MATH 421 Modern Algebra II

Spring 2012

 

 

Professor: Dr. Janet Vassilev
Office: SMLC 324

Office Hours:  TWR 11 am -12 pm and by appointment.
Telephone: 505 277-2214
email: jvassil@math.unm.edu

webpage: http://www.math.unm.edu/~jvassil

Texts :  Fields and Galois Theory, by John Howie.

Course Meetings:  The course lectures will be held in SMLC 356 on Tuesdays and Thursdays at 12:30-1:45 pm. 

Topics:  Theory of fields, algebraic field extensions, and Galois theory.

Daily Quizes (100 points): The first 5 minutes of every class (excluding exam days) will consist of an open notebook quiz on the concepts of the previous lecture.  The quizzes will be worth 5 points each.  I will drop your 4 lowest quizzes and average the remaining quizzes to obtain a score out of 100.

Homework (200 points):  Homework will be assigned weekly on Thursdays and will be 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 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 by Theorem 3.  Each week around 4 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 Tuesday, October 4 and Tuesday, November 15.  The Final is on Thursday, May 10, from 10 am-12 pm. 

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 Modern Algebra II):

Date

Section

Topic

Homework

1/17

2.1

Principal Ideal Domains and Euclidean Domains

1/19

2.2

Unique Factorization Domains

Homework 1

1/24

2.2

Noetherian rings and Unique Factorization Domains

1/26

2.3, 1.3

Polynomial Rings, Field of Fractions

Homework 2

1/31

2.4

Irreducible polynomials

2/2

3.1

The degree of an extension

Homework 3

2/7

3.2

Extensions and Polynomials

2/9

3.2

Extensions and Polynomials

Homework 4: 3.1, 3.2, 3.4, 3.5, 3.6, 3.7, 3.9, 3.11, 3.13

2/14

3.3

Polynomials and Extensions

2/16

3.3

Polynomials and Extensions

Homework 5

2/21

5

Splitting Fields

2/23

Review

2/28

Midterm 1

3/1

6

Finite Fields

Homework 6: 5.1, 5.3, 5.4, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6(ii)

3/6

7.1, 7.2

Monomorphisms between Fields,

Automorphisms, Groups and Subfields

3/8

7.2

Automorphisms, Groups and Subfields

Homework 7: 6.7, 7.1, 7.2, 7.3, 7.5

3/20

7.2

Automorphisms, Groups and Subfields

3/22

7.3

Normal Extensions

Homework 8

3/27

7.4

Separable Extensions

3/29

7.4, 7.5

Separable Extensions

The Galois Correspondence

Homework 9

4/3

7.6

The Fundamental Theorem of Galois Theory

4/5

7.6, 7.7

The Fundamental Theorem of Galois Theory Continued

Homework 10

4/10

Review

4/12

Midterm 2

4/17

7.6

The Fundamental Theorem of Galois Theory Continued, Free Groups and relations

4/19

8.1

Quadratics, Cubics and Quartics, solutions by radicals

Homework 11

4/24

8.2, 8.3

Cyclotomic Polynomials, Cyclic Extensions

4/26

10

Groups and Equations

Homework 12

Due on day of the final as part of your final exam grade.

5/1

10

Groups and Equations

5/3

Review

5/10

Final Exam 10 am