Text : Abstract Algebra 3rd Edition by Dummit and Foote
Course Requirements:1) Homework
(200 points): Homework will be assigned weekly on Wednesdays
and will
be collected the following Thursday by 8 am under my office
door.
Homework
will not be graded unless it is written in order
and labeled
appropriately. The definitions and theorems
in the
text and
given in class are your tools for the homework proofs. If
the theorem has a name, use it. Otherwise, I
would prefer that you fully
describe the theorem in words, than state by Theorem
3. Each week around 4 or 5 of the assigned problems will be
graded. The
weekly assignments will each be worth 20 points. I will
drop your lowest two homework scores
and the remaining homework will be averaged to get a score out of 200.
2) Exams
(400
points): I will give two midterms (100 points each) and a final
(200
points). There are no make up exams. If a test is
missed,
notify me as soon as possible on the day of the
exam.
For the midterms only, if you have a legitimate and documented
excuse, your grade will be recalculated without that test using the
percentage that you receive on the final exam. The
Midterms
are tentatively scheduled for Monday September 30 and Monday, November 11.
The Final is on Friday, December 13, from 12:302:30 pm.
Grades:
General guidelines
for letter grades (subject to change due to the class "curve"; but they won't get any more
strict):
90100%  A; 8089%  B; 7079%  C; 6069%  D; below 60%  F.
In
assigning Final Grades for the course, I will compare your grade on all
course
work (including the Final) and your grade on the Final Exam. You
will
receive the better of the two grades.
Tentative Schedule (for Dr. Vassilev's Modern Algebra II):
Date 
Section 
Topic 
Homework 
8/19 
1.11.5 
Groups and Examples 

8/21 
1.62.1 
Subgroups, Homomorphisms and Actions 
1.1 29, 31 1.3 8, 12, 14 1.4 7, 10 1.6 17, 18, 23 Due 8/29 8 am 
8/23 
2.2 
Subgroup Examples 

8/26 
2.3 
Cyclic groups  
8/28 
2.4, 3.1 
Subgroups generated by a subset, Cosets and Quotient Groups  2.1 6, 8, 12 2.2 9, 14 2.3 16, 24, 26 2.4 14, 18 Due 9/5 8 am 
8/30 
3.2 
Lagrange's Theorem 

9/4 
3.3 
Isomorphism Theorems, Composition Series 
3.1 22, 24, 36, 38 3.2 4, 10, 18, 19 3.3 3, 8 Due 9/12 
9/6 
3.4, 3.5 
Holder's Theorem 

9/9 
3.5 
The Alternating Group 

9/11 
4.1 
Groups Actions and Representations of Permutations  3.4 5, 7, 11 3.5 3, 4, 12, 15 4.1 1, 7 Due 9/19 
9/13 
4.2 
Cayley's Theorem 

9/16 
4.3 
Class Equation 

9/18 
4.4 
Automorphisms 
4.2 9, 11, 14 4.3 5, 13, 17, 23, 27, 33 Homework Due 9/26 
9/20 
4.5  Sylow's Theorems 

9/23 
4.5  Sylow's Theorems  
9/25 
4.5  _{}Sylow's Theorem Examples  
9/27 
Review  
9/30 
_{ }Midterm 1  
10/2 
4.6 
Simplicity of A_{n} 

10/4 
5.15.2, 5.4  Direct products of groups and the , Recognizing Direct Products  
10/7 
5.2 
Fundamental Theorem of Finitely Generated Abeliean Groups  
10/9 
5.2 
Fundamental Theorem of Finitely Generated Abeliean Groups  
10/14 
5.2 
Fundamental Theorem of Finitely Generated Abeliean Groups  
10/16 
5.5 
Semidirect Products  
10/18 
5.5 
Semidirect Products continued  
10/21 
6.1 
Nilpotent Groups  
10/23 
6.1 
More on nilpotent and solvable groups  
10/25 
6.2, 6.3  Groups finale 

10/28 
7.17.2 
Rings, Polynomial Rings, Matrix Rings and Group Rings  
10/30 
7.1, 7.3  Ring Homomorphisms and Quotient Rings, Ideals  
11/1 
7.4, 7.5  Properties of Ideals and Rings of Fractions 

11/4 
7.6  Chinese Remainder Theorem  
11/6 
8.1  Euclidean Domains  
11/8 
Review  
11/11 

Midterm 2  
11/13 
8.2, 8.3  Principal Ideal Domains, Unique Factorization Domains  
11/15 
8.3  Unique Factorization Domains  
11/18 
9.19.3  Polynomial Rings over Fields, Gauss' Lemma  
11/20 
9.4, 9.5  Irreducibility Criteria, Polynomial Rings over Fields II  
11/22 
10.1  Modules  
11/25 
10.2  Module Homomorphisms  
11/27 
10.3  Free Modules  
12/2 
Review  
12/4 
Review  
12/6 
Review  
12/13 
Final Exam 12:30  2:30 pm 
Accomodation Statement:
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