Professor:
Dr. Janet Vassilev
Office: SMLC 324
Office
Hours: M 2 pm, W 11
am12 noon, F 10 am11am and by appointment.
Telephone: (505)
2772214
email: jvassil@math.unm.edu
webpage:
http://www.math.unm.edu/~jvassil
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

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

