MATH 521 - Abstract Algebra

Spring 2015

 

 

Professor: Dr. Janet Vassilev
Office: SMLC 324

Office Hours:  MF 1-1:50, W 10 - 10:50 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 Mitchell Hall 221 on Mondays, Wednesdays and Fridays at 9:00-9:50 am. 

Topics:  Module Theory, field theory, 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, February 23 and Monday, April 6.  The Final is on Wednesday, May 6, 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

1/12

10.1,10.2

Modules and Module Homomorphisms

 

1/14

10.3     

Direct Sums and Free Modules

10.1 5, 8, 9, 10; 10.2 4, 6, 8, 9, 10

1/16

10.4 

Tensor Products

 

1/21

10.4 

Tensor Products

10.3 9, 12, 13; 10.4 2, 3, 5, 7, 12, 16, 19

1/23

10.5

Exact Sequences and Projective Modules


1/26

10.5

Injective Modules

 

1/28

10.5

Injective Modules

 10.5 1, 2, 3, 7, 10, 12, 15, 16

1/30

10.5  

Flat Modules

 

2/2

11.1-11.2

Linear Algebra Review

 

2/4

11.3  

Dual Vector Spaces

10.5 5, 9, 20, 22 and 11.3 4, 5

2/6

11.5

Tensor Algebras

 

2/9

11.5

Tensor Algebras continued

 

2/11

12.1

Modules over PIDs


2/13

 12.2

Rational Canonical Form

 11.5 1, 5, 13 and 12.2 9, 10, 11, 14

2/16

 12.2

Rational Canonical Form

 

2/18

12.3

Jordan Canonical Form


2/20


Review

 

2/23


Midterm 1

 

2/25

13.1

Field Extensions

12.3 3, 5, 21, 24, 31; 13.1 1, 3 and 13.2 2, 4, 7

2/27

13.2

Algebraic Extensions

 

3/2

13.3

Ruler and Compass Constructions

 

3/4

13.4

Splitting Fields

 13.2 9, 12, 14, 18; 13.3 4, 5; 13.4 4, 6

3/6

13.4

Algebraic Closures

 

3/16

13.5

Separable Extensions

 

3/18

13.6

Cyclotomic Extensions

 13.5 1, 3, 5, 8, 10; 13.6 1, 3, 6

3/20

14.1

Field Automorphisms

 

3/23

14.1

Field Automorphisms

 

3/25

14.1

Field Automorphisms

 14.1 5, 6, 8, 10; 14.2 3, 5, 9, 12

3/27

 14.2

Fundaamental Theorem of Galois Theory

 

3/30

 14.2

Fundamental Theorem of Galois Theory

 

4/1

 14.2

Fundamental Theorem of Galois Theory

 

 4/3

  Review

 4/6

  Midterm 2

4/8

14.4

Primitive element Theorem

 14.2 15, 17, 18, 22, 23

4/10

14.4

  Primitive element Theorem

4/13

14.5

  Abelian Extensions

4/15

14.6

  Galois Groups of Polynomials

 14.4 1, 2, 5; 14.5 3, 8; 14.6 22, 23

4/17

14.7

  Solvable and Radical Extensions: Insolvability of the Quintic

4/20

14.9

 Transcendental Extensions

4/22

15.1

  Noetherian Rings

 14.6 2, 6, 13, 15; 14.7 3, 9, 10

4/24

15.2

  Radicals and Affine Varieties

4/27

15.3

  Hilbert's Nullstellensatz

4/29

15.3

  Hilbert's Nullstellensatz

5/1

  Review

5/6

Final Exam

7:30 am