Carrie Cromwell
Project Advisor: Dr. Vonn Walter

This paper describes the properties prime numbers and how to test numbers for primality. The first chapter is an introduction to prime numbers. Chapter two discusses different deterministic methods to test for primes. The third chapter introduces more properties of primes that distinguish them from cmoposite numbers. The final chapter describes different probabilistic tests for primes.

Leaha Filippi
Project Advisor: Dr. Anthony Lo Bello

In this senior comprehensive project, we will solve the Problem of Points, also known as the Division Problem.

Christina Ann Galli
Project Advisor: Dr. Aaron Cinzori

In 1993, the FBI's Criminal Justice Information Services Division approved the Wavelet/Scalar Quantization Standard for digitizing and compressing its fingerprint archives. The fingerprints are digitized using pixels measuring 1/250,000 square inches and 256 shades of gray. The resulting digital image is normalized and compressed by Huffman encoding a quantized discrete wavelet transform subband decomposition. This standard uses specific encoders for the subband decomposition, quantization encoding, and Huffman encoding. However, the compressed data format allows for a universal decoder. Thus, the decoder reconstructs an image compressed by any encoder.

Gregory M. Johnson
Project Advisor: Dr. Vonn Walter

In this senior project, for finite p-groups and groups of order pq,for p and q prime, we will show the folling 8 things:
(i) For a group of order p3, the center of the group will either have an order of p or p3.
(ii) For a group of order p3, if the group is abelian, then there are only 3 possible isomorphism classes.
(iii) All non-abelian groups of order p3 are extra-special.
(iv) All non-abelian groups of order p3 are either dihedral or quaternions when p is even.
(v) The complete classification for groups of order 8.
(vi) A group of order pq, for p>q prime, has a normal subgroup of order p.
(vii) A non-abelian group of order pq, is a semi-direct product.
(viii) There can not be non-isomorphic, non-abelian groups of order pq.

Kristopher L. Knepper
Project Advisor: Dr. Tamara J. Hummel

In this senior comprehensive project I discuss the theory behind the Leontief Input-Output model, a complex and widely used method for empirically analyzing economies on the disaggregate. The paper begins by giving the reader a brief history of Wassily Leontief himself and his model. I then state some of teh necessary mathematical facts from linear algebra that are necessary for understanding of the text. After the introduction, I note a few major theorems necessary for an initial understanding of the model followed by proof arguments to assure that the claims do, in fact, carry weight. I include examples throughout the text to illustrate the theory.

Jimmy Manes
Project Advisor: Prof. Anthony Lo Bello

No abstract.

Molly A. McGuckin
Project Advisor: Dr. Ronald E. Harrell

Investigating one of the many patterns found in the Fibonacci secquence, we will determine which terms of the Fibonacci sequence are divisible by a given non-prime integer n.

Robyn Nelson
Project Advisor: Dr. Aaron C. Cinzori and Dr. Shafiqur Rahman

Since it is difficult, and in most cases impossible, to solve a complex ferromagnetic or antiferromagnetic system analytically, one must use computer simulation methods in order to sudy such a system. Various computer simulation methods have been developed to study such complex systems. In order to test these methods, they are used on simpler systems that can be solved analytically. This serves as a check so increasingly complex systems may be studied with greater confidence in the findings. One such method is the Monte Carlo Method which can be used to gain information for the creation of a single histogram. The single histogram method is then used to create other histograms at different temperatures near the original temperature at which the date was collected.

Nicholas J. Paladino
Project Advisor: Dr. Tamara J. Hummel

This profect is based on a representation of musical chords as sets in Z12 and polygons arranged on a twelve-point circle. Subsequent definitions and theorems are given and proven regarding manipulation of such sets and polygons. Operations applied to the sets include transposition and inversion, mirroring the same transformations done on chords in music and the set of these functions is shown to be a group under function composition. Stated theorems and proofs include the hexachord and common tones theorems, as well as the definition of an equivalence relation on the set of all pitch class sets. Finally, there is an introduction to the circle of fifths and its consequences.

Eric A. Poli
Project Advisor: Dr. Anthony J. Lo Bello

In this project we prove that htere exists a measurable function f and a measurable set such that the inverse image of the measurable set under f is not measurable. Also, we will show that this measurable set is not a Borel set.

Brendan Toland
Project Advisor: Dr. Aaron Cinzori

This project takes a close look at methods used for ranking college football teams. In college football, there are a large number of teams who play a small number of games. This makes it very hard to determine who is the best team based on so little information. Further adding to the problem, there is no playoff format in college football. The top teams in the country each paly in just one bowl game at the end of the season. So based on the regular season of ten or twelve games, it must then be decided who are the top two teams in the country out of over one hundred teams, so those top two teams can play for the national championship. Becasue of this unique problem, many people have created mathematical models that rank the teams.

In the following pages I will describe two such models: the model that is currently used by college football, and a model created by a mathematician named James Keener which relies on the Perron-Frobenius Theorem. I will then describe my own model that I have created, and look at how it fared in predicting the national champion.

Al Trezza
Project Advisor: Dr. Anthony Lo Bello

In this senior comprehensive project, we will do a statistical analysis of the November 2000 Presidential election in Florida. We will use this analysis in order to make a prediction as to who actually should have won the election in Florida as well as the Presidency.

Michael J. Williams
Project Advisor: Aaron Cinzori

This paper reports original findings from research on the traveling salesman problem. A brief history of the problem preempts the description of research and results on a variation of the classic problem. The problem entails minimizing the number of days found in a tour of 30 major League Baseball cities. Formulation and application of two algorithms will be discussed followed by the results ensuing from these algorithms.

Timothy J. Wrona
Project Advisor: Ron Harrell