Mathematics and Computer Science

# 1998 Senior Theses

- Blake Armstrong: Four Unforgettable Mathematicians
- Laura Brandebura: Introduction to Wavelets and Multiresolution Analysis
- Martin Eckles: Compiler Construction
- Shiloh Harder: Bond Lattices
- Jeff Johnston: Three-dimensional Volumetric Modeling of Ophiomorpha Using Two-dimensional Surfaces
- Brian Raines: Inverse Limits and Link-Expansive Chains
- Shane Wanamaker: Counting Systems of Distinct Representatives
- David Warren: Partitions and Their Young's Lattices

*Four Unforgettable Mathematicians*

Blake Armstrong

Advisor: Ze'ev Barel

Brief Description of Paper:

Despite being held back by society and their families, female mathematicians did contribute a great deal to the did contribute a great deal to the development of mathematics. Hypatia (c. 370-415), Maria Agnesi (1718-1799), Sophie Germain (1776-1831), and Sophia Kovalevskaya (1850-1891) were four such contributors. We will discuss the biographies of these four women and highlight the mathematical accomplishments for which each is most recognized.

--Blake Armstrong

*Introduction to Wavelets and Multiresolution Analysis*

Laura Brandebura

Advisor: Dwayne Collins

Brief Description of Paper:

The paper presents an analysis of signals as functions in L^2(R) by means of orthonormal bases for L^2(R) via multiresolution analysis.

--Laura Brandebura

Laura is currently studying meteorology at the University of Oklahoma.

*Compiler Construction*

Martin Eckles

Advisor: Ali Kooshesh

Brief Description of Paper:

Compilers translate input programs from one programming language to another. The construction of a compiler is a complicated task. This paper deals with some of the theoretical and implementational issues in writing a compiler.

--Martin Eckles

*Bond Lattices*

Shiloh Harder

Advisor: David Sutherland

Brief Description of Paper:

In this paper, we characterize the bond lattices for several specific classes of graphs. Then we describe the graph automorphisms for each type of bond lattice.

-- Shiloh Harder

*Three-dimensional Volumetric Modeling of Ophiomorpha Using Two-dimensional Surfaces*

Jeff Johnston

Advisor: Lars Seme

Brief Description of Paper:

In the study of extinct burrowing animals, often the only remaining record is their fossilized burrows. A mathematical model is developed trows. A mathematical model is developed to take two-dimensional data of fossilized Ophiomorpha burrows to create a three-dimensional representation of the burrow network. Using this model, we can better study the extent of the burrow network without having to scrape and document a large volume of work.

--Jeff Johnston

Jeff is currently studying biology and mathematics at Emory University.

*Inverse Limits and Link-Expansive Chains*

Brian Raines

Advisor: Dwayne Collins

Brief Description of Paper:

A sufficient condition for two maps, f and g, on [0,1] to generate homeomorphic inverse limits will be presented.

--Brian Raines

Brian is currently studying mathematics at the University of Missouri-Rolla.

*Counting Systems of Distinct Representatives*

Shane Wanamaker

Advisor: Dwayne Collins

Brief Description of Paper:

This talk introduces methods of counting the number of possible SDR's under certain restrictions.

-- Shane Wanamaker

*Partitions and Their Young's Lattices*

David Warren

Advisor: David Sutherland

Brief Description of Paper:

In this paper, I extended previous work in partitions and two dimensional lattices to include partitions with representative three-dimensional lattices. The paper also looks at conjugate lattices and the relationship between them.

--David Warren