Text : A First Course in Abstract Algebra, 7^{th} Edition By John Fraleigh.
Course Requirements:1) Daily
Quizzes (100 points): The first 5 minutes of
every class (excluding
exam days) will consist of an open notebook quiz on the concepts of the
previous lecture. The quizzes will be
worth 5 points each. I will drop your 4
lowest quizzes and average the remaining quizzes to obtain a score out
of 100.
2) 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.
3) Exams
(400
points): I will give two midterms (100 points) 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 February 26 and Monday, April 15.
The Final is on Wednesday, May 8, from 7:309:30 am.
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 
1/14  27 
Ideals in F[x]  
1/16  29 
Introduction to Extension Fields  27: 6, 8, 14, 30 32 29: 2, 4, 8, 16, 18, 23, 24, 25, 33 Due 1/24 
1/18  29  Simple Extensions  
1/23  30  Vector spaces over arbitrary fields  29: 29, 30, 31 30: 4, 6, 15, 21, 24, 25 Due 1/31 
1/25  31  Algebraic Extensions  
1/28  31  Algebraic Closures  
1/30  31  Existence of the algebraic closure of a field  31: 3, 8, 12, 19, 23, 24, 26, 27, 29, 30, 31, 34 32: 2 Due 2/7 
2/1  32  Geometric Constructions  
2/4  33  Finite Fields  
2/6  34  Isomorphism Theorems for Groups  33: 4, 8, 9, 12, 14 34: 3, 5, 8, 9 Due 2/14 
2/8  35  Subnormal and Normal Series  
2/11  35  Jordan Holder  
2/13  36  Sylow Theorems  35: 4, 6, 8, 14, 17, 18, 22, 25, 26 36: 2, 4, 10, 11, 13, 18 Due 2/21 
2/15  36  Sylow Theorems continued  
2/18  37  Applying the Sylow Theorems  
2/20  38  Free Abelian Groups  36: 15, 19, 22 37: 3, 4, 5, 7 38: 3, 8, 11 Due 3/4 In class 
2/22  Review  
2/25  Midterm 1  
2/27  38  Proof of the Fundamental Theorem of finitely generated abelian groups  
3/1  39, 40 
Free groups and group presentations  
3/4  45  PIDs and UFDs  
3/6  45  PIDs are UFDs  39: 3, 5, 10, 12 40: 4, 8, 13 45: 10, 21, 25, 26 Due 3/21 
3/8  45  More on UFDs  
3/18  Class cancelled 

3/20  46  Euclidean Domains  45: 29, 33, 34 46: 2, 12, 13, 15, 16, 17 Due 3/28 
3/22  47  Gaussian Integers and multiplicative norms  
3/25  48  Automorphisms of Fields  
3/27  49  Isomorphism Extension Theorem  47: 3, 6, 8, 14 48: 4, 8, 12, 18, 29, 35 Due 4/4 
3/29  49  Isomorphism Extension Theorem  
4/1  50  Splitting Fields  
4/3  50/51  Splitting fields and multiplicity  49: 2, 6, 8, 10, 13 50: 6, 9, 14, 18, 19 Due 4/11 
4/5  51  Separable Extensions 

4/8  51  Perfect Fields  
4/10  52  Totally Inseparable Extensions  51: 2, 5, 9, 11, 12, 13 52: 1, 2, 5, 6, 7 Due 4/19 
4/12  Review  
4/15  Midterm 2 

4/17  53  Galois Theory 
53: 4, 6, 12, 15, 16, 17, 18(a,b), 19, 23, 24 Due 4/25 
4/19  53/54  Galois Theory continued 

4/22  54  Illustrations of Galois Theory  
4/24  55  Cyclotomic Extensions  54: 4, 5, 7, 9, 10, 11, 13 55: 7, 9, 13 
4/26  56  Insolvability of the quintic  
4/29  56  Insolvability of the quintic  
5/1  Review  To turn in on day of final (5/8) 55: 14 & 56: 5. These are worth 40 points of the exam grade. 

5/3  Review  
5/8  Final Exam 7:30 am 
Accomodation Statement:
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academic support to students who have disabilities. If you think
you need alternative accessible formats for undertaking and completing
your coursework, you should contact this service right away to assure
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