# MATH 322 - Modern Algebra

Fall 2017

Professor: Dr. Janet Vassilev
Office: SMLC 324

Office Hours:  MWF 10:20-10:50 am, MWF 2-2:30 pm and by appointment.
Telephone:
(505) 277-2214
email: jvassil@math.unm.edu

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

## Cardinality and Equivalence relations

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

## Binary Operations

1: 22, 23
2: 1, 5, 8, 11, 17, 24, 26, 27, 28, 36

## Groups

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

## Finitely generated groups

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

## Orbits and cycles

7: 4, 5
8: 2, 4, 6, 16, 32, 35, 36, 40, 41, 49
9: 2, 8, 10, 12, 16, 23

## Alternating groups

9: 29, 30, 31, 32, 34, 35

## Direct products of groups

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

## Homomorphisms

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

## Factor Groups

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

## Group Actions

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

## Rings

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

## Integral Domains

19:1, 2, 17, 23, 24, 25, 27, 28, 29

## Field of Quotients

20: 4, 10, 12, 14, 18, 23, 27, 28
21: 1, 4, 12, 14, 15

## Factorization of polynomials

22: 2, 4, 5, 8, 10, 12, 17, 23, 25, 27
23: 2, 9, 13, 14

## Factor Rings and Ideals

23: 19, 21, 25, 28, 34, 35
26: 10, 12, 13, 16, 24, 26, 27, 30