SUNY at Stony Brook MAT 313:
Fall 2020
MAT 313

MAT 313:
Fall 2020

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General Information
Syllabus
Exams

Syllabus(subject to change)

Lecture

Day

Topic

Chapter

Homework Assignments

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1

Aug 25

The integers / Introduction to abstract algebra

Ch. 0, 1

2

Aug 27

Groups and subgroups

Ch. 2, 3

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

3

Sept 1

Cyclic groups

Ch. 4

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

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

4

Sept 3

Permutation groups

Ch. 5

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

5

Sept 8

Isomorphisms, External direct product

Ch. 6, 8

Ch5: 9, 17, 25, 28

6

Sept 10

Cosets, Lagrange Theorem

Ch. 7

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

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

7

Sept 15

Normal subgroups and Factor groups

Ch. 9

Ch7: 13, 17, 25, 27

8

Sept 17

Group Homomorphisms

Ch. 10

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

9

Sept 22

Fundamental Theorem of finite abelian groups

Ch. 11

Ch10:8,24,28,56

10

Sept 24

Further topics on Groups

Ch 24

Ch11: 10, 12

11

Sept 29

Rings

Ch.12,

Ch24:1,3,7

12

Oct 1

Practice Midterm 1.

Review groups

Part 2

13

Oct 6

Midterm 1 (covering group theory)

14

Oct 8

Integral domains   

Ch.13

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

15

Oct 13

Ideals and Factor rings

Ch. 14

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

16

Oct 15

Ring Homomorphisms

Ch. 15

Ch14: 6, 10, 37, 38, 39

17

Oct 20

Polynomial Rings

Ch. 16

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

18

Oct 22

Factorization of Polynomials

Ch. 17

Ch16: 11, 13, 18, 21, 42

19

Oct 27

Divisibility in integral domains

Ch. 18

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

20

Oct 29

Vector Spaces

Ch. 19

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

21

Nov 3

Extension Fields Practice Midterm 2.

Ch. 20

Ch19: 5, 12, 14, 22, 26

22

Nov 5

Midterm 2 (covering ring theory)

23

Nov 10

Algebraic Extensions

Ch. 21

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

24

Nov 12

Finite Fields

Ch. 22

Ch21: 3, 8, 14, 24, 33

25

Nov 19

Further topics on Fields

Ch22: 4, 9, 10, 24

26

Nov 17

Topics

27

Nov 19

Topics

28

Nov 24

 Thanksgiving

No class is session

29

Nov 26

Thanksgiving

No class is session

 

30

Dec 1

Review Practice Final.

31

Dec 3

Review



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