MATH 520 - Abstract Algebra

Fall 2012

 

 

Professor: Dr. Janet Vassilev
Office: SMLC 324

Office Hours:  MF 2-3 pm W 9-10 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 SMLC 352 on Mondays, Wednesdays and Fridays at 11-11:50 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 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

8/20

1.1, 2.1

Groups and subgroups

 

8/22

1.2-1.5

Examples of Groups

 HW 1

8/24

2.3, 1.7, 3.1

Cyclic Groups,Group Actions and Cosets

 

8/27

1.7, 3.2, 4.1

Group Actions and Lagrange's Theorem

 

8/29

2.2,  4.3

Subgroups defined by actions and the class equation

 HW 2

8/31

3.1, 3.2, 3.3

Quotient groups and 1st Isomorphism Theorem

 

9/5

3.3

Isomorphism Theorems

 HW 3

9/7

4.2

Cayley's Theorem

 

9/10

3.2, 4.3

Cauchy's Theorem

 

9/12

4.5

Sylow Theorems

HW 4

9/14

4.5

Sylow Theorems

 

9/17

1.3

Symmetric Groups

 

9/19

3.5, 4.6

The Alternating Group

HW 5

9/21

 

Review

 

9/24

 

Midterm I

 

9/26

3.5, 4.6

The Alternating Group Continued

HW 6

9/28

4.4

Automorphisms vs Inner Automorphisms

 

10/1

5.1, 5.4

Direct Products

 

10/3

3.4, 6.1

Nilpotent and Solvable Groups

HW 7

10/5

5.2

Classification of finitely generated abelian groups

 

10/8

5.2

Classification of finitely generated abelian groups

 

10/10

5.2

 Classification of finitely generated abelian groups

 

10/15

6.3, 5.5

Free Groups, Semidirect Products

 

10/17

5.5

Semidirect Products

 HW 8

10/19

7.1, 10.1

Rings and Modules

 

10/22

7.3, 10.2

Ring and Module homomorphisms, Quotient Rings and Quotient Modules

 

10/24

7.4, 7.6

Properties of ideals, Chinese Remainder Theorem

 HW 9

10/26

8.2, 8.3

PID's and UFD's

 

10/29

 

Review

 

10/31

 

Midterm II

 

11/2


Went over midterm

 

11/5


Euclidean domains

 

11/7


Factorization of polynomials

HW 10

11/9


Irreducibility criteria

 

11/12


Localization

 

11/14


Localization continued

HW 11

11/16



 

11/19

 


 

11/21

 


 

11/26



 

11/28



15.1 9, 10, 16, 20, 26

15.2 3, 8, 11, 31, 32

11/30



 

12/3



 

12/5

 

Review

 

12/7

 

Review

 

12/12

 

Final exam

 10 am