Math 4140 Final Exam
Due Monday May 16th before 12:00.
No late papers will be accepted.
Problem 5 coding theory For each of the following lengths n and minimum distances d, give an upper bound on the size of an error correcting code
with those parameters
Math 4140 Homework 3 (Due: Friday Feb. 17th)
Problem 1 Find the automorphism group of the Petersen graph. You must prove your answer
is correct. Hint: rst used the orbit stabilizer lemma to get the size then use a presentation of
the graph given in the rs
Math 4140 Homework 4 (Due: Friday March 16th)
Problem 1 Prove the the (4, 6)-cage has 26 vertices using the geometric construction on Z3 from class.
3
Solution: From class we know the cage is a bipartite graph whose vertices are the
one and two dimensiona
An Introduction to
Biological Dierence Equations
Math 182 - Fall 2002
Daniel A. Ashlock
Department of Mathematics
Iowa State University
Ames, Iowa 50011
danwell@iastate.edu
1
Contents
1 Fibbonachis Rabbits
Students that have already encountered calculus w
Math 4140 Homework 2 Key
Problem 1 Suppose that f (n) = 7f (n 1) 16f (n 2) + 12f (n 3) and that f(0)=2,
f(1)=5, and f(2)=11. Find a closed for for f (n).
Answer:
f (n)
r3
r3 7r2 + 16r 12
(r 2)2 (r 3)
f (n)
=
=
=
=
so
=
so
=
=
=
A+C
2A + 2B + 3C
4A + 8B +
Math 4140 Homework 5 (Due: Friday March 30th)
Problem 1 15 pts Find the code that is the null space of the following matrix and give its
minimum distance.
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
0
Solution: Notice that the rst four c
Math 4140 Homework 1 Key
Problem 1 How many strings over the alphabet cfw_A, B, C fail to have adjacent repeated
letters? Your answer should be a function of the length n of the string. So, for example:
3 of length one: A, B, C
6 of length two: AB, AC, BA
Chapter 5
Rings
Nothing proves more clearly that the mind
seeks truth, and nothing reects more glory
upon it, than the delight it takes, sometimes
in spite of itself, in the driest and thorniest
researches of algebra.
- Bernard de Fontenelle
This chapter
3
Math 4140 Midterm
Due Monday March 5th
Problem 5 Suppose we have a nite set of
points P and a set of lines L that are subsets
of P so that every pair of points are in exactly one line. If we make a bipartite graph
G(V, E) with V = P L and
Directions: Wo
Chapter 6
Graphs
The origins of graph theory are humble, even frivolous.
N. Biggs, E. K. Lloyd, and R. J. Wilson
(Graph Theory: 1736-1936)
to see if this is a good name. Recall that a relation
is a set of ordered pairs while edges of a graph are
unordered