MATH 322/422 - Modern Algebra

Fall 2015

Professor: Dr. Janet Vassilev
Office: SMLC 324

Office Hours:  M 2 pm, W 11 am-12 noon, F 10 am-11am 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 Mitchell 221 on Mondays, Wednesdays and Fridays from 9-9:50 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 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, 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.  The Midterms are tentatively scheduled for Monday September 21 and Monday, November 2.  The Final is on Wednesday, December 9, from 7:30 am-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

Section

Topic

Homework

8/17

0

Sets, Relations and Functions

 

8/19

0

Cardinality and Equivalence relations
0: 4, 12, 14, 15, 16, 17, 26, 31, 34, 35
1: 32, 34, 36, 37

8/21

0, 1, 2

Equivalence classes, Examples of algebraic structures, Binary operations

 

8/24

2

Binary Operations

8/26

3

Isomorphic Structures

 2: 2, 4, 8, 17, 24, 27, 36
3: 2, 4,  16, 27

8/28

4

Groups

 

8/31

5

Subgroups

9/2

6

Cyclic groups

 4: 19, 20(a,b), 25, 29, 32, 35
5:20, 36, 39, 51, 54

9/4

6

Cyclic Groups

 

9/9

7

Finitely generated groups

6: 10, 18, 28, 32, 33, 35, 45, 46, 50, 55

9/11

8

Dihedral groups

 

9/14

8

Groups of permutations

 

9/16

9

Orbits and cycles

 7: 2, 4, 5
8: 2, 4, 6, 8, 32, 35, 36

9/18

 

Review

 

9/21

 

Midterm 1

 

9/23

9

 Alternating groups

8: 40, 41, 43, 46
9: 2, 9, 12, 16, 23, 29, 31, 34

9/25

10

Cosets and Lagrange

9/28

10

Cosets and Lagrange


9/30

11

Direct products of groups

 10: 4, 6, 7 (Use our D_4 with H={e,f_v}), 9, 10 (Use our D_4 with H={e,r^2}), 15, 19, 28, 33, 39, 40

10/2

11

Finitely generated abelian groups


10/5

13

Homomorphisms


10/7

13

Homomorphisms

 11: 5, 8, 16, 23, 24, 32, 36, 39
13: 4, 5, 33, 34, 49

10/12

14

Factor Groups


10/14

14

Factor Groups

 13: 18, 19, 22, 32, 44, 50
14: 3, 10, 15, 23, 27, 31, 34

10/16

15

More on Factor Groups


10/19

15

More on Factor Groups


10/21

16

Group Actions

 14: 33, 35, 36
15: 2, 5, 12, 13, 19, 28, 30, 31, 37

10/23

16

Group Actions


10/26

17

Group Actions and Counting


10/28

17

Group Actions and Counting

 16: 1,2, 3, 8, 11, 12, 15
17: 1, 2, 7

10/30

 

Review


11/2

 

Midterm 2

 

11/4

18

 Rings

 18: 10, 12, 15, 23, 33, 37, 40, 44, 46, 50, 55

11/6

18

 Rings


11/9

19

Integral Domains

11/11

20

Fermat's and Euler's Theorems

 19: 9, 10, 13, 17, 24, 26, 29
20: 4, 12, 13, 23

11/13

21

Field of Quotients


11/16

22

Polynomial Rings


11/18

23

Factorization of polynomials

 21:  1, 4, 12
22: 3, 5, 7, 11, 12, 23, 24, 25

11/20

26

Factor Rings and Ideals


11/23

26

Factor Rings and Ideals



11/25

27

Prime and Maximal Ideals

 23: 2, 9, 14, 19, 25, 28, 35
26: 3, 10, 24, 26

11/30

27

Prime and Maximal Ideals

 

12/2

 

Review

 

12/4

 

Review

 

12/9

 

Final exam

 7:30 am