Applications of Image Processing to Automate Tumor Image Quantifications

Caylor Booth

Advisor: Ryan Botts

This project develops a Java-based computer program that automates tumor image analysis through objective classification of pixels. This project then examines other image processing methods, like filtering and edge detection, to determine if they would expedite this analysis.


On the Alexander Polynomial and Related Invariants

Joy Chieh-Jung Chen

Advisor: Catherine Crockett

A key problem in the study of knot theory involves distinguishing which knots are equivalent and which are not.  To differentiate knots, their invariants, or characteristics, are compared. One such invariant is the Alexander Polynomial; its properties and relationships to other invariants, particularly the unknotting  number, are explored.


An Analysis of the Effects of PLNU's Enrollment Cap on Student Values

Kassandra Ham

Advisors: Maria Zack and Greg Crow

In 1999, Point Loma Nazarene University reached its city imposed enrollment cap. As a result, Point Loma became more selective in admitting students to the undergradute program. By compiling and analyzing data from surveys distributed to incoming freshman and graduating seniors at PLNU since 1993, it is possible to examine the effects of the enrollment cap on the values of students and see how they align with PLNU's core values.


The History and Mathematics of Perspective Devices

Olivia Heunis

Advisor: Maria Zack

Perspective is a method, governed by the physical laws of optics, which creates the illusion of a three-dimensional space on a two-dimensional surface. The development of perspective in art owes much of its progress to various perspective devices, that is, mechanized contraptions used by artists to understand and reproduce images with adherence to the laws of optics. This project aims to trace the development of perspective devices through the inspection of several key examples, and thoroughly examine the mathematics by which they function.


Simulation-Based Application of Artificial Intelligence to General Game Playing

Sean Lewis

Advisor: Jeff McKinstry

The goal behind General Game Playing (GGP) is to develop an intelligent agent that will automatically learn how to play different games at the expert level without any human intervention. Many intelligent GGP programs have used the game-tree search approach, but this may not be the best approach. Throughout my project, I implement the Monte Carlo/Upper Confidence bounds applied to Trees (UCT) simulation-based approach, which if not implemented correctly, may be the better decision-making algorithm.


John Wallis and Quadratures

Catherine Quimby

Advisor: Maria Zack

This project examines the influence of John Wallis' work in finding the quadrature of the circle and the development of the cycloid curve by mathematicians over time. It then looks at how the two topics fit together and lead to the development of integral calculus.