Math 516 Fall 2017

Section 13724,  02:00-02:50 MWF TH 309
Office Hours: M 10:30-11:30, TU 2:30-3:30 or by appointments
Lawrence Ein , 405 SEO, 3-2372, ein@uic.edu
Department of Mathematics, Statistics, and Computer Science

• Description
• Homework
• Description

516 Abstract Algebra I
4 Hours.
Prerequisite: Math 330 and Math 425 or equivalent, or permission of the instructor.
Text: David Dummit and Richard Foote, Abstract Algebra, John Wiley

This is the first basic graduate algebra course.
The course is designed to cover the basic topics in algebra which would be needed
for a student who intends to pursue research not only in algebra but in various other areas. The following are some of the basic notions that we"ll study:
Group Theory, Ring Theory and Module Theory
are covered in this first course.

The topics to be covered are:
The Sylow Theorems, Holder's Program, The Structure Theorem for Finitely Generated Modules over a Principal Ideal Domain
Chapters I - Chapter 12

Grading Policy: Homework (25%), Midterm Exam (25%) and Final (50%). The Take_home Midterm Exam will due on 10-15-17.

Homework

HOMEWORK 1. Due Wednesday 09/06/17:

1.1: 1, 2, 8, 9, 12, 18, 21, 23, "29", 34

1.2: 1, 2, 3, 4, 5, 9, "10", 11, 12, 13, 17

1.3: 1, 3, 4, 6, 10, 11, 12, 13, "17", "20"

1.4: 1, 3, 4, 7, 10, "11"

HOMEWORK 2. Due Wednesday 09/13/17

1.5: 1, "3"

1.6: 1, 2, 3, 6, 11 14, 15, 16, 18, 19. 20 21, 22, "25"

1.7: 2, 3, 5, 11, "12" 16, 17, 18, 19, "20" 21

HOMEWORK 3, Due 2/7/14

2.1: 1, 2, 3, 6, 7, 9, 10, 11, 12, 14, "15", 17

2.2: 1, 2, 5, 7, "10", 12, 13, 14

2.3: 1, 3, 6, 12, "13" 15, 17, 19, 20 "21", 22, 23, 25, 26

2.4: 2, 6, 10, 11, 12, 14, 15, 16, "17", 18, 19

HOMEWORK 4, Due 09/27/17

2.5: 1, 3, 6, 7, 11, 14, "14", 15

3.1: 1, 2, 4, 6, 8, 9, 12, 14, 15, 17, 18, 21, 22, 23, "34", 40, "42"

3.2: 1, 4, 5, 6, 8, 9, "11", 14, 16, 17, 18, "19", 23

3.3: "1", 3, "7", 9, 10

HOMEWORK 5. Due 10/03/17

3.4: 1, 3, 4, 5, 8, 9, "11"

3.5: 2, 3, 4, 6, "9", 10, 11, 15, "17"

4.1: 1, "2", 3, 4, "7", 9, 10

4.2: 1, 3, 5, 7, 8, 10, "11", 12, 13, 14

HOMEWORK 6. Due 10/11/ 17

4.3: 2, 4, 8, 10, 13, 17, 22, "27", 33, 36

4.4: 1, 3, 6, 7, 8, 11, 13, 17, "18"

4.5: 1, 3, 4, 8, 12, 13, 15, 18, 19, "22", 24, 29, "33", 35, 36, 43, 45, 46, 48, 52

4.6: 1, "2", 3, 5, 6

HOMEWORK 7. Due 10-18-17

5.1: 1, "2", 4, 5, 6, 7, "11", 14, 18

5.2: 1, 2, 5, 7, 8, 12, 13, 14, 16

5.4: 1, 2, 6, "8", 10, 11, 13, "16", 17, 19, 20

5.5: 1, 2, 3, 7, "10", 11, "16", 20

HOMEWORK 8, Due 10-25-17

7.1: 1, 2, 5, 6, 7, 11, 12, 14, 15, 18, 21, "23", "25" "26", 28

7.2: 2, "3", 4, 5, "6", "7", 12, "13"

7.3: 4, 5, "10", 15, 18, 19, 21, 25, "29", "33", 34, 35, 37

7.4: 1, 4, 7, 8, 10, "11", 12, 14, 16, "19", 22, "30", 31, "32", 34, 35, "37", "41"

7.5: 1, 3, 5

HOMEWORK 9. Due 11-1-17

7.6: 1, 2, "5", 6, "8", 10, "11"

8.1: 1, 3, 4, 5, 7, "8", "9", 11, 12

8.2: 1, 2, 3, 4, 5, "6", 8

8.3: 1, 3, "6", 7, 8, 9

HOMEWORK 10. Due 11-8-17

9.1: 3, 4, "5", 10, 13, 16, "17"

9.2: 1, 4, "5", 10, 12, 13

9.3: 1, 4

9.5: 1, 3, 6, 6

HOMEWORK 12. Due 11-15-17

10.1: 1, 5, 6, 8, 11, 12, 15, "19", 22

10.2: 4, 6, 9, "13"

10.3: 1, 2, 7, 11, 12, 17, 18, "23", "27"

10.4: "1", 2, 3, 6, "7", 8, 11, 16, 18, "25"

10.5: 1, 2, 4, 7, 8, 9, 11, "12", 15, "16", 18, 20, "21", "25" 26, 27, 28