Math 332
Name:
Quiz 1
1. [10 points] If |a| = 100, what is the order of a12 ?
2. [10 points]
(a) List all possible generators for Z18 .
(b) List all elements of order 18 in Z90 .
3. [10 points] How many elements of Z310 have prime order?
4. [10 points] If
Homework 1
Math 332, Spring 2013
A
These problems must be written up in L TEX, and are due this Friday, February 8.
1. Consider the following matrix, whose entries are elements of the eld Z11 .
7 4
4 3
A =
(a) Find the eigenvalues of A. Your answers shoul
Homework 2
Math 332, Spring 2013
A
These problems must be written up in L TEX, and are due this Friday, February 15.
1. Let G = (0, ) R, and dene a binary operation on G by the formula
(a, b) (c, d) = (ac, bc + d)
for all (a, b), (c, d) G. Prove that G fo
Homework 3
Math 332, Spring 2013
A
These problems must be written up in L TEX, and are due this Friday, February 22.
1. Let G =
a b
0 1
a, b R and a = 0 .
(a) Use the two-step subgroup test to prove that G is a subgroup of GL(2, R).
(b) Prove that the cen
Takehome Midterm
Math 332, Spring 2013
A
These problems must be written up in L TEX, and are due this Sunday, April 14.
Rules: This is a midterm exam, not a homework assignment. You must solve the problems
entirely on your own, and you should not discuss
Homework 4
Math 332, Spring 2013
A
These problems must be written up in L TEX, and are due this Friday, March 1.
1. (a) Determine the isomorphism types of U (3), U (4), U (5), U (6), U (7), and U (8).
(b) List the elements of U (15), and determine the ord