MATH 521 - Abstract Algebra

Spring 2013

 

 

Professor: Dr. Janet Vassilev
Office: SMLC 324

Office Hours:  MWF 11 am - 12 pm or 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 SMLC 352 on Mondays, Wednesdays and Fridays at 10-10:50 am.

Topics:  ModuleTheory, Field Theory and Galois Theory

Homework (200 points): Homework will be assigned on Wednesdays and collected the following Wednesday at the beginning of class.  Homework will not be graded unless it is written in order and labeled appropriately.  The definitions and theorems given in class and in the text will be your tools for the homework proofs.  If the theorem has a name, use it.  Otherwise, I would prefer you to fully describe the theorem with words, than state by Theorem 3.  Each week 4 or 5 of the problems will be graded.  The weekly assignments will be given a score out of 20 points.  I will drop the lowest two homework assignments and average the remaining 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 Monday, September 29 and Wednesday, November 5.  The Final is on Wednesday, 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

1/14

10.1-10.3

Review of Modules and Direct Products

 

1/16

10.3, 10.4

Free Modules and Extension of  Modules using Tensor Products

10.2: 6, 9, 10, 11, 12, 13

10.3: 2, 7, 9, 11

1/18

10.4

Tensor Products

 

1/23

10.4

Tensor Products

10.4: 2, 3, 6, 7, 10, 12, 16, 19, 25

due on 2/4

1/25

10.5

Exact Sequences


1/28

10.5

Projective Modules

 

1/30

10.5

Injective Modules

10.5: 1, 2, 3, 6, 7

due on 2/8

2/1

10.5

Injective Z-modules

 

2/4

10.5

Flat Modules

 

2/6

11.1-11.4

Linear Algebra Review and Dual Vector Spaces

10.5: 15, 16, 21, 25, 28

11.3: 1, 4

2/8

11.5

Tensor Algebras

 

2/11

11.5

Symmetric Algebras

 

2/13

11.5

Exterior Algebras

11.5: 4, 6, 8, 13

12.2: 8, 10, 14

Due 2/25

2/15

 

Review

 

2/18

 

Midterm I

 

2/20

12.2

Rational Canonical Form


2/22

12.2, 12.3

Rational Canonical Form, Jordan Canonical Form

 

2/25

12.3, 13.1

Jordan  Canonical Form, Field Extensions

 

2/27

13.1

Field Extensions

12.3: 5, 9,  18, 22, 37

13.1: 2, 3, 6

3/1

13.2

Algebraic Extensions

 

3/4

13.2

Algebraic Extensions

 

3/6

13.4

 Splitting Fields

13.2 4, 8, 9, 12, 14, 16, 18

13.4 2, 4

3/8

13.4

Algebraic Closures

 

3/18


No Class

 

3/20

13.5

Separability

 13.5 1, 2, 4, 5, 8

3/22

13.6

Cyclotomic Fields

 

3/25

14.1

Fixed Fields

 13.6 1, 3, 4, 6, 8

14.1 1, 8, 9

3/27

14.1

Galois Extensions

 

3/29

 14.1

Galois Extensions

 

4/1

 

Take Home Midterm II

 

4/3

14.2

The Galois Correspondence

 

4/5

14.2

The Galois Correspondence

 

4/8

14.4

Joins and Intersections of Galois Extensions


4/10

14.5

Abelian Extensions

 14.2: 5, 6, 8, 9, 13, 23, 29

14.4: 4, 6

4/12

14.5

Abelian Extensions

 

4/15

14.6

Galois Groups of Polynomials


4/17

14.6

Galois Groups of Polynomials

14.5: 1, 7, 8

14.6: 2(a,b), 7, 11, 13, 14

 

4/19

 14.7

Solvability by radicals

 

4/22

 14.7

Insolvability by the quintic

 

4/24

14.9

Transcendental Extensions

 14.7: 4, 7, 9, 12, 19

14.9: 6, 7, 9,

4/26

14.9

Transcendental Extensions

4/29


Review

 

5/1


Review

 

5/3

 

Review

 

5/10

 

Final exam

 7:30 am

Take home problems 14.6 15 and 48