MATH 3790 - Assignment 1
Due: Sept 23
September 17, 2003
1. Prove that
3
3 is irrational.
First assume for a contradiction that 3 3 is a rational number. Then
we can write p = 3 3. Rearranging, we get
q
p3 = 3q 3
We can now note that the number of 3s in t
MATH 3790 - Assignment 4
Due Nov 27
November 20, 2003
1. Given a graph G with n vertices, prove that if d(v)
then G is connected.
n
2
for all v V (G)
Assume for a contradiction that G is not connected. Then there are 2 vertices x, y which are in dierent
MATH 3790 - Assignment 2 Solutions
Due Oct 16
October 17, 2003
1. Show that there is no polynomial p with integer coecients such that
p(1) = 4 and p(3) = 7.
We begin by assuming that such a polynomial exists, and examine the following equations and taking
MATH 3790 - Assignment 3 Solutions
Due Nov 6
November 6, 2003
1. State and prove the AM-GM inequality for 3 terms.
We need to show that for three non-negative integers x, y, z we have that
x+y+z
3 xyz. To begin, we make the substitution x = a3 , y = b3 ,