MATH
520 – Abstract Algebra
Fall 2008
Professor: Dr.
Janet Vassilev
Office: Humanities
Office Hours: MF 11 am-12:30 pm and by
appointment.
Telephone: 
(505) 277-2214
email: jvassil@math.unm.edu
webpage: http://www.math.unm.edu/~jvassil
Text : Abstract
Algebra, 3rd Edition, by David
Dummit and Richard Foote.
Course
Meetings: The course lectures will be held in Humanities 424 on
Mondays, Wednesdays and Fridays at 10-10:50 am.
Topics: Theory of groups,
permutation groups, Sylow theorems, introduction to
ring theory, polynomial rings, principal ideal domains.
Homework
(200 points): Homework will be assigned weekly on Wednesdays and will
be collected the following Wednesday. Late homework will be penalized
20% off per each day that it is late. 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 that you plan to use, than state
“by Theorem 3”. Each week I will select about 4 or 5 of the assigned
problems to grade. 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.
Exams (500
points): I will give two midterms (100 points) and a final (300
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. The Midterms
are tentatively scheduled for Monday, September 29 and Wednesday, November
5. The Final is on Friday, December 19, from 7:30-9:30 am.
Grades: General guidelines
for letter grades (subject to change; but they won't get any more strict):
90-100% - A; 80-89% - B; 70-79% - C; 60-69% - 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 Abstract Algebra):
Date
|
Chapter
|
Topic
|
Homework
|
8/25
|
1.1, 2.1
|
Introduction to
algebraic structure on a set
|
|
8/27
|
1.2-1.5
|
Examples of
Groups
|
|
8/29
|
1.6
|
Homomorphisms and Isomorphisms
|
|
9/3
|
1.7
|
Group Actions
|
|
9/5
|
2.2
|
Subgroups
defined by actions
|
|
9/8
|
2.3
|
Cyclic groups
|
|
9/10
|
2.4
|
Subgroups
generated by subsets
|
|
9/12
|
2.5
|
Lattices and the
lattice of subgroups of a group
|
|
9/15
|
3.1
|
Quotient Groups
|
|
9/17
|
3.2
|
Lagrange’s
Theorem
|
|
9/19
|
3.3
|
Isomorphism
Theorems
|
|
9/22
|
3.4
|
Composition
Series
|
|
9/24
|
3.5
|
Alternating
Group
|
|
9/26
|
|
Review
|
|
9/29
|
|
Midterm I
|
|
10/1
|
4.1
|
Group Actions
revisited
|
|
10/3
|
4.2
|
Groups acting
by left multiplication
|
|
10/6
|
4.3
|
Groups acting
by conjugation
|
|
10/8
|
4.4
|
Automorphisms
|
|
10/10
|
4.5
|
Sylow Theorems
|
|
10/13
|
4.5
|
Sylow Theorems continued
|
|
10/15
|
4.6
|
Simplicity of An
|
|
10/20
|
5.1
|
Direct Products
|
|
10/22
|
5.2
|
The Fundamental
Theorem of Finitely Generated Abelian Groups
|
|
10/24
|
5.4
|
Recognizing
Direct Products
|
|
10/27
|
5.5
|
Semidirect Products
|
|
10/29
|
6.1
|
Nilpotent and
Solvable Groups
|
|
10/31
|
6.3
|
Free Groups
|
|
11/3
|
|
Review
|
|
11/5
|
|
Midterm II
|
|
11/7
|
7.1
|
Rings
|
|
11/10
|
7.2
|
Examples of
Rings
|
|
11/12
|
7.3
|
Ring
homomorphism and Quotient Rings
|
|
11/14
|
7.4
|
Ideals
|
|
11/17
|
7.5
|
Rings of
Fractions
|
|
11/19
|
7.6
|
Chinese
Remainder Theorem
|
|
11/21
|
8.1
|
Euclidean
Domains
|
|
11/24
|
8.2
|
PID’s
|
|
11/26
|
8.3
|
UFD’s
|
|
12/1
|
9.1
|
Polynomial
Rings
|
|
12/3
|
9.2
|
Polynomial
Rings over Fields
|
|
12/5
|
9.3
|
Polynomial
Rings which are UFD’s
|
|
12/8
|
9.4
|
Irreducibility
Criteria
|
|
12/10
|
|
Review
|
|
12/12
|
|
Review
|
|
12/19
|
|
Final exam
|
|