MATH 3140, Abstract Algebra 1, section 002
Prof. Monk
Spring 2008

Files to download are in .pdf form.
Web page updated May 2, 2008: solutions for assignment #13.
Web page updated April 29, 2008: review exercises solutions, right here!

Course information

ASSIGNMENT #1:
1. Read Preface ``To the student''.
2. If you have not taken linear algebra, read Linear algebra notes #1.
3. If you are not familiar with complex numbers, read Appendix A.5.
4. Read pages 1-22.
5. Do exercises 2, 4(a), 6(a), 10, 15 on pages 13-15 and 1(b), 6(a), 10, 16 on pages 22-23, to be turned in on Wednesday Jan. 23.

ASSIGNMENT #2
1. Read pages 24-42; skip pp. 29-32.
2. Read the following notes on solving linear congruences.
3. Read the following proof of Proposition 1.4.8
4. Do exercises 4, 10, 12, 26 on pages 32-34; for 4, find all solutions; hint for 26: use the binomial theorem; read notes on the binomial theorem if you are not familiar with it; also do exercises 9, 10, 18, 22 on pages 43-44. All these exercises to be turned in on Wednesday January 30.

ASSIGNMENT #3
1. Read pages 47-69.
2. Read notes on finite sets.
3. Do exercises 5, 9(e), 10(b), 20 on pages 60-61; also do exercises 1(b), 5, 7, 9 on pages 69-70; all exercises to be turned in on Wednesday Feb. 6.

ASSIGNMENT #4
1. Read pages 71-100.
2. Do exercises 3, 5, 11, 14 on pages 84-85; and exercises 2(b), 6, 22, 24 on pages 101-102; all exercises to be turned in on Wednesday Feb. 13

ASSIGNMENT #5
1. Read pages 102-122.
2. Read the notes on groups of order 6, and the notes on the general linear group of degree 2 over the 2-element field.
3. Do exercises 2, 10, 19, 24(a) on pages 113-114; for 24(a), also show that a has infinite order iff the inverse of a has infinite order; also do exercises 2, 8, 9, 10 on page 123. There is a correction for 9(c) on page 123: show that every subgroup different from (Z times Z) has the indicated form. Hint: if the subgroup is not equal to (C sub 1), take an element (a,b) of it with |b-a| different from zero and minimum. All exercises to be turned in on Wednesday Feb. 20.

REMINDER: TEST 1 ON FEB. 22.

ASSIGNMENT #6
1. Read pages 124-140.
2. Do exercises 2, 10, 11, 24 on pages 132-134. Hint for 24: try mapping x to 1/x -1 for any nonzero real number x. Also do exercises 3(a), 10, 15, 16 on page 141. All exercises to be turned in on Friday Feb. 29.

ASSIGNMENT #7.
1. Read pages 142-162.
2. Do exercises 3, 4, 17, 19 on pages 150-151. Also do exercises 7(b),(d), 11, 14, 19 on pages 163-164. All exercises to be turned in on Friday Mar. 7.

ASSIGNMENT #8.
1. Read pages 164-189.
2. Do exercises 4, 7, 13, 18 on page 176, and exercises 2, 5(d), 7, 22 on pages 189-191. All exercises to be turned in on Friday Mar. 14.

ASSIGNMENT #9.
1. Read pages 192-209.
2. Do exercises 2(c), 8, 13 on pages 201-202 (For 13, find all the monic polynomials of degree at most 3 over Z_3, and do part (c); this problem has double the usual credit, since it is long). Also do exercises 6, 14, and 21(f) on pages 210-211. All exercises to be turned in on Friday Mar. 21.

REMINDER: TEST 2 ON FRIDAY APRIL 4

ASSIGNMENT #10.
1. Read pages 211-233.
2. Do exercises 3(d), 5(d), 9, 16 on pages 218-220; and exercises 4(a), 14, 17, 21 on pages 234-236. All exercises to be turned in on Wednesday Apr. 9.

ASSIGNMENT #11.
1. Read pages 236-259.
2. Do exercises 2, 11, 14, 16 on pages 249-250; and exercises 9, 11, 14, 21 on pages 259-261. All exercises to be turned in on Wednesday Apr. 16.

ASSIGNMENT #12.
1. Read pages 262-275.
2. Do exercises 1, 8, 10, 11 on page 267; and exercises 2, 4, 6, 9 on page 276. All exercises to be turned in on Wednesday Apr. 23.

ASSIGNMENT #13
1. Read pages 276-293.
2. Do exercises 1(f), 2(c), 4, 10 on page 282; and exercises 1, 2, 4 on page 288. All exercises to be turned in on Wednesday Apr. 30.

REVIEW ON Apr 30, May 2.

REMINDER: FINAL EXAM ON TUESDAY MAY 6, 4:30-7PM, IN THE USUAL CLASSROOM ECCR116.



MISCELLANEOUS NOTES:

Solution of exercise 6(b) on page 23

Definition of polynomials

TEST SOLUTIONS:
Test 1.
Test 2.

EXERCISE SOLUTIONS:
Assignment 1.
Assignment 2.
Assignment 3.
Assignment 4.
Assignment 5.
Assignment 6.
Assignment 7.
Assignment 8.
Assignment 9.
Assignment 10.
Assignment 11.
Assignment 12.
Assignment 13.