MICS Student Research

A focused female student writes down notes in class wither her pencil

Students who pursue a major in the Department of Mathematical, Information & Computer Sciences have a unique opportunity to conduct research alongside experienced faculty. This student research involves the methodical formation of a scholarly honors project. The goal of this project and its process is to prepare students for the world of post-baccalaureate scholarship and research.

You will work closely with a department faculty mentor to develop a project on a topic of your choosing, and the research will culminate as you make a presentation of your findings at a conference during the spring semester. In preparation for the presentation, you will be coached through the various stages of conducting a research project and transforming your work into a scholarly presentation and paper. The Department of Mathematical, Information & Computer Sciences will strongly support you as a research student, and you can look forward to working with your faculty mentor throughout the research, editing, and presentation processes, gaining invaluable advice and guidance every step of the way.

2016-17 Student Research

How Frequently are ISCR Elements Recombining to Produce Novel Antibiotic-Resistant Bacteria?
Rachel Platz
Advisor: Dr. Ryan Botts

Antibiotic-resistant bacteria pose a risk to public health. The CDC reported two million cases of antibiotic-resistant infection per year in the United States and twenty-three thousand led to death. Bacteria acquire antibiotic resistance genes, ARGs, through recombination and different mobile genetic elements. In recent studies, ISCR elements have been recognized as a powerful ARGs capture and movement system. It is important to understand how these elements are evolving; specifically, how frequently they are recombining and capturing ARGs to move and create bacteria with novel combinations of antibiotic resistance. We analyzed the evolutionary history of ISCR elements and the genes they frequently carry to determine if recombination of the elements is slower than evolution of individual genes.

The Relationship Between Mathematics and Military Education Based on the Eighteenth-Century French Text, Nouveau Cours De Mathématiques, À L'Usage, Bernard Forest de Bélidor
Elizabeth Kenyon
Advisor: Dr. Maria Zack

This paper investigates the relationship between mathematics and military tactics in the eighteenth century. Surely armies and militiamen needed some sort of instruction in order to have an understanding of defense and military tactics. The process of education is the focus of this study. By translating various sections of Bernard Forest De Bélidor's text, Nouveau Cours De Mathématiques, À L'Usage written in 1725, it is possible to demonstrate the manner in which mathematical concepts were used to instruct militaries. Upon translating four "applications," two concentrated on geometry and the other two focused on trigonometry, the relationship between mathematics and military strategies can be demonstrated. This paper analyzes a few of the "applications" individually to better gain an understanding of how militaries could use mathematical information. These applications serve as illustrations as to how to employ the methods learned from earlier sections in the text. The primary idea is that with a strong mathematical foundation, soldiers would be better equipped in battle and would be better able to construct various military structures.

Spiritual Formation in Student-Athletes
Hayley Richardson
Advisors: Dr. Greg Crow & Dr. Maria Zack

The research conducted in this project statistically analyzes the spiritual formation and practices of students at Point Loma Nazarene University. Specifically, it looks at the differences between the student-athletes and the non-student-athletes at Point Loma as it pertains to their spiritual formation and practices. From this research, it was determined that student-athletes have about the same or worse spiritual formation and practices then their non-athlete counterparts. As a result of this study, the Point Loma Athletic Department can see areas in which it can seek to design experiences and practices that enhance the spiritual formation of its students-athletes.

2015–16 Student Research

Data Analysis on PLNU Students
Kathleen Wilson
Advisors: Dr. Greg Crow and Dr. Maria Zack

This project explores PLNU student behavior. From surveys taken by students throughout their time at PLNU, it can be seen whether this time has had a positive or negative impact on the development of things such as personality and spirituality.

Assessing Methods for Analyzing MacTel
Joseph Conrad, Jonathan Paul, and Annie Thwing
Advisors: Dr. Ryan Botts and Dr. Lori Carter

This project produces realistic data analogous to Macular Telangiectasia, which can be used to assess signal analysis tools. One of these tools is the Wavelet Transform, a tool for signal analysis and compression in identifying and establishing the significance of the contributing factors of genetic diseases. 

2014–15 Student Research

Analysis of a Neural Network-Based Public Key Protocol
Aaron McKinstry
Advisor: Dr. Jesus Jimenez

Kanter et al. (2002) proposed a key exchange protocol that uses the convergence of interacting neural networks. A variant of the protocol was analyzed by Shamir et al. (2002). In this paper, the variant protocol is analyzed. A theory of non-updating steps is proposed as an explanation for a dimensional phenomenon exhibited by the protocol, and then falsified by simulation. The protocol is then mathematically analyzed as a Markov chain; convergence follows from its properties, and it is proved the neural networks do not always converge.

2013-14 Student Research

Statistical Analysis on Chapel Attendance
Amy Hinds
Advisors: Dr. Greg Crow and Dr. Maria Zack

The research conducted in this project statistically analyzes the trends in PLNU's chapel attendance; it looks at how likely a student is to attend chapel based on certain attributes and characteristics. The aim of this study is to better understand the composition of PLNU's chapel congregation and predict future patterns of chapel attendance.

