DEPARTMENT
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ALUMNI STUDENTS LINKS
SENIOR PROJECT GUIDELINES
Class of 2000
Senior Abstracts
Shari L. Bigley
Project Advisor: Dr. Stephen Bowser
This project is a review and alteration of The Hotelling Game
by Michael Friedlander and David Sumpter. Their article discusses the
idea of an imaginary town containing two identical shops which sell
the exact same goods. The customers that live in the town have to decide,
based on price and cost of travel, from which store to purchase exactly
one unit of goods. Only one turn of the game is considered as the two
shops decide which price to set for their good. The goals for both shops
are to maximize their amount of market share, and as a result, their
profit. The concepts of Harold Hotelling and the term Nash equilibrium
are discussed as they relate to the pricing game.
The transformation from a one-dimensional setting with one street into
a two-dimensional atmosphere with many streets gives excitement to the
simple idea of Friedlander and Sumpter. Along with obtaining a new idea,
the mathematics becomes more complex as the game is changed.
Kelly Broderick
Project Advisor: Dr. Ron Harrell
The objective of this senior project is to determine the set of all
convex polygons which will tile the plane.
Nadya Lee Davis
Project Advisor: Dr. Michael J.J. Barry
This senior project will explore two different questions, "What
is the minimal triangulation of a compact surface?" and "What
complete graphs and complete bi-graphs can be embedded on the sphere,
torus, and double torus?"
Amanda Carlson
Project Advisor: Dr. Michael Barry
This comp is an exploration of a function which sums the powers of
the digits of a number. Upon repetitive applications of the function,
the result is either 1 or it falls in a cycle of numbers and remains
there. I have used applications from number theory to show that this
function holds for general bases.
David P. McWright
Project Advisor: Dr. Anthony Lo Bello
This paper addresses Guiseppe Vitali's nonmeasurable set and the properties
of Lebesgue outer measure. The desirable properties of an extension
of length are discussed and several are proved to hold for Lebesgue
outer measure. As well, a charactorization is given of those sets, for
which all of the desirable properties hold. A construction of the Vitali
nonmeasurable set is given as well as a proof that the set is indeed
nonmeasurable.
Asa Page
Project Advisor: Dr. Aaron Cinzori
The Black-Scholes analysis was originally developed to value options
but has since proven to apply to a wide range of portfolios. This paper
will outline the derivation of the Black-Scholes method. The idea of
an asset with intermittent production dependent on some underlying market
price will be developed, and the Black-Scholes method will be extended
to cover this.
Candace Jean Pasquinelli
Project Advisor: Dr. Michael J.J. Barry
In my project, I will be discussing and showing the curves of a plane,
discussing topics such as the length of a curve, infinite length, and
finally winding numbers. In considering the topic, length of a curve,
I will be proving the properties of the length of a graph of a function
of a curve. Next, I will be proving that a given function, in fact,
has infinite length. Finally, I will show how the equation of a winding
number of a curve is formulated. Throughout my senior project, I will
also show non-trivial examples and computations of the suggested topics.
Martha Pitcher
Project Advisor: Dr. Aaron C. Cinzori
In this senior project, the Pythagorean and equal-tempered tuning systems
will be constructed. Continued fractions are presented as an approximation
to the solution of 2x = 3y. Differential
equations are used to describe position functions of free and forced
vibrations of tones. These position functions are used to evaluate perfect
fifths in the Pythagorean and equal-tempered systems.
Julie Ritchey
Project Advisor: Dr. Vonn Walter
Stated simply the goal of this project is to show that there are no
non-abelian simple groups with orders between 361 and 503 with the exception
of 420 and 480. This will be done by applying Burnside's theorems, Sylow's
theorems, corollaries and other basic group theory principles.
Jean Russell Robertson
Project Advisor: Dr. Stephen Bowser
The intention of this project is to illustrate the connection between
Markov Matrices and the Leontief Input-Output Model. This objective
is attained by giving a necessary background on matrices and Markov
Processes. Then finally integrating economic concepts.
Jamie L. Shanter
Project Advisor: Dr. Tamara J. Hummel
In this project I discuss the idea of power and using power indices
in voting games. This paper begins with the ideas of conflict, power
and modeling. In chapter 2, I have tried to explain some of the terminology
and theory behind voting games. In chapter 3, I have defined two power
indices, the Shapley-Shubik and the Banzhaf. I have also demonstrated
some examples of both indices. In chapter 4, I have examined larger
voting bodies and demonstrated, mostly by real-world examples, the idea
behind using power indices to determine voting power. In my final thoughts,
I have tried to encourage the reader to further develop the understanding
of when to use which index.
Allison E. Smith
Project Advisor: Dr. Vonn Walter
In this senior project, we will show that for all finite groups G,
the following 5 statements are equivalent:
(i) G is nilpotent.
(ii) Every subgroup of G is subnormal.
(iii) G satisfies the normalizer condition.
(iv) Every maximal subgroup of G is normal.
(v) G is the direct product of its Sylow subgroups.
