Table of Contents:

• 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