MATH 322 - Modern Algebra

Fall 2018

Professor: Dr. Janet Vassilev
Office: SMLC 324

Office Hours:  MW 10:20-10:50 am, F 12:25-12:55, WF 2-2:30 pm, M 3-3:30 and by appointment.
Telephone: (505) 277-2214
email: jvassil@math.unm.edu

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

Text :  A First Course in Abstract Algebra, 7th Edition  By John Fraleigh.

Course Meetings:  The course lectures will be held in Dane Smith Hall 226 on Mondays, Wednesdays and Fridays from 11-11:50 am. 

Topics:  Groups, rings, homomorphisms, permutation groups, quotient structure, ideal theory, fields.

Daily Quizzes (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 Wednesdays and will be collected the following Wednesday by 10 pm under my office door.  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, than state by Theorem 3.  Each week around 4 or 5 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 using the percentage that you receive on the final exam.  The Midterms are tentatively scheduled for Monday September 24 and Monday, November 5.  The Final is on Wednesday, December 12, from 10 am-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

8/20

0

Sets, Relations and Functions

 

8/22

0

Cardinality and Equivalence relations

0: 12, 14, 16, 17, 18, 19, 28, 30, 31, 33, 34

8/24

0

Equivalence relations continued

 

8/27

0

Equivalence classes and partitions

8/29

2

Binary Operations

 1: 22, 31, 33, 36
2: 2, 4, 5, 8, 20, 24, 26, 27, 28, 36

8/31

2

Binary Operations

 

9/5

3

Isomorphic structures

 3: 2, 4, 7, 10, 11, 16, 24, 27, 28
4: 2, 4, 5, 10

9/7

4

Groups

9/10

5

Subgroups

 

9/12

6

Cyclic subgroups and groups

4: 23, 25, 29, 32, 35, 41
5: 4, 6, 15, 16, 20, 39, 47, 54, 56

9/14

6

Cyclic groups continued

 

9/17

8

Dihedral Groups

 

9/19

8

Dihedral Groups and Permutations

 6: 6(use euclidean algorithm to express gcd in terms of the given integers), 10, 18, 23, 32, 34, 37, 44, 46, 50

9/21

 

Review

 

9/24

 

Midterm 1

 

9/26

8

Permutations and Cayley's Theorem

 8: 2, 5, 9, 16, 24, 32, 35, 36, 40, 41
9: 2, 8, 10, 14, 34

9/28

9

Orbits and Cycles and the Alternating groups

10/1

9,10

Alternating group and intro to left cosets


10/3

10

Cosets and Lagrange

 10: 4, 12, 15, 19, 20, 24, 30, 32, 33, 39, 40, 44

10/5

11

Finitely generated abelian groups


10/8

13

Homomorphisms


10/10

13

Homomorphisms

 11:  6, 8, 11, 14, 18, 23, 24, 32, 34, 36
13: 18, 20, 22, 26

10/15

14

Factor Groups


10/17

14

Factor Groups

 11: 46, 50
13: 29, 32, 36, 38, 42, 44, 45, 50
14: 5, 6, 10, 14, 21, 22, 23

10/19

15

More on Factor Groups


10/22

15

More on Factor Groups


10/24

16

Group Actions

 14: 31, 35, 36
15: 5, 8, 9, 14, 19, 37
16: (1, 2, 3 please use our notation for D_4 in these problems), 8, 12, 13

10/26

16

Group Actions


10/29

17

Group Actions and Counting

10/31

18

Rings

 16: (9,10 use our notation not that of the book), 11
17: 2, 7, 8

11/2

 

Review


11/5

 

Midterm 2

 

11/7

18

 Rings and ring homomorphisms

 18: 10, 12, 18, 25, 33, 37, 38, 44, 46, 50, 55
19: 10, 17, 28, 29

11/9

19

 Integral Domains


11/12

20

Fermat's and Euler's Theorems

11/14

21

Field of Quotients

 20:  4, 5, 6, 10, 12, 14, 18, 23, 27, 29
21: 4, 12, 14, 15

11/16

21

Field of Quotients


11/19

22

Polynomial Rings


11/21

23

Factorization of polynomials

 22: 3, 5, 9, 13, 21, 23, 25, 27
23: 2, 4, 10

11/26

26

Factor Rings and Ideals


11/28

26

Factor Rings and Ideals

23: 14, 16, 19, 25, 28, 34, 35

26: 3, 4, 10, 13, 25, 27

11/30

27

Prime and Maximal Ideals

12/3

27

Prime and Maximal Ideals

 

12/5

 

Review

 

12/7

 

Review

 

12/12

 

Final exam

 10 am