MATH
421: Modern Algebra II
Spring 2014
Professor:
Dr. Janet Vassilev
Office: SMLC 324
Office
Hours: TWTh 11 am-12 noon and by appointment.
Telephone: 
(505)
277-2214
email: jvassil@math.unm.edu
webpage: http://www.math.unm.edu/~jvassil
Text
: Undergraduate Algebra, Third Edition by Serge Lang or A First Course in Abstract Algebra, 7th Edition by
John Fraleigh.
Course
Meetings: The course lectures will be held in SMLC 356 on Tuesdays
and Thursdays at 9:30-10:45 am.
Topics: Theory of fields, algebraic field extensions, advanced group theory
and Galois theory.
Daily
Quizzes (100 points): The first 5 minutes of everyday (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 Thursday, February 27 and Thursday, April 23.
The Final is on Tuesday, May 13, from 7:30 pm-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 Modern Algebra II):
Date
|
Section
|
Topic
|
Homework
|
1/21
|
F(18,19,26)L(III:1-3) |
Rings and Ideals and Factor Rings
|
|
1/23
|
F(27, 21)L(III:3,4) |
Special Factor Rings and associated ideals, Quotient Fields
|
Homework 1
|
1/28
|
F(23)L(IV:1-5) |
Factorization of Polynomials |
|
1/30
|
F(45)L(IV:6) |
Principal Ideal Domains and Unique Factorization Domains |
Homework 2
|
2/4
|
F(46) |
Euclidean Domains and Gaussian Integers
|
|
2/6
|
F(47) |
Multiplicative Norms
|
Homework 3
|
2/11
|
F(47,29)L(VII:1) |
Multiplicative norms continued and Introduction to Field Extensions
|
|
2/13
|
F(30)L(V:1,2) |
Vector spaces, bases and dimension |
Homework 4
|
2/18
|
F(31)L(VII: 1) |
Algebraic Extensions |
|
2/20 |
F(31)L(VII: 1) |
Algebraic Extensions continued |
Homework 5
|
2/25
|
Review
|
||
2/27
|
Midterm 1
|
||
3/4
|
F(31, 33)L(VII: 1,VIII:1,2) |
Algebraic Closures of Fields and Finite Fields
|
|
3/6
|
F(34) |
Isomorphism Theorems
|
Homework 6
|
3/11
|
F(34, 35) |
Isomorphism Theorems,
|
|
3/13
|
F(35) |
Series of Groups |
Homework 7
|
3/25
|
F(37)L(II:9) |
Sylow Theorems
|
|
3/27
|
F(37)L(II:9) |
Sylow Theorems |
Homework 8
|
4/1
|
F(48, 49)L(VII:2) |
Automorphisms of Fields
|
|
4/3
|
F(49)L(VII:2) |
Isomorphism Extension Theorem |
Homework 9
|
4/8
|
F(50,51)L(VII:2)
|
Splitting fields
|
|
4/10
|
F(51)L(VII:3) |
Separable Extensions |
Homework 10
|
4/15
|
F(51)L(VII:3) |
Separable Extensions and Totally Inseparable Extensions
|
|
4/17
|
F(52,53)L(VII:4,5) |
Galois Theory |
Homework 11 |
4/22
|
Review
|
||
4/24
|
Midterm 2
|
||
4/29
|
F(52,53)L(VII:4,5) |
Galois Theory
|
|
5/1
|
F(54)L(IV: 7,8)
|
Polynomials in several variables and symmetric polynomials |
Homework 12 |
5/6
|
F(55, 56)L(VII:6) |
Solvability by radicals and Insolvability of the Quintic |
|
5/8
|
Review |
||
5/13
|
Final exam
|
|