Professor:
Dr. Janet Vassilev
Office: SMLC 324
Office
Hours: MW 10:2010:50 am, F 12:2512:55, WF 22:30 pm, M 33:30 and by appointment.
Telephone: (505)
2772214
email: jvassil@math.unm.edu
webpage:
http://www.math.unm.edu/~jvassil
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

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

