MATH
521 – Abstract Algebra
Spring 2009
Professor: Dr.
Janet Vassilev
Office: Humanities
Office Hours: MWF 10 am-11 am 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 422 on Mondays,
Wednesdays and Fridays at 9-9:50 am.
Topics: Module theory, field theory, Galois theory.
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, 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.
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. The Midterms
are tentatively scheduled for Wednesday, February 25 and Wednesday, April
8. The Final is on Friday, May 15, 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
|
1/21
|
10.1, 10.2
|
Modules and
Module Homomorphisms
|
|
1/23
|
10.3
|
Free Modules
and Direct sums
|
|
1/26
|
10.4
|
Tensor Products
|
|
1/28
|
10.4
|
Tensor
continued
|
|
1/30
|
10.5
|
Exact Sequences
|
|
2/2
|
10.5
|
Projective and Injective
Modules
|
|
2/4
|
10.5
|
Flat Modules
|
|
2/6
|
11.1, 11.2
|
Vector Spaces
and Linear Transformations
|
|
2/9
|
11.3, 11.4
|
Dual Vector
Spaces and Determinants
|
|
2/11
|
11.5
|
Tensor Algebras
|
|
2/13
|
11.5
|
Symmetric and Exterior
Algebras
|
|
2/16
|
12.1
|
Modules over
PID’s
|
|
2/18
|
12.1
|
Modules over
PID’s continued
|
|
2/20
|
12.2
|
Rational
Canonical Form
|
|
2/23
|
|
Review
|
|
2/25
|
|
Midterm 1
|
|
2/27
|
12.2
|
Rational
Canonical Form continued
|
|
3/2
|
12.3
|
|
|
3/4
|
13.1
|
Field
Extensions
|
|
3/6
|
13.2
|
Algebraic
Extensions
|
|
3/9
|
13.3
|
Straightedge
and Compass Constructions
|
|
3/11
|
13.4
|
Splitting
Fields and Algebraic Closures
|
|
3/13
|
13.5
|
Separable and
Inseparable Extensions
|
|
3/23
|
13.6
|
Cyclotomic
Extensions
|
|
3/25
|
14.1
|
Intro to Galois
Theory
|
|
3/27
|
14.2
|
The Fundamental
Theorem Galois Theory
|
|
3/30
|
14.2
|
The Fundamental
Theorem Continued
|
|
4/1
|
14.3
|
Finite Fields
|
|
4/3
|
14.4
|
Primitive
Element Theorem
|
|
4/6
|
|
Review
|
|
4/8
|
|
Midterm II
|
|
4/10
|
14.5
|
Abelian
Extensions
|
|
4/13
|
14.6
|
Galois Groups
of Polynomials
|
|
4/15
|
14.7
|
Solvable and
Radical extensions
|
|
4/17
|
14.8
|
Galois groups
over the rationals
|
|
4/20
|
14.9
|
Transcendental
Extensions
|
|
4/22
|
15.1
|
Affine
Algebraic Sets
|
|
4/24
|
15.2
|
Radicals and
Affine Varieties
|
|
4/27
|
15.3
|
Integral
Extensions
|
|
4/29
|
15.3
|
Hilbert’s
Nullstellensatz
|
|
5/1
|
15.4
|
Localization
|
|
5/4
|
15.5
|
Spectrum of a
Ring
|
|
5/6
|
|
Review
|
|
5/8
|
|
Review
|
|
5/15
|
|
Final exam
|
|