Jeremy Beh
Project Advisor: Dr. Steve Bowser

This senior comprehensive project invewtigates Stokes's Theorem, where we can use this theorem, and its applications. A proof of a special case of Stokes's Theorem is given, and then this proof is extended to make an argument for the original theorem. This same procss is also done for Green's Theorem, a result closely related to Stokes's Theroem. Then there are discussions of where and how Stokes's Theorem can be used.

Thomas M. Everest
Project Advisor: Dr. Tamara J. Lakins

The two main goals of this project are firstly to define the concept of the order of an integer modulo n, and secondly to define and investigate properties of primitive roots for an integer. To obtain these goals, we first review definitions and prove past theorems in number theroy that aid us in our current calculations. The second chapter defines both the order of an integer and the concept of primitive roots, providing a base for Chapters 3 and 4, in which we prove that htere exist primitive roots for all primes, and also for composite numbers of a particular form.

Cristin M. Giancola
Project Advisor: Dr. Anthony Lo Bello

This senior comprehensive project discusses the F-Distribution in detail and then applies the theory to Tippett's problem of the lengths of cuckoo eggs deposited in the nests of other birds.

Bryan J. Hunter
Project Advisor: Dr. Tamara J. Lakins and Dr. Robert S. Roos

One of the fascinating topics in computer science and mathematics is the notion of a noncomputable function. Two examples of noncomputable functions are the Busy Beaver function and the Shift function. Given a postitive integer n, the Busy Beaver function outputs the maximum number of 1s that a halting n-state Turing machine with a tape alphabet {0,1} can write, when started on an initially blank tape (i.e., all 0s). Given a positive integer n, the Shift function outputs the maximum number of moves a halting n-state Turing machine with a tape alphabet {0,1} can make when started on an initially blank tape. In this project we will show that the Busy Beavre function, the Shift function, and other related functions are noncomputable.

Mark Imling
Project Advisor: Dr. Anthony Lo Bello

In this article we will develop and prove a theorem that will give us the expected waiting time until the occurrence of a given pattern of heads and tails.

Crystal A. Mance
Project Advisor: Dr. Ronald E. Harrell

This project is an examination of the welfare system using linear programming. Definitions and notation dealing with linear programming are discussed according to the simplex method. These are then applied to examples pertaining to the welfare system in America.

Ryan M. O'Grady
Project Advisor: Dr. Anthony Lo Bello

In this paper, we will examine the work of De Moivre and Laplace concerning the normal approximation to the Binomial Distribution. We will then use similar methods to exhibit a bivariate normal approximation to the Trinomial Distribution.

Ryan J. Ollock
Project Advisor: Dr. Anthony Lo Bello

The method of geometric constructions is a lost art in today's world. This paper takes a look at many of the achievements of the ancient Greek mathematicians in the field of geometric constructions. We will then look at the famous Greek construction problem which went unsolved for over 2000 years, the problem of trisecting an angle, and then produce its solution.

Fabrizio Polo
Project Advisor: Dr. Anthony Lo Bello

In this paper, the probability of winning the Genoan Lottery is calculated for a generalized prize scheme. Then, the lottery is generalized to a graph theoretic structure wherein the expected total number of sequences and expected number of sequences of specified length are calculated.

Eric Porter
Project Advisor: Dr. Anthony Lo Bello

This project is a continuation of David Mancuso's senior project which was completed in the Fall Semester of 2001. I continued his work and performed an analysis and correction of Propositions 35-48 of Book I of Euclid's Elements of Geometry. I followed the guidelines laid down by David Hilbert in his reformulation of Euclid's work.

Daniel A. Princic
Project Advisor: Dr. Anthony Lo Bello

This paper examines the randomness of the Powerball Multi-State Lottery draws using the Chi-Squre Goodness of Fit Test, Genoan Lottery Test, Poker Test, and Runs Test.

Landon Proctor
Project Advisor: Dr. Tamara J. Lakins

This senior project explores some of the mathematics resulting from attempts to solve what is called Post's problem in recursion theory. Though ultimately unsuccessful in resolving the problem for which they were invented, simple and hyper-simple sets proved to be sufficiently complex and stuctured in their own right ot warrant further investigation. Therefore this paper will introduce the concepts necessary to derive some basic theorems about such sets, with the purpose of utilizing standard recursion-theoretic proof techniques new to the author.

Lauren Sprys
Project Advisor: Dr. Anthony Lo Bello

This Senior Project describes the St. Petersburg Paradox.