Senior Projects | Department of Mathematics | BYU-Idaho

# Mathematics Senior Projects

Either Math 498R (an internship) or Math 499R (a senior project) is required for all Mathematical Science Majors.

## Faculty Reference

Either Math 498R (an internship) or Math 499R (a senior project) is required for all Mathematical Science Majors. Below is a list of faculty and some of their mathematical interests. Feel free to contact any faculty member to discuss these topics and senior projects. It is a good idea to look into projects well before you are a senior. 
 
Faculty and Topics of Interest: 
 
Allen, Katie: Data Science 
 
Amidan, Brett: Statistics 
 
Bessey, Kent: Mathematical Card Magic (Group Theory, Graph Theory, Combinatorics, and Probability), Lexical Spaces (Topology & Topological Graph Theory), Measure Theory, Electromagnetism, Quantum Electrodynamics 
 
Brown, Dave 
 
Cameron, Greg 
 
Chilton, Larry: Computational Mathematics, Data Science, Simulation, Problem Solving 
 
Cox, Paul: Mathematical Biology, Discrete Dynamical Systems, Differential Equations, Time Series, Stochastic Processes 
 
Cromar Ryan 
 
Goodsell Troy 
 
Hathaway, J. 
 
Johnson, Craig: Statistics 
 
Johnson, Katrina: Math Biology, Data Science 
 
Lewis, Matthew: Sports Analytics, Math Biology, and Math Education 
 
Martin, Curtis: Background in Electrical Engineering. Electromagnetics, Image Processing, Pattern Recognition, Artifical Neural Networks, Human Perception (the visual system), Antennas 
 
Moon, Bonnie: Complex Analysis 
 
Morring, Brent: Statistics, Math Education, Data Science 
 
Nelson, Curtis: Combinatorics, Linear Algebra 
 
Nygaard, Jackie: Mathematics Education, Education Program Evaluation, Community involvement in K12 Education, and Appreciative Inquiry 
 
Palmer, David: Statistics, Data Science 
 
Romrell, Danae: Math Education, Action research on how students learn math including homework, online learning, mobile learning, and motivation for learning 
 
Rose, Jason: Mathematical Biology/Physiology, Partial Differential Equations, Dynamical Systems, Stochastic Processes 
 
Saunders, Garrett: Biostatistics, Machine Learning 
 
Sinkovic, John: Graphs, Linear Algebra 
 
Woodruff, Ben: Inquiry Based Learning, Multivariable Calculus, Linear Algebra, Abstract Algebra, Geometric Group Theory, Differential Geometry, Topology 
 
*****Note:**** **Not all faculty nor topics are listed here. If you have interests in other topics, please talk to a faculty member and he/she can direct you to someone in the department.**

## Past Senior Projects

Students in the biology department have been studying the effects of Parkinson's disease in the brains of mice. They have examined mice that have been infected with Parkinson's disease and examined pictures of the brains. By doing so, they have been trying to get a measurement of the density of the neural matter by hand. Kimmee worked to create a computer program that will analyze an image of a mouse brain and calculate the density for them. By careful statistical analysis a precise measurement on the density in the brains can be calculated. Kimmee also compared the results from her program with the results that the biology department has received to ensure that the results are as accurate as possible. 
 
Student: Kimmee Simpkinson 
Advisor: Garrett Saunders

As a physics major, Logan explored various branches of mathematics that have applications to physics. The project began with a general study of topology from Munkres, but eventually turned to a study of topics written by a particle physicist. Some of the more advances topics including adjoints of vector spaces and homology theory. The goal was to become more exposed to advanced mathematical topics that physicists use. 
 
Student: Logan Carpenter 
Advisor: Ben Woodruff

Thomas used Monte Carlo methods to analyze and compare strategies to games. This project included learning how to use object oriented programming in Python. One particular game was the popular card game Dominion, comparing various modifications of both the Smithy and Chapel strategies. 
 
Student: Thomas Brower 
Advisor: Ben Woodruff

While exploring introductions to number theory and Galois theory, many of the ideas centered on the unsolvability of the quintic. Eventually, this project focused on discovering several proofs that the symmetric group on 5 elements is an unsolvable group. 
 
Student: McKay Visser 
Advisor: Ben Woodruff

Corbin completed most of the Full Stack Web Developer nanodegree through Udacity. See Udacity.com for more information. 
 
Student: Corbin Buckley 
Advisor: Ben Woodruff

Thomas developed a portion of an R package based on models/tools in the Visual Sample Plan software (vsp.pnnl.gov). Also reviewed relevant literature. 
 
