Math 31  
Topics in Algebra

Fall, 2005

General Information

Syllabus

Homework

Exam Notes


Homework assignments

Homework assignments are to be handed in weekly. In general, assignments for a given week are to be submitted in class the following Wednesday.


Final Assignment

Monday, November 14:
  • Study: Chapter 18
  • Homework due Monday, November 28: Chapter 18 exercises: 2, 13.


Wednesday, November 16:
  • Study: Chapter 19, start of 20
  • Homework due Monday, November 28: Chapter 19 exercises: 3, 5, 27.


Thursday, November 17:
  • Study: Chapter 20
  • Homework due Monday, November 28: Chapter 20 exercises: 1, 5, 7, 8 (don't write out the multiplication table).


Friday, November 18:
  • Study: Chapter 20
  • Homework due Monday, November 28: Chapter 20 exercises: 16, 30, 32, 34.



Week of November 7 – November 11, 2005

Monday, November 7:
  • Study: Chapter 16: Through the Division Algorithm
  • Homework due Wednesday, November 16: Chapter 16 exercises: 1, 3, 6, 12.


Wednesday, November 9:
  • Study: Chapter 16, first part of Ch. 17
  • Homework due Wednesday, November 16: Chapter 17 exercises: 12, 13, 14.


Friday, November 11:
  • Study: Ch. 17
  • Homework due Wednesday, November 16: Chapter 17 exercises: 7, 10, 23, 24.



Week of October 31 – November 4, 2005

Monday, October 31:
  • Study: Chapter 14: Up to Prime and Maximal Ideals
  • Homework due Wednesday, November 9: Chapter 14 exercises: 5, 7, 10, 11, 15, 31.


Wednesday, November 2:
  • Study: Chapter 14
  • Homework due Wednesday, November 9: Chapter 14 exercises: 22, 25, 33, 36.


Friday, November 4:
  • Study: Chapter 15:
  • Homework due Wednesday, November 9: Chapter 15 exercises: 6, 10, 11, 25, 41a.



Week of October 24 – October 28, 2005

Monday, October 24:


Monday, October 24:
  • Study: Chapter 10
  • Homework due Wednesday, November 2: Chapter 10 exercises: 19, 24, 29.


Wednesday, October 26:
  • Study: Chapter 12
  • Homework due Wednesday, November 2: Chapter 12 exercises: 2, 3, 4 (try looking at familiar finite rings), 6, 17, 23.


Friday, October 28:
  • Study: Chapter 13
  • Homework due Wednesday, November 2: Chapter 13 exercises: 6, 10, 18, 39, 46, 48.



Week of October 17 – October 20, 2005

Monday, October 17:
  • Study: First Half of Chapter 9
  • Homework due Wednesday, October 26: Chapter 9 exercises: 1, 7 (this is a great criteria to determine normality at times), 14.
  • Suggested Problems: Chapter 9 exercises: 5, 10, 11, 17, 37.


Wednesday, October 19:
  • Study: Chapter 9
  • Homework due Wednesday, October 26: Chapter 9 exercises: 31, 49 (use problem 7 to show the normality conditions quickly).
  • Suggested Problems: Page 230: 2, 11, 17


Thursday, October 20:
  • Study: Chapter 10
  • Homework due Wednesday, October 26: Chapter 10: 6, 14, 15.
  • Suggested Problems: Chapter 10: 5, 7, 9, 10.



Week of October 10 – October 14, 2005

Monday, October 10:
  • Study: Chapter 7
  • Homework due Wednesday, October 19: Chapter 7 exercises: 1, 2, 3, 8, 12, 14, 19.


Wednesday, October 12:
  • Study: Chapter 7
  • Homework due Wednesday, October 19: Chapter 7 exercises: 15, 16, 17, 27, 31, 33, 40.
  • Interesting Reading (not at all required for the course): RSA Cryptography Basics


Friday, October 14:
  • Study: First half of Chapters 6 and 8.
  • Homework due Wednesday, October 19: Chapter 6 exercises: 1, 4, 5. Chapter 8 exercises: 3, 7, 10, 12 (hint: you can use exercise 4).



Week of October 3 – October 7, 2005

Monday, October 3:
  • Study: Finish Chapter 4
  • Homework due Wednesday, October 12: Chapter 4 exercises: 8, 14, 16, 19, 21, 29, 43.


Wednesday, October 5:
  • Study: Start of Chapter 5
  • Homework due Wednesday, October 12: Chapter 5 exercises: 1, 2, 3a, 3b, 4, 17, 18a.
  • Interesting Reading (not at all required for the course): Rubik's Cube


Friday, October 7:
  • Study: Chapter 5
  • Homework due Wednesday, October 12: Chapter 5 exercises: 6, 9c, 9d, 11, 13, 18b, 24, 30.

Week of September 26 – September 30, 2005

Monday, September 26:
  • Study: Chapter 3 up to Finite Group Subgroup Test.
  • Homework due Wednesday, October 5: Chapter 3 exercises: 1, 4, 5, 14, 39, 46.


Wednesday, September 28:
  • Study: Finish Chapter 3.
  • Homework due Wednesday, October 5: Chapter 3 exercises: 8, 9, 16, 19.
  • Hint for 16: A good general strategy to show that A = B when A and B are both sets is to first show that A is contained in the set B then show that B is contained in A; ie, every element of A is in B and every element of B is in A.


Friday, September 30:
  • Study: First half of Chapter 4.
  • Homework due Wednesday, October 5: Chapter 4 exercises: 1, 2, 4, 5, 6, 15.
  • Optional Good Practice Problems: Page 90 exercises: 1, 5, 6, 10 (contrast to problem 18), 23.


Week of September 21 – September 23, 2005

Wednesday, September 21:
  • Study: Skim Chapter 0. Chapter 1.
  • Complete Assignment 0. Due by Monday's class at my office.
  • Homework due Wednesday, September 28: Chapter 1 exercises: 2, 3 (justify!), 5, 10 (you may assume the statements in problems 6 - 8), 12.


Friday, September 23:
  • Study: Chapter 2.
  • Homework due Wednesday, September 28: Chapter 2 exercises: 1, 3, 5, 6, 14, 20 (problem 16 offers a hint), 27.