Math 432
Exam 1
October 4, 2011
You must show all work to receive any credit.
All problems are worth 14 points unless otherwise indicated.
1. Dene * be a binary operation dened on the set Z by
a.
b.
c.
d.
xy =x+y2
Prove or disprove that * is a commutative
Math 432
Exam 2
November 8, 2011
Key
1. Mark each of the following statements as True or False. Justify any
False answers with either a counterexample or result from the text.
a. Let G =< a > be a cyclic group of order n. If r divides n, then G has a
subg
Math 432
Exam 3
December 8, 2011
Key to exam 3
You must show all work to receive any credit.
(1) Let S be the set of all complex numbers of the form a + b 3i where a and
b are integers. Prove or disprove that S is an integral domain.
We will start by show
Finite Permutation Groups
Dr. Costa
October 27, 2011
1. Let f = (1, 3, 5, 4, 2)(1, 4, 3, 5). So f is a product of two cycles. Do
these cycles commute?
No, (1,3,5,4,2)(1,4,3,5)=(1,2)(3,4,5) while (1,4,3,5)(1,3,5,4,2)=(1,5,3)(2,4)
2. Express f as a product
World Academy of Science, Engineering and Technology 77 2011
Theory of Fractions in College Algebra Course
Alexander Y. Vaninsky
1
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