MATH 520 - Abstract Algebra

Fall 2017

 

 

Professor: Dr. Janet Vassilev
Office: SMLC 324

Office Hours:  MWF 10:20 am-10:50 am and 2 pm-2:30 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 352 on Monday, Wednesday and Friday from 11-11:50.

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, October 2 and Monday, November 13.  The Final is on Wednesday, December 13, from 10 am-12 noon. 

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
Section
Topic
Homework
8/21
1.1-1.5
Groups and Examples

8/23
1.6-2.1
Subgroups, Homomorphisms and Actions
1.1 9, 20, 22, 24, 25, 31
1.2 6
1.3 11, 16, 18
8/25
2.2
Subgroup Examples

8/28
2.3
Cyclic groups
8/30
2.4, 3.1
Subgroups generated by a subset, Cosets and Quotient Groups 1.4 10, 11
1.6 3, 17, 18
1.7 16, 18
2.1 6
2.3 16, 19
9/1
3.2
Lagrange's Theorem

9/6
3.3
Isomorphism Theorems, Composition Series
2.4 3, 13
3.1 3, 5, 11, 22, 36
3.2 10, 11, 18
9/8
3.4, 3.5
Holder's Theorem 

9/11
3.5
The Alternating Group

9/13
4.1
Groups Actions and Representations of Permutations 3.2 19, 20
3.3 3, 4
3.4 1, 7, 11
3.5 2, 4, 12
9/15
4.2
Cayley's Theorem

9/18
4.3, 4.4
Class Equation, Automorphisms

9/20
4.5
Sylow's Theorems
4.1 2, 7, 9
4.2 9, 14
4.3 23, 24, 27
4.4 7, 8
9/22
4.5 Sylow's Theorems

9/25
4.5 Sylow's Theorems
9/27
4.5 Sylow's Theorem Examples 4.4 18
4.5 13, 16, 18, 24, 30, 38
9/29

Review
10/2
 Midterm 1
10/4
4.6
Simplicity of An
Homework
10/6
5.1-5.2, 5.4 Direct products of groups and the , Recognizing Direct Products
10/9
5.2
Fundamental Theorem of Finitely Generated Abeliean Groups
10/11
5.2
Fundamental Theorem of Finitely Generated Abeliean Groups 5.1 1, 2, 4, 14
5.2 4, 7
5.4 7, 11
10/16
5.2
 Fundamental Theorem of Finitely Generated Abeliean Groups
10/18
5.5
Semidirect Products  4.4 3, 5
5.5 6, 11, 12, 18
10/20
5.5
Semidirect Products continued
10/23
6.1
Nilpotent Groups 
10/25
6.1
More on nilpotent and solvable groups 6.1 1, 8, 9, 14, 17, 18, 21, 25
10/27
6.2, 6.3 Groups finale

10/30
7.1-7.2
Rings, Polynomial Rings, Matrix Rings and Group Rings
11/1
7.1, 7.3 Ring Homomorphisms and Quotient Rings, Ideals 6.2 8, 11
6.3 4
7.1 7, 9, 12, 14, 15, 26
7.2 3
11/3
7.4, 7.5 Properties of Ideals and Rings of Fractions

11/6
7.6 Chinese Remainder Theorem
11/8
8.1 Euclidean Domains 7.3 5, 8, 22, 34
7.4 10, 12, 19, 36
7.5 2
7.6 1, 4
11/10

Review 
11/13
Midterm 2
11/15
8.2, 8.3 Principal Ideal Domains, Unique Factorization Domains  8.1 3, 4, 7, 9
8.2 1, 3, 5, 6
11/17
8.3 Unique Factorization Domains
11/20
9.1-9.3 Polynomial Rings over Fields, Gauss' Lemma
11/22
9.4, 9.5 Irreducibility Criteria, Polynomial Rings over Fields II 8.3 6
9.1 4, 8, 12
9.2 5
9.3 4
11/27
10.1 Modules
11/29
10.2 Module Homomorphisms
12/1
10.3  Free Modules
12/4

Review
12/6

Review
12/8

Review
12/13

Final Exam 10 am- 12 noon

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