Mathematics and Computer Science

2013 Senior Theses

2013 Senior Projects

Fall 2012
Monday, November 19, MCRey 315
3:00Sarah Pullen, Modeling Project-Based Learning by Applying Markov Chains to Board Games
Spring 2013
Monday, April 1, MCRey 315
3:00Calvin Cochran, Shuffle Posets and their Hasse Diagrams
3:30Clarissa Burton, Using Wireless Routers for Positioning of Android-Based Devices
4:00Andres Ramirez, Achieving an Approximate Localization Value for Autonomous Robots
Tuesday, April 2, MCRey 315
3:00Kaleigh Clary, Identification of Transformed Characters
3:30Eric Lew, An Observation of Chess Piece Placement Patterns
4:00Safari Sibomana, Speed Limit Number Recognition
4:30Lauren Irby, Paths Through Rectangular Point Lattices
Wednesday, April 3, MCRey 315
3:00Lauren Beck, Voting and Fairness: The Condorcet Criterion
3:30John Dyer, Digitizing the Hendrix housing process
4:00Innocent Bushayija, On the Gauss-Markov Theorem
4:30Jeannette Inema, Analysis of the Current Status of IPv6 Deployment
Tuesday, April 30, MCRey 315
11:00Patrick Karangwa, Modeling and Simulation of Outpatient Clinic


Presenter:Lauren Beck
Title:Voting and Fairness: The Condorcet Criterion
Presentation:Wed 3 Apr, 3:00pm, MCRey 315
Advisor:Prof. Lars Seme

Abstract: We begin by exploring differences between common voting methods that use ranking ballots. To determine which is more fair, we examine a fairness criterion, the Condorcet criterion. If a Condorcet candidate appears frequently in an election, we can deem it as an appropriate standard for comparing voting methods. We then test the likeliness of having a Condorcet candidate in an election, and find that because it is so common, we can use it to compare the different voting methods.

Presenter:Clarissa Burton
Title:Using Wireless Routers for Positioning of Android-Based Devices
Presentation:Mon 1 Apr, 3:30pm, MCRey 315
Advisor:Dr. Carl Burch

Abstract: A person can find where they are in an unknown location by using a GPS receiver. However, problems arise when the area that one is in is very dense or requires fine altitude distinction for navigation. I use wireless routers to attempt to locate Android devices on the third floor of MCReynolds.

Presenter:Innocent Bushayija
Title:On the Gauss-Markov Theorem
Presentation:Wed 3 Apr, 4:00pm, MCRey 315
Advisor:Dr. Duff Campbell and Dr. Tom Stanley

Abstract: We consider a population distribution where the dependent variable is a function of several independent variables. Then by random sampling the population, the Sample Regression Function (SRF) slope coefficient estimators are obtained by the method of Ordinary Least Squares (OLS). Then, we prove independently the Gauss-Markov Theorem which states that the SRF estimators, under certain assumptions, are the best linear unbiased estimators of the population slope coefficient estimates.

Presenter:Kaleigh Clary
Title:Identification of Transformed Characters
Presentation:Tue 2 Apr, 3:00pm, MCRey 315
Advisor:Dr. Gabe Ferrer

Abstract: With the advent of tablet and touch screen computing, the number of applications that utilize text recognition technologies is rapidly increasing. These applications rely on accurate identification of text characters, which may or may not be oriented uniformly. This project explores methods to identify characters that may have been altered with translation, rotation, or skew. Our approach uses transformation matrices to correct character orientation by manipulating the set of pixels representing the characters. Machine learning was used to identify the properly oriented characters.

Presenter:Calvin Cochran
Title:Shuffle Posets and their Hasse Diagrams
Presentation:Mon 1 Apr, 3:00pm, MCRey 315
Advisor:Dr. David Sutherland

Abstract: Shuffle posets are poset variations which contain listings composed of all, some, or none of the elements of ordered alphabets A and B such that the listings preserve the order of the alphabets within their structures. We impose a partial order and display the shuffle posets as lattices, opening the door for the inspection of group-like structures. The subject of this project is the investigation of shuffle poset properties and the nature of their Hasse diagrams. In particular, combinatorics and abstract algebra are used to prove theorems regarding the partial order on shuffle posets and to inspect the graph automorphisms of these Hasse diagrams for isomorphisms to well-known algebraic groups.

Presenter:John Dyer
Title:Digitizing the Hendrix housing process
Presentation:Wed 3 Apr, 3:30pm, MCRey 315
Advisor:Dr. Carl Burch

Abstract: The current housing process at Hendrix is meticulous and requires large amounts of human resources to accomplish repetitive tasks. In my project I explore the creation of a user interface in the context of attempting to update the current housing system.

