Assignment Number
Due Date

Problems

Assignment 1
Wednesday, January 21, 2009

Problems 0.4, 0.9, 0.16, 0.17, 0.18
Please be careful to
write clear and complete proofs to answer these 5 exercises. Your
proofs should make logical sense and be something that any BC math
major could pick up and read and understand. (My typed answers
for this assignment, which I will put on this web page after the HW is
handed in, are 1 1/2 pages total. You can be complete and
succinct at the same time.)

Assignment 2
Wednesday, January 28, 2009

Problems 1.3, 1.4, 1.5,
1.6, 1.9
Problems 2.1, 2.4c, 2.5, 2.8, 2.10
Problems 3.4, 3.5, 3.9, 3.11, 3.12
Important Note: For these and all future problems, please be sure
to explain and justify your
answers, and not just to answer the question without
explanation. For example, in problem 1.3, if * is not a binary
operation, explain why it is not. This is done by indicating why the
definition on page 10 fails to be satisfied. In problems 1.4 and
1.5 explain your answers. For each part of problem 1.6, either
explain why * is commutative or else give a counterexample to show that
it is not, and similarly for associative. In problem 1.9,
justify your answers. Similarly for the problems in Sections 2
and 3.

Assignment 3
Friday, February 6, 2009

Problems 3.10, 3.15
Problems 4.5, 4.10, 4.13, 4.14, 4.15a, 4.20, 4.22, 4.25 
Assignment 4
Friday, February 13, 2009

Problems 5.1 a, d, e, f, g, 5.7, 5.9, 5.14, 5.16, 5.18, 5.24, 5.25

Assignment
5
Monday, February 23, 2009

Problems 5.5, 5.6, 5.8.
Problems 6.1c, 6.2ab, 6.3, 6.7, 6.14.
Problems 7.7, 7.8.
Problems 8.2ab, 8.3, 8.4, 8.7

Assignment
6
Monday, March 16, 2009

Problems 9.5, 9.9, 9.16
Problems 10.1, 10.2, 10.5, 10.6, 10.7, 10.8

Assignment
7
Monday, March 23, 2009

Problems 10.16, 10.19
Problems 11.1, 11.2, 11.3, 11.4, 11.7, 11.16, 11.23. Note:
For problem 11.3, recall that Z(G) was defined on pg. 46.

Assignment
8
Monday, March 30, 2009

Problems 12.1abcd, 12.3,
12.4abcdef, 12.8, 12.13, 12.21
Problems 13.1, 13.5 (use the Fundamental Homomorphism Theorem), 13.7
(ditto), 13.14 (ditto).
Problem 15.6

Assignment 9
Monday, April 6, 2009

Problems 16.1, 16.3,
16.9b,c, 16.13a, 16.16.
Notes: i) 16.9: we did part (a) in class; you may use
it in solving part (b).
ii) For 16.16, the word "idempotent" is defined in 16.14.
All you need is the definition.

Assignment 10
Friday, April 24, 2009

Problems 17.1 (you must
explain briefly why for each part), 17.6, 17.9, 17. 14, 17.27, 17.30
Problem 18.2

Assignment 11
Recommended ONLYdo not hand in.

Problem 19.3 (a),(b), 19.4
(a).
Problem 20.7


