MATH 520 - Abstract Algebra

Fall 2014

 

 

Professor: Dr. Janet Vassilev
Office: SMLC 324

Office Hours:  M 10 am- 12 pm and W 11 am-12 pm 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 124 on Tuesdays and Thursdays at 9:30-10:45 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 Thursdays and collected the following Thursday 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 Tuesday, October 7 and Thursday, November 20.  The Final is on Tuesday, December 9, 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

8/19

1.1-1.2

Groups and examples of Groups

 

8/21

1.3-1.7

Homorphisms and Group Actions

 HW 1

8/26

2.1-2.2

Subgroups

 

8/28

2.3-2.4

Cyclic and finitely generated subgroups

1.6: 17, 18, 20; 1.7: 14, 15, 18; 2.1: 6, 10; 2.2: 9; 2.3: 24, 25 or HW 2

9/2

3.1-3.2

Quotient Groups , Cosets and Lagrange's Theorem


9/4

3.3

Isomorphism Theorems

 3.1: 5, 14, 22, 31, 36, 41; 3.2: 10, 11, 18, 19 or HW 3

9/9

3.4

Composition Series and Holder's Theorem

 

9/11

4.1-4.2

Cayley's Theorem

 HW 4

9/16

4.3

The Class Equation

 

9/18

4.5

Sylow Theorems

HW 5

9/23

4.5

Sylow Theorems

 

9/25

3.5, 4.6

The Alternating Group

 HW 6

9/30


Complete Groups


10/2

 

Review

 

10/7

 

Midterm I

 

10/14

5.1, 5.4

Direct Products


10/16

6.1

Nilpotent and Solvable Groups

 HW 7

10/21

5.3

Fundamental Theorem of Finitely Generated Abelian Groups

 

10/23

5.3

Fundamental Theorem of Finitely Generated Abelian Groups

HW 8

10/28

5.3

Determining quotients of Free abelian groups

 

10/30

5.5, 7.1

Semidirect products, Rings

 HW 9

11/4

7.3, 7.4

Ring homomorphisms, Quotient Rings and Ideals

 

11/6

7.5, 7.6

Rings of Fractions, Chinese Remainder Theorem

 HW 10

11/11

8.1-8.2

Euclidean Domains and PID's

 

11/13

8.3

UFD's

 HW 11

11/18

Review

 

11/20


Midterm II

 

11/25

9.1-9.3

Polynomial Rings

 

12/2

 9.4-9.5

Polynomial Rings continued

 

12/4

 

Review

 

12/9

 

Final exam

 7:30 am