By Justin A. Brown

The Fundamental Group of Compact Surfaces with no Boundary

April 2003

Advisor: Dr. Jesus Jimenez


The main objective of this project is to study properties of topological spaces by means of algebraic objects, in our case groups. The first homotopy group functor, also known as the first fundamental group functor, as well as a family of homology group functors, from the category of topological spaces to the category of groups is defined. The fundamental group of compact surfaces with no boundary is computed, and the homology groups of the circle, the sphere, and the torus are also computed. One can see that these groups serve to classify the topological spaces mentioned.


By Joshua French

The Study of Freshman Attrition Rates of Point Loma Nazarene University

April 2003

Advisor: Dr. Greg Crow


What factors predict which students will leave Point Loma Nazarene University by the spring semester of their freshman year? In order to answer this question, a model was built using binary logistic regression to predict the transition between the fall and spring semesters of a student’s freshman year. Prior to building this model, one-third of the students from the 1993-2000 cohort years were randomly filtered out of the data used to build the model. After completion of model building, these students were used to determine the validity of the model. Upon verification that the model was reasonably accurate, the variables proven to be significant are now reported, along with their relative importance in determining whether a student will stay for both semesters of their freshman year. Hopefully, the university’s Cabinet will then use these findings in order to institute programs that aid “at risk” students in continuing their education into the second semester of their freshman year.


By Gina Joyce Frye

An Analysis of Vector Spaces of Functions Using Linear Algebra and Real Analysis

April 2003

Advisor: Dr. Sheldon Sickler


We examined vector spaces of functions. Bases for some of these vector spaces have been built using Fourier and Taylor series. Matrices have been employed to represent the linear transformations of differentiation and integration. Inner products on vector spaces of functions have also been defined and examined. The study of inner products has become vital in defining a new form of convergence and examining the implications of this convergence as it relates to pointwise and uniform convergence.


By Matt DeVuyst

Branch Delay Simulation

December 2002

Advisor: Dr. Lori Carter


Branch prediction is a field of research that tries to enable the computer pipeline hardware to make good predictions as to what the next instruction to be executed might be, before the result of a branch instruction is known. If the guess is correct, the pipeline can efficiently process subsequent instructions; but if the prediction is wrong, then the predicted instruction(s) will have to be flushed part way through execution and the correct next instruction executed. This is obviously inefficient for the pipeline.

The goal of this project was to create a simulation to explore some of the different branch prediction techniques currently implemented for pipelines. The simulation allows for visualization of the pipeline and branch prediction schemes. It measures the efficiency of the different branch prediction schemes as compared to perfect prediction (when the prediction is always correct) and no prediction at all. Results from experimentation with the simulator suggest that a combination of prediction techniques might be the best way to resolve the control hazard problem.