Spring 2014 Math 330
Homework III
III.1 Determine the adjacency matrix, M for the following graph assuming
the vertices are alphabetically ordered.
>A
O
C
F
/
/
Do
/
>B
>E
G
III.2 How many ways are th
Spring 2014 Math 330
Homework I Solutions
In all of these problems, proofs should be proofs by induction.
I.1 Prove that for all n Z+
12 + 22 + + n2 =
n(n + 1)(2n + 1)
6
Proof. We proceed by Mathemati
Spring 2014 Math 330
Homework VI Solutions
VI.1 How many dierent ways are there to answer a test which consists of
three true/false questions, 5 5-item multiple choice questions, and a
nal problem who
Spring 2014 Math 330
Homework IV
For Problems 1 to 4, determine the following properties of the network.
(a) Switch Type
(b) Number of Switches
(c) Diameter
(d) Maximum Congestion
IV.1 The network bel
Spring 2014 Math 330
Homework II
II.1 Use Euclids Algorithm to nd the Greatest Common Divisor of 21212121
and 12121212.
II.2 What is the Greatest Common Divisor and Least Common Multiple of
the number
Spring 2014 Math 330
Homework V
For Problem 1 to 5, solve the recurrence relation.
VI.1
an = 5an1 6an2
a0 = 1, a1 = 0
VI.2
an = 4an2
a0 = 0, a1 = 4
VI.3
an = 6an1 9an2
a0 = 1, a1 = 2
VI.4
an = 7an1 12
Spring 2014 Math 330
Homework IV Solutions
For Problems 1 to 4, determine the following properties of the network.
(a) Switch Type
(b) Number of Switches
(c) Diameter
(d) Maximum Congestion
IV.1 The n
Spring 2014 Math 330
Homework VII
VII.1 Use induction to prove
n
(2k 1) = n2
k=1
VII.2 Use induction to prove
n
(3k 2) =
k=1
n(3n 1)
2
VII.3 Use the Pulverizer to nd the inverse of 13 in Z49 .
VII.4 F
Spring 2014 Math 330
Homework VI
VI.1 How many dierent ways are there to answer a test which consists of
three true/false questions, 5 5-item multiple choice questions, and a
nal problem whose answer
Spring 2014 Math 330
Homework III Solutions
III.1 Determine the adjacency matrix, M for the following graph assuming
the vertices are alphabetically ordered.
/
>A
O
F
0
1
0
M = 0
0
0
0
/
0
0
0
0
1
0
0
Spring 2014 Math 330
Homework II Solutions
II.1 Use Euclids Algorithm to nd the Greatest Common Divisor of 21212121
and 12121212.
gcd(21212121, 12121212) = gcd(12121212, 9090909)
= gcd(9090909, 303030