Fall 2017
Syllabus
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 
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 
Ch. 17 
Ch16: 11, 13, 18, 21, 42 
19 
Nov 2 
Midterm 2 (covering ring theory) 
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 
Mikhail
Movshev
4108
Math Tower
Department
of Mathematics
Stony
Brook University
Stony
Brook, NY 117943651
Phone:
6316328271
Fax:
6316327631