Mathematics Integrated with Computers and Applications I
MATH 1p40

Summer 2014
Problem Set 5 Solutions
Due: Monday, March 7 at 9 PM
Problem 1. An undirected graph G has width w if the vertices can be arranged in a se
quence
v 1 , v 2 , v3 , . . . , v n
such that each vertex vi i
Mathematics Integrated with Computers and Applications I
MATH 1p40

Summer 2014
Problem Set 8 Solutions
Due: Monday, April 11 at 9 PM
Problem 1. An electronic toy displays a 44 grid of colored squares. At all times, four are
red, four are green, four are blue, and four are yellow
Mathematics Integrated with Computers and Applications I
MATH 1p40

Summer 2014
Problem Set 3 Solutions
Due: Tuesday, February 22 at 9 PM
Problem 1. An urn contains 75 white balls and 150 black balls. While there are at least
2 balls remaining in the urn, you repeat the following
Mathematics Integrated with Computers and Applications I
MATH 1p40

Summer 2014
Problem Set 4 Solutions
Due: Monday, February 28 at 9 PM
Problem 1. Prove all of the following statements except for the two that are false; for
those, provide counterexamples. Assume n > 1. When prov
Mathematics Integrated with Computers and Applications I
MATH 1p40

Summer 2014
Problem Set 2 Solutions
Due: Monday, February 14 at 9 PM
Problem 1. Use induction to prove that
1
1
1
1
1
1
1
1
1
=
2
3
4
n
n
for all n 2.
Solution. The proof is by induction on n. Let P (n) be the
Mathematics Integrated with Computers and Applications I
MATH 1p40

Summer 2014
Problem Set 6 Solutions
Due: Monday, March 28 at 9 PM
Problem 1. Sammy the Shark is a nancial service provider who offers loans on the fol
lowing terms.
Sammy loans a client m dollars in the morning
Mathematics Integrated with Computers and Applications I
MATH 1p40

Summer 2014
Problem Set 7 Solutions
Due: Monday, April 4 at 9 PM
Problem 1. Every function has some subset of these properties:
injective
surjective
bijective
Determine the properties of the functions below, and
Mathematics Integrated with Computers and Applications I
MATH 1p40

Summer 2014
Problem Set 9 Solutions
Due: Monday, April 25 at 9 PM
Problem 1. There are three coins: a penny, a nickel, and a quarter. When these coins are
ipped:
The penny comes up heads with probability 1/3 and
Mathematics Integrated with Computers and Applications I
MATH 1p40

Summer 2014
Problem Set 10 Solutions
Due: Monday, May 2 at 9 PM
Problem 1. Justify your answers to the following questions about independence.
(a) Suppose that you roll a fair die that has six sides, numbered 1,
Mathematics Integrated with Computers and Applications I
MATH 1p40

Summer 2014
Problem Set 11 Solutions
Due: 5PM on Friday, May 6
This is a miniproblem set. The rst problem reviews basic facts about expectation.
The second and third are typical nal exam questions.
Problem 1. Ans
Mathematics Integrated with Computers and Applications I
MATH 1p40

Summer 2014
Problem Set 1 Solutions
Due: Monday, February 7 at 9 PM
Problem 1. The connectives (and), (or), and (implies) come often not only in com
puter programs, but also everyday speech. But devices that comp