Elliptic Curve Cryptography
Ethan Wade
Advisor: Dr. Jesus Jimenez

Plane curves of the form Ax^3+Bx^2 y+Cxy^2+Dy^3+Ex^2+Fxy+Gy^2+Hx+ly+j=0 are called elliptic curves. These curves have been studied for hundreds of years and have cropped up in many areas such as physics, factoring, and cryptography. It is the latter this paper focuses on. Currently, the National Security Agency (NSA) and the Central Security Service (CSS) strongly advocate for the use of elliptic curve cryptography (ECC) due to its remarkable efficiency when it comes to an equal level of security of other methods such as RSA and Diffie-Hellman (DH), which are widely in place as of the writing of this paper. With that in mind, this paper sets out to explore the mathematics and methods behind ECC.

Plasmid Identification Using Gene Clusters
Kristen Petersen
Advisor: Dr. Ryan Botts

Plasmid mediated antibiotic resistance has made treating bacterial infections difficult and costly. Machine learning is used to identify common gene patterns within individual plasmids, as well as across multiple plasmids. Common survival strategies can be used to indicate where the plasmid is likely to be found.

2012-13 Student Research

Applications of Image Processing to Automate Tumor Image Quantifications
Caylor Booth
Advisor: Dr. Ryan Botts

This project developed a Java-based computer program that automates tumor image analysis through objective classification of pixels. The project then examined other image processing methods, like filtering and edge detection, to determine if they would expedite this analysis.

On the Alexander Polynomial and Related Invariants
Joy Chieh-Jung Chen
Advisor: Dr. Catherine Crockett

A key problem in the study of knot theory involves distinguishing which knots are equivalent and which are not. To differentiate knots, their invariants, or characteristics, are compared. One such invariant is the Alexander Polynomial; its properties and relationships to other invariants, particularly the unknotting number, are explored.

An Analysis of the Effects of PLNU's Enrollment Cap on Student Values
Kassandra Ham
Advisors: Dr. Maria Zack and Dr. Greg Crow

In 1999, PLNU reached its city-imposed enrollment cap. As a result, it became more selective in admitting students to the undergraduate program. By compiling and analyzing data from surveys distributed to incoming freshman and graduating seniors at PLNU since 1993, it is possible to examine the effects of the enrollment cap on the values of students and see how they align with PLNU's core values.

The History and Mathematics of Perspective Devices
Olivia Heunis
Advisor: Dr. Maria Zack

Perspective is a method, governed by the physical laws of optics, which creates the illusion of a three-dimensional space on a two-dimensional surface. The development of perspective in art owes much of its progress to various perspective devices, that is, mechanized contraptions used by artists to understand and reproduce images with adherence to the laws of optics. This project aims to trace the development of perspective devices through the inspection of several key examples, and thoroughly examine the mathematics by which they function.

Simulation-Based Application of Artificial Intelligence to General Game Playing
Sean Lewis
Advisor: Dr. Jeff McKinstry

The goal behind General Game Playing (GGP) is to develop an intelligent agent that will automatically learn how to play different games at the expert level without any human intervention. Many intelligent GGP programs have used game-tree search, but this may not be the best approach. Throughout this project, the Monte Carlo/Upper Confidence bounds applied to Trees (UCT) simulation-based approach is implemented, which may be the better decision-making algorithm.

John Wallis and Quadratures
Catherine Quimby
Advisor: Dr. Maria Zack

This project examines the influence of John Wallis' work in finding the quadrature of the circle and the development of the cycloid curve by mathematicians over time. It then looks at how the two topics fit together and lead to the development of integral calculus.

2011-12 Student Research

An Analysis of Trends in Chapel Attendance Patterns
Chanell Anderson and Lauren Waggoner
Advisors: Dr. Greg Crow and Dr. Maria Zack

Chapel is an integral part of nearly every student’s time at PLNU. Every Monday, Wednesday, and Friday provides a time for the student body to gather together as a whole along with faculty and staff to participate in Christ-centered community. Prior to fall 2011, students enrolled in 12 or more units and all residential students with freshman or sophomore standing were required to attend 36 chapels each semester and students with junior or senior standing were required to attend 28. In fall 2008, the student-led service Time Out was offered to students as another opportunity to receive chapel credit during the week. Through spring 2009, students could receive a maximum of three chapel credits per week, meaning Time Out could count as an alternate third chapel credit for a given week. This policy changed in fall 2009, however, and in a given week students could earn up to four chapel credits if they were to attend each chapel service and Time Out. Because of flexibility in acquiring chapel credits, it can be valuable from a chapel programming perspective to understand the makeup of the congregation at different points of the semester. This project explores the last five years of chapel attendance, from fall 2006 to spring 2011, to better understand trends in attendance patterns, identify any emerging trends related to student demographics in the congregation throughout each semester, and determine if there are any correlations between the chapel speaker and who is in attendance. This will build off the research project completed by Marilee Rickett, a 2010 PLNU graduate, who began analysis work on chapel attendance from 2006 to 2009.

Image Compression Using Tensor Decomposition
Nathaniel McClatchey
Advisors: Dr. Ryan Botts and Dr. Jesus Jimenez

This paper describes multidimensional image compression using canonical polyadic tensor decomposition. It suggests methods for decomposing two- and higher-dimensional tensors, then describes how the result may be used for compression. Finally, the results of this technique are compared with the results of other popular image compression techniques.

The Calculus of Variations
Tyler Levasseur
Advisors: Dr. Ryan Botts and Dr. Jesus Jimenez

The purpose of this paper is to explain the fundamental techniques of the calculus of variations. This includes explaining the details of the derivations of the Euler-Lagrange equation and the Beltrami identity, and their applications to the brachistochrone problem.