MT310, Section 01, Spring 2009

Homework Assignments (from Abstract Algebra:  A First Course, by Dan Saracino.  Second Edition.)


NOTE:  HOMEWORK SOLUTIONS HAVE BEEN REMOVED FROM THIS WEBSITE AS THE COURSE IS OVER.

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 ONLY---do not hand in.


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

Problem 20.7


Last Revised:  May 13, 2009.