Topics in Algebra

Fall, 2005

## 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.