By Christine Todd

The Four Color Theorem

Spring 2005

Advisor: Dr. Maria Zack

Abstract:

This project takes a detailed look at the Four Color Theorem that was posed back in 1852 and eventually proved in 1976. Based upon the book Four Colours Suffice by Robin Wilson, this project examines particular mathematicians and their processes that furthered the solution of the theorem. It will focus on the work of Cayley, Kempe, and Heawood, as well as the use of computers in the final proof that Appel and Haken published.

 

By Sarah Richardson

Data Mining Using Weka

Spring 2005

Advisors: Dr. Greg Crow and Dr. Maria Zack

Abstract:

With increasing computer power, higher knowledge of statistical and learning algorithms, and improved data collection and management, a new field of study has blossomed in recent years. This field of study is called data mining. By definition, data mining is the extraction of implicit, previously unknown, and potentially useful information from data. This is done using a process that combines mathematical statistics with computer science based machine learning. The programs/algorithms that are used to do data mining sift through the data and attempt to find patterns in an efficient manner. This project will use the data mining tool Weka to analyze student placement testing information from the Mathematical, Information and Computer Sciences Department at Point Loma Nazarene University.

 

By Ryan Imel

Recruitment Based on Geographical Information Systems

Spring 2005

Advisor: Dr. Greg Crow

Abstract:

This project is designed to assist the admissions department at Point Loma Nazarene University in targeting the best locations for marketing the university to new students. My main task will be to gather and compute statistical information, and incorporate it in a GIS program called ArcView, through which I can create maps that display and store this information in an insightful way. I will be analyzing the number of underrepresented youth and those of Nazarene background in comparison to total population in my quest to find the most successful marketing areas. All the information will be collaborated to give the admissions staff a better sense of where they need to focus their marketing efforts to be the most successful.

 

By Melanie Hail

Development of an Efficient Class Scheduling Algorithm

Spring 2005

Advisor: Dr. Lori Carter

Abstract:

Constraint guided scheduling is a field of research that tries to create the most efficient schedule given certain restrictions. Algorithmic techniques are used to increase the efficiency of the scheduling process. Greedy algorithms make the best local choice without seeing the big picture. Priority algorithms associate a priority with a variable and schedule the highest priority variable first. Backtracking algorithms add the capability of changing a past choice if this choice has affected future progress.

The goal of this project is to use these algorithms and techniques to create an efficient scheduling system for the Department of Mathematical, Information and Computer Sciences. The constraints on the schedule include class length, availability of professors, and limited resources, such as rooms. To find the most effective scheduling process, this project will measure the efficiency of programs using combinations of the algorithmic techniques.

 

By Brady Acheson

Reed-Solomon Codes

Spring 2005

Advisor: Dr. Jesus Jimenez

Abstract:

We review some elements of Linear Algebra and Finite Fields and then we give a general presentation of linear codes and how they are used in digital communications. We construct a special kind of linear codes called Reed-Solomon codes and present a syndrome decoding method for them.

 

Jedidiah Butler

The Calculus of Newton

Spring 2005

Advisor: Dr. Maria Zack

Abstract:

This study seeks to understand the Calculus of Isaac Newton. It can be split into two parts. The first is the history behind Newton’s Calculus, how it started, developed and any obstacles he encountered along the way. The second part is to understand the theory of Newton’s Calculus. His methods differ from those of today. This project will research the methods of Newton’s Calculus, particularly his Method of Fluxions.