MAT 313: Abstract Algebra

Lecture

Day

Topic

Chapter

Homework Assignments

1

Aug 29

The integers / Introduction to abstract algebra

Ch. 0, 1

2

Aug 31

Groups and subgroups

Ch. 2, 3

Ch1 (pg. 35{38): 1, 2, 7, 13

Sept 5

No class in session

3

Sept 7

Cyclic groups

Ch. 4

Ch2 (pg. 52{55): 3, 5, 18, 28

Ch3 (pg. 64{69): 10, 13, 22, 24

4

Sept 12

Permutation groups

Ch. 5

Ch4 (pg. 81{86): 1, 3, 8,22, 32, 49, 59

5

Sept 14

Isomorphisms, External direct product

Ch. 6, 8

Ch5: 9, 17, 25, 28

6

Sept 19

Cosets, Lagrange Theorem

Ch. 7

Ch6: 4, 18, 20, 29,39, 42

Ch8: 8, 13, 27, 28,44, 47, 53

7

Sept 21

Normal subgroups and Factor groups

Ch. 9

Ch7: 13, 17, 25, 27

8

Sept 26

Group Homomorphisms

Ch. 10

Ch9: 1, 4 [Note: you only need know the definition of normal subgroup]11, 14, 25

9

Sept 28

Fundamental Theorem of finite abelian groups

Ch. 11

Ch10:8,24,28,56

10

Oct 3

Practice Midterm 1.

Review groups

Part 2

Ch11: 10, 12

11

Oct 5

Midterm 1 (covering group theory)

Part 2

12

Oct 10

Further topics on Groups

13

Oct 12

Rings

Ch. 12, 13

14

Oct 17

Integral domains

Ch. 13

Ch12: 6, 15, 21, 28, 33, 40

15

Oct 19

Ideals and Factor rings

Ch. 14

Ch13: 5, 8, 9, 10, 26, 28, 38, 45

16

Oct 24

Ring Homomorphisms

Ch. 15

Ch14: 6, 10, 37, 38, 39

17

Oct 26

Polynomial Rings

Ch. 16

Ch 15: 10, 15, 28, 42, 44

18

Oct 31

Factorization of Polynomials

Practice Midterm 2. and its solutions

Ch. 17

Ch16: 11, 13, 18, 21, 42

19

Nov 2

Midterm 2 (based on subsections 127-234 from sections 6-11)

Part 3

20

Nov 7

Divisibility in integral domains

Ch. 18

Ch17: 7, 11, 14, 23, 10, 15, 16, 22

21

Nov 9

Vector Spaces

Ch. 19

Ch18: 8, 13, 15, 17, 30, 35

22

Nov 14

Extension Fields

Ch. 20

Ch19: 5, 12, 14, 22, 26

23

Nov 16

Algebraic Extensions

Ch. 21

Ch20: 5, 7, 12, 19, 25,29, 31, 32, 34

24

Nov 21

Finite Fields

Ch. 22

Ch21: 3, 8, 14, 24, 33

Nov 23

Thanksgiving

No class is session

25

Nov 28

Further topics on Fields

Ch22: 4, 9, 10, 24

26

Nov 30

Topics

27

Dec 5

ReviewPractice Final.

28

Dec 7

Review