By Tyler Corwin

Thickness and Stick Number of Knots

April 2004

Advisor: Dr. Jesus Jimenez

Abstract:

Knot theory, a branch of topology, studies knotted closed curves in 3-dimensional space, their deformations, and their properties or invariants. In this research, we have chosen to concentrate on the following properties: crossing number, stick number, thickness, and curvature in an attempt to understand these characteristics of knots. Pertaining to crossing number, we shall attempt to better define the bounds on the minimum crossing number of a stick knot and fully understand the relationships between a knot’s crossing number, its minimum stick number, its size and length, and its type. We shall investigate the derivation of the known bounds on the stick number of a polygonal knot and try to understand the relationship between thickness and curvature of a knot in 3-dimensional space. Upon achieving a comprehensive background in the study of knots, we will attempt to reach new conclusions concerning knots and their properties.

 

By Paul Kelly

The Development of a Computer Resource Page for Point Loma Nazarene University

April 2004

Advisor: Dr. Lori Carter

Abstract:

The proposed distinction project will consist of designing and developing a web page for Point Loma Nazarene University containing information on computer hardware and software specifications primarily for incoming students. On this web page students will be able to 1) find computing requirements, including those specific to their majors, 2) find help designing their own personal computer systems, and 3) find information on how their computers will interface with the PLNU network. This web page will have a similar goal as that already in existence at www.ptloma.edu/computers but will provide additional resources for students.

 

By Sarah Littler

A Mathematical Perspective on Art

April 2004

Advisor: Dr. Maria Zack

Abstract:

This project investigates the mathematical roots of linear perspective in art. The project has two main components. The first component is a study of the mathematical work on linear perspective done in the15th through 17th centuries. This is the time period when Brunelleschi, Franceschi, Alberti, and da Vinci were studying the mathematical aspects of linear perspective. Using this information drawings with standard linear perspective are created using Maple and other specialized software. The second component is a study of “distorted” perspective. Computer tools and hand calculations are used to take a piece of artwork done in correct linear perspective and mathematically alter the perspective to create a distortion.

 

By Spencer Williams

August 2003

Advisor: Dr. Lori Carter

Abstract:

For the summer of 2003, Dr. Lori Carter set several tasks before me. The first task was to take

programs created by students in her spring 2003 Java programming class, find bugs in those programs, and correct those bugs.

The second task was to write tutorials for those programs and then implement the programs and tutorials into a user-friendly web site that could be used for future classes at PLNU.

The third task was to write a couple of my own programs that could also be used in computer science classes at Point Loma. For a detailed explanation of the project go to http://mcs.ptloma.edu/swilliams abstract continued.htm