Presenter:Jeannette Inema
Title:Analysis of the Current Status of IPv6 Deployment
Presentation:Wed 3 Apr, 4:30pm, MCRey 315
Advisor:Dr. Dwayne Collins

Abstract: The Internet Protocol, IP, is a system of digital message formats and rules for exchanging message between devices connected to a network. IP supports unique addressing for all the devices on the network for an exchange of information to be established. There are two main Internet Protocol versions; Internet Protocol Version 4, IPv4, and Internet Protocol version 6, IPv6. IPv6 was made available for deployment since 1999 and was designed to respond to the exhaustion of IPv4 available addresses available to allocate. As of now, even though IPv4 available addresses are almost exhausted, IPv6 network traffic remains very small compared to IPv4 network traffic. This project studies past and current statistics of IPv6 deployment to determine why IPv6 has not been fully deployed 14 years after it was made available and when there are no more IPv4 addresses to allocate. The project analyses the main factors that impact IPv6 deployment and makes predictions for the future IPv6 deployment.

Presenter:Lauren Irby
Title:Paths Through Rectangular Point Lattices
Presentation:Tue 2 Apr, 3:00pm, MCRey 315
Advisor:Prof. Lars Seme

Abstract: In a rectangular point lattice of dimensions N vertices down and M vertices across, it is possible to define a path through the vertices from the left-hand side to the right-hand side of the lattice. This project explored the properties of these paths, including the number of total paths on a given lattice, the number of paths associated with each node, and the probabilities of these paths.

Presenter:Patrick Karangwa
Title:Modeling and Simulation of Outpatient Clinic
Presentation:Tue 30 Apr, 11:00am, MCRey 315
Advisor:Dr. Dwayne Collins

Abstract: This project models the set-up of the outpatient clinic and efficiency is the key target, it is measured by the time patients spend waiting for the service and how clinic resources are being used. I allowed the adjustments on initial clinic appointment and nurses, that was done by constructing different scenarios and used queuing theory to examine the possible improvement in efficiency basing on scenarios results.

Presenter:Eric Lew
Title:An Observation of Chess Piece Placement Patterns
Presentation:Tue 2 Apr, 3:30pm, MCRey 315
Advisor:Prof. Lars Seme

Abstract: The project focuses on two goals. The first is to recreate the N-Queens problem, that is, to determine the maximum number of queens that can be placed on an NxN chessboard, where N represents the number of squares on the side of the board, such that no two queens are attacking each other. The second goal is to determine the least number of queens that can be placed on a board such that every square on the board is attacked. The project will be completed using a mix of empirically determined data that enumerates piece placement and the patterns that emerge from their placement.

Presenter:Sarah Pullen
Title:Modeling Project-Based Learning by Applying Markov Chains to Board Games
Presentation:Mon 19 Nov, 3:00pm, MCRey 315
Advisor:Dr. Chris Camfield

Abstract: I modeled an educational practice called project-based-learning as I discovered how to utilize Markov Chains and elements from linear algebra to analyze different board games. Finding information about the game length of Chutes and Ladders and about which Monopoly properties are most advantageous to invest in, I learned mathematics the way it should be learned: in the context of something you are truly curious about and enjoy.

Presenter:Andres Ramirez
Title:Achieving an Approximate Localization Value for Autonomous Robots
Presentation:Mon 1 Apr, 4:00pm, MCRey 315
Advisor:Dr. Gabe Ferrer

Abstract: The SLAM problem is known as the Simultaneous Localization and Mapping problem. It is a technique used by robots in order to create maps of an unknown environment while simultaneously localizing itself within the created map. The research does not create a full solution for the SLAM problem but rather attempts to create a solution to a subproblem: robot localization. More specifically, an approximate localization value was calculated by implementing a particle filter. Although this research is a subproblem of a much more complex issue, it is definitely a stepping stone to potentially achieve a full solution for the SLAM problem at an undergraduate level.

Presenter:Safari Sibomana
Title:Speed Limit Number Recognition
Presentation:Tue 2 Apr, 4:00pm, MCRey 315
Advisor:Dr. Dwayne Collins

Abstract: Real-time object recognition systems are usually expected to analyze and interpret images captured from a substantially non-homogeneous environment. This imposes various additional computational complexities for resolving noise, which is likely not incurred when dealing with images taken from a fairly homogeneous environment. In this project, we attempt to identify speed limit numbers represented in binary images that presumably are captured using a camera mounted on a moving vehicle. By analyzing a shape of a contour representing a digit in the image, we collect features that enable us to accurately characterize the corresponding number.