Student: Thomas Johansen 
Advisor: J. Hathaway

A (0,1)-matrix problem. McKay studied a class of (0,1)-matrices, wrote computer code to implement some recent theorems in the area, and proved a theorem about the cardinality of a class of matrices. Also reviewed relevant literature. 
 
Student: McKay Visser 
Advisor: Curtis Nelson

Jeffrey performed statistical modeling for a large dairy farm in Southern Utah. 
 
Student: Jeffrey Nielson 
Advisor: Craig Johnson

This project focused on analyzing a video with the goal of finding objects in the video. For example, suppose you had hundreds of hours of surveillance video from an airport and wanted to know if a certain person had been in the airport during the observation time. 
 
Students: Mitchell Breinholt, Alexander Douglas, and Stefanie Nestor 
Advisor: Larry Chilton

Students prepared for the actuary exam P (Probability) and exam FM (financial mathematics). This project is best done in groups. 
 
Students: Pierce Kamstra, Chris Fitzgerald, Mark Miller, Travis Loebs, Michael Espli 
Advisor: Larry Chilton

This project attempts to identify at risk students at the beginning of the semester to enable early intervention. 
 
Student: Carla Brookey 
Advisor: Larry Chilton

Specialized cameras are capable of creating a point cloud of an object. A point cloud is a collection of points in 3-space on the surface of an object. The point cloud is constructed by making millions of distance measurements from the camera to different points on the surface of the object. Given this distance data, one can create an accurate 3D model of the surface of the object. Unfortunately, when these models are created automatically (without human supervision), they often have defects. This project attempted to find holes (defects) in the models that do not exist in the modeled object. There are many applications including industrial safety, where remote inspection tools and simulations would enable companies to identify potential safety hazards and risks. INL sponsored this project. 
 
Student: Katie Larson, Zhengyu Pan 
Advisor: Larry Chilton

This project focuses on reconstructing very small objects from partial information measured from the diffraction pattern/Fourier transform. Ellen studied the image formulation process and its relationship to the Fourier transform. Wailam implemented the Error Reduction phase retrieval algorithm. Austin implemented two additional phase retrieval algorithms and compared their properties. 
 
Students: WaiLam Chan, Ellen Jensen, Austen Jones 
Advisor: Larry Chilton

Due to the students' long-term goal of working in Business Intelligence, projects were designed in this industry. Both students are currently working in the Business Intelligence industry. 
 
Students: Rob Clark, Trent Edvalson 
Advisor: Larry Chilton

Kinsey Cox studied the properties of inverse problems, where the challenge is to determine the properties of the system based on observations of the system. She illustrated these principles with a few examples. Daniel studied how to identify radio-isotopes based on their gamma radiation energy spectrum and gamma decay time history. 
 
Students: Kinsey Cox, Daniel Watkins 
Advisor: Larry Chilton

Austin analyzed FBI crime data using time series analysis using R. 
 
Student: Austin Kennedy 
Advisor: Ryan Cromar

Sarah revised a stochastic model for cancer progression to include new growth functions. 
 
Student: Sarah Taylor 
Advisor: Jason Rose

Justin performed a study of NCAA March Madness bracket predictions using standard methods as well as an original logistic regression approach. 
 
Student: Justin Conway 
Advisor: Garrett Saunders

Lila studied the use of conformal mappings to model various physical phenomenon. The study focused on the modeling of airflow with the Joukowsky Transformation. 
 
Student: Lila Barrett 
Advisor: Bonnie Moon

Crystal studied the Shape of Space and another text in order to learn more about topology and hyperbolic geometry. 
 
Student: Crystal Lawrence 
Advisor: Ben Woodruff

Sam studied the topic of Game Theory - which built off the student's background of economics. 
 
Student: Sam Clyde 
Advisor: Ben Woodruff

Tara studied homological algebra which would assist in graduate school. 
 
Student: Tara Fife 
Advisor: Ben Woodruff

Nicholas studied encryption schemes which would assist in preparing for a job with the NSA or other similar type of work. 
 
Student: Nicholas Lines 
Advisor: Ben Woodruff

- Abstract Algebra
- Biostatistics,
- Combinatorics
- Complex Analysis
- Differential Equations
- Differential Geometry
- Discrete Dynamical Systems
- Dynamical Systems
- Inquiry Based Learning
- Linear Algebra
- Machine Learning
- Mathematical Biology/Physiology
- Multivariable Calculus
- Partial Differential Equations
- Statistics
- Stochastic Processes
- Time Series
- Topology