Professor:
Dr. Janet Vassilev
Office: SMLC 324
Office
Hours: MWF 10:2010:50 am, MWF 22:30 pm and by appointment.
Telephone: (505)
2772214
email: jvassil@math.unm.edu
webpage:
http://www.math.unm.edu/~jvassil
Date

Section

Topic

Homework

8/21

0

Sets,
Relations and Functions


8/23

0

Cardinality and Equivalence
relations

0: 2, 4, 7, 12, 15, 16, 17, 19, 25, 26, 28, 29, 32, 35 
8/25

0, 1

Equivalence classes, Examples of algebraic structures


8/28

2

Binary Operations 

8/30

2

Binary Operations 
1: 22, 23 2: 1, 5, 8, 11, 17, 24, 26, 27, 28, 36 
9/1

3

Isomorphic Structures 

9/6

4

Groups

3: 5, 6, 12, 17, 21, 24, 27 4: 8, 10, 19, 25, 31, 32, 35 
9/8

5

Subgroups_{} 

9/11

6

Cyclic
Groups


9/13

7

Finitely
generated groups

5: 2, 4, 20, 36, 39, 43, 47, 56 6: 28, 32, 36, 46, 49, 50 
9/15

8 
Dihedral
groups


9/18

8

Groups of permutations 

9/20

9 
Orbits and cycles 
7: 4, 5 8: 2, 4, 6, 16, 32, 35, 36, 40, 41, 49 9: 2, 8, 10, 12, 16, 23 
9/22


Review


9/25


Midterm
1


9/27

9

Alternating
groups


9/29

10 
Cosets and Lagrange 

10/2

10 
Cosets and Lagrange 

10/4

11 
Direct
products of groups

10: 2, 4, 12, 16, 19, 24, 26, 28, 30, 32, 33, 35, 39 
10/6

11 
Finitely generated abelian groups 

10/9

13 
Homomorphisms 

10/11

13 
Homomorphisms

11: 6, 14, 16, 19, 24, 32, 36, 39, 46, 50 13: 5, 8, 17, 20, 22, 34 
10/16

14

Factor Groups 

10/18

14

Factor
Groups

13: 44, 45, 49, 50 14: 2, 6, 12, 21, 23, 30, 31, 34, 35 
10/20

15

More on Factor Groups 

10/23

15

More on Factor Groups 

10/25

16

Group
Actions

15: 2, 10, 19, 28, 29, 37 16: 2, 8, 11, 12 
10/27

16

Group
Actions


10/30

17

Group Actions and Counting 

11/1

18

Rings

17: 2, 7 18: 10, 12, 16, 18, 24, 33, 39, 41, 43, 46, 50 
11/3


Review 

11/6


Midterm 2 

11/8

19 
Integral Domains 
19:1, 2, 17, 23, 24, 25, 27, 28, 29 
11/10

19

Integral Domains


11/13

20

Fermat's and Euler's Theorems 

11/15

21

Field of Quotients 
20: 4, 10, 12, 14, 18, 23, 27, 28 21: 1, 4, 12, 14, 15 
11/17

21

Field of Quotients 

11/20

22

Polynomial
Rings


11/22

23 
Factorization of polynomials 
22: 2, 4, 5, 8, 10, 12, 17, 23, 25, 27 23: 2, 9, 13, 14 
11/27

26

Factor
Rings and Ideals


11/29

26

Factor Rings and Ideals 

12/1

27

Prime and Maximal Ideals 

12/4

27 
Prime and Maximal Ideals 

12/6


Review


12/8


Review


12/15


Final
exam

