MATH 521 Ė 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 ďby Theorem 3Ē.  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. Vassilevís 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 PIDís

 

2/18

12.1

Modules over PIDís 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

Jordan Canonical Form

 

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

Hilbertís Nullstellensatz

 

5/1

15.4

Localization

 

5/4

15.5

Spectrum of a Ring

 

5/6

 

Review

 

5/8

 

Review

 

5/15

 

Final exam