nilpotent and solvable groups  6.1 1, 8, 9, 14, 17, 18, 21, 25 
10/27 
6.2, 6.3  Groups finale 

10/30 
7.17.2 
Rings, Polynomial Rings, Matrix Rings and Group Rings  
11/1 
7.1, 7.3  Ring Homomorphisms and Quotient Rings, Ideals  6.2 8, 11 6.3 4 7.1 7, 9, 12, 14, 15, 26 7.2 3 
11/3 
7.4, 7.5  Properties of Ideals and Rings of Fractions 

11/6 
7.6  Chinese Remainder Theorem  
11/8 
8.1  Euclidean Domains  7.3 5, 8, 22, 34 7.4 10, 12, 19, 36 7.5 2 7.6 1, 4 
11/10 
Review  
11/13 
Midterm 2  
11/15 
8.2, 8.3  Principal Ideal Domains, Unique Factorization Domains  8.1 3, 4, 7, 9 8.2 1, 3, 5, 6 
11/17 
8.3  Unique Factorization Domains  
11/20 
9.19.3  Polynomial Rings over Fields, Gauss' Lemma  
11/22 
9.4, 9.5  Irreducibility Criteria, Polynomial Rings over Fields II  8.3 6 9.1 4, 8, 12 9.2 5 9.3 4 
11/27 
10.1  Modules  
11/29 
10.2  Module Homomorphisms  9.4 1, 8, 13, 16, 10.1 5, 8, 10, 13 10.2 8, 9 
12/1 
10.3  Free Modules  
12/4 
Review  
12/6 
Review  
12/8 
Review  
12/13 
Final Exam 10 am 12 noon 