Professor: Dr.
Janet Vassilev
Office: SMLC 324
Office Hours: MWF 9:20 am9:50 am and 1pm1:30 pm and by
appointment.
Telephone: (505) 2772214
email: jvassil@math.unm.edu
webpage: http://www.math.unm.edu/~jvassil
Date 
Section 
Topic 
Homework 
8/22 
1.11.5 
Groups and Examples 

8/24 
1.62.1 
Subgroups, Homomorphisms and Actions 
1.1 20, 22, 24, 25, 31 1.2 4, 5 1.3 8, 14 1.4 10 
8/26 
2.2 
Subgroup Examples 

8/29 
2.3 
Cyclic groups  
8/31 
2.4, 3.1 
Subgroups generated by a subset, Cosets and Quotient Groups  1.6 17, 18, 23 1.7 8, 14, 15, 18 2.1 15 2.2 9 2.3 24 2.4 10 
9/2 
3.2 
Lagrange's Theorem 

9/7 
3.3 
Isomorphism Theorems, Composition Series 
3.1 3, 22, 26, 36, 40 3.2 4, 10, 11, 18, 19 
9/9 
3.4, 3.5 
Holder's Theorem and The Alternating Group 

9/12 
4.1 
Groups Actions and Representations of Permutations 

9/14 
4.2 
Cayley's Theorem 
3.3 3, 4 3.4 2 3.5 2, 3, 15, 16 4.1 1, 2 4.2 14 
9/16 
4.3 
Class Equation 

9/19 
4.4 
Automorphisms 

9/21 
4.5 
Sylow's Theorems 
4.3 4, 5, 13, 22, 23, 24, 27 4.4 1, 7, 8 
9/23 
4.5  Sylow's Theorems 

9/26 
4.5  _{} Sylow's Theorems  
9/28 
Review  4.5 14, 16, 17, 18, 22, 33, 35, 38  
9/30 
Midterm 1  
10/3 
4.6  Simplicity of A_{n, }  
10/5 
5.15.2,5.4 
Direct products of groups and the Fundamental Theorem of Finitely Generated Abeliean Groups, Recognizing Direct Products 
4.6 3, 5 5.1 1, 4, 5, 12 5.2 4, 8 5.4 11, 15 
10/7 
5.5  Semidirect Products 

10/10 
5.5 
Semidirect Products continued  
10/12 
6.1 
Nilpotent and Solvable Groups  5.5 6, 8, 11, 18 
10/17 
6.1 
Nilpotent and Solvable Groups Continued  
10/19 
6.3 
Free Groups  6.1 1, 7, 14, 17, 18, 21, 22, 24 6.3 2, 11 
10/21 
7.1, 7.2 
Rings, Polynomial Rings, Matrix Rings and Group Rings  
10/24 
7.3 
Ring Homomorphisms and Quotient RingsEuclidean Domains 

10/26 
7.4 
Ideals  7.1 3, 7, 12, 14, 15, 17, 20, 26 7.2 2, 3(b,c) 7.3 16, 22, 29 
10/28 
7.5 
Rings of Fractions  
10/31 
7.6 
Chinese Remainder Theorem  
11/2 
8.1 
Euclidean Domains 
7.4 6, 7, 10, 27, 30, 35, 37 7.5 3 7.6 1 
11/4 
8.2  Principal Ideal Domains 

11/7 
8.3  Unique Factorization Domains  
11/9 
Review  8.1 7, 9 8.2 3, 5, 6 8.3 6(a,b) 9.3 3, 4 

11/11 
Midterm 2  
11/14 
9.19.3  Polynomial Rings over Fields, Gauss' Lemma  
11/16 
9.4, 9.5  Irreducibility Criteria, Polynomial Rings over Fields II 
9.4 1, 2, 5, 6, 8, 9, 12, 16, 18 9.5 1, 3 
11/18 
10.1  Modules  
11/21 
10.2  Module Homomorphisms and Quotient Modules  
11/23 
10.3  Direct Sums and Free Modules  10.1 5, 8, 9, 10, 19 10.2 4, 6, 9, 13 
11/28 
10.3  Direct Sums and Free Modules  
11/30 
10.4  Tensor Products 
10.3 1, 7, 12, 13, 14 10.4 2, 3, 6 
12/2 
10.4  Tensor Products  
12/5 
Review  
12/7 
Review  
12/9 
Review  
12/14 
Final Exam 10 am 12 noon 