Math 3152/9043 Midterm 16 Feb 2012
Please show all work and justify your answers carefully. Time: 80 minutes
Question:
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Last
Total
Points:
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60
Score:
Name (print):
(6) 1. (a) How many 13 letter words can be made from the letters
Math 3152
February 10, 2012
Homework Two some solutions
1(a): If f (x) = an xn is the reciprocal of cos(x) = 1 x2 /2 + x4 /4! , the equality of power
n=0
series f (x) cos(x) = 1 gives equality for all coecients. The rst few of these are:
a0 =1;
a1 =0;
1
Math 3152
March 23, 2012
Homework Four Solutions
(1.1): Lets use the exponential counting formula by setting up an exponential family. The approach
used to count all permutations with a xed number of cycles can be modied: let Dn = if
n is odd, and let th
Math 3152
April 14, 2012
Fifth problem set solutions
1. Problems for Math 3152 and 9043
(1.1) The regular tetrahedron has 12 orientation-preserving symmetries.
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Let G be the group of symmetries of its faces.
(a) Compute the cycle indicator polynom