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:

Bessey, Kent: Mathematical Card Magic (Group Theory, Graph Theory, Combinatorics, and Probability), Lexical Spaces (Topology & Topological Graph Theory), Measure Theory, Electro-Magnetism, Quantum Electrodynamics.

Cox, Paul: Mathematical Biology, Discrete Dynamical Systems, Differential Equations, Time Series, Stochastic Processes.

Chilton, Larry: Computational Mathematics, Data Science, Simulation, Problem Solving.

Johnson, Craig: Statistics.

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.

Nelson, Curtis: Combinatorics, Linear Algebra.

Nygaard, Jackie: Mathematics Education, Education Program Evaluation, Community involvement in K12 Education, and Appreciative Inquiry.

Palmer, David: Statistics. Project Ideas:

- 1) BYU-I Class Waitlist Analysis Obtain daily data pulls from the Institutional Research Department to get time stamped history of registrations, waitlist, and drops. The goal is to analyze this data and ultimately metrics to inform students of their likelihood of getting into a class based on their waitlist # and time until class starts (or until the add/drop deadline). Ideally it would be great to provide this information to the student in real time as they decide whether to get on the waitlist or not. But for the first phase of the project we are simply exploring the feasibility of getting the necessary data and creating the metrics. Currently I am planning to do the analysis in R.

- 2) Team Maker Tool Building. Help build a software tool that will algorithmically separate a class into teams based on certain survey questions. The algorithms and tools are based on a tool created by a team based at Purdue University with money from National Science Foundation grants. Until last year the platform was free. I would like to build a tool that replicates what their Team Maker tool does. Currently I am planning to do the analysis in R.

- 3) Book of Mormon Analysis. The Book of Mormon quotes a lot of Isaiah’s writing. If the ancient people had the writings one could expect that as their language and culture shifted, quoting from the original Isaiah text would gradually move away from a literal recitation of his writings. In other words, if the degree to which Isaiah is quoted word for word decreases, this could be interpreted as evidence that the Book of Mormon truly does represent writings of an ancient people. (The alternative explanation being that Joseph Smith became more careless in his citing of Isaiah as the book progressed). However, a lack of matching word for word does not necessarily indicate evidence for the contrary. The project may include developing a more precise research question, decide what is the benchmark for comparing Book of Mormon Isaiah writing against, how to measure the degree of match/mismatch, collect data and make conclusions as well as generate other research questions.

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.

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 Projects

**Biostatistics.** 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.

** Math and Physics. **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.

** Game Strategies. **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.

** Number Theory and Galois Theory. **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.

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

**Statistical sample size designs.**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.

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

**Statistical Modeling.** Performed statistical modeling for a large dairy farm in Southern Utah. Student: Jeffrey Nielson; Advisor: Craig Johnson

**Invariant Visual Similarity and Separation Preserving Map (iVSSPM).** This project focused on analyzing video with the goal of finding objects in 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

**Actuary Exam Preparation.** 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 Esplin; Advisor: Larry Chilton

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

**3D point cloud analysis.**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 these 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

**Coherent Diffraction X-Ray imaging.**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

**Business Intelligence.** 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

**Inverse Problems.** 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

**Time Series Analysis.** Analyzed FBI crime data using time series analysis using R. Student: Austin Kennedy; Advisor: Ryan Cromar

**Mathematical Biology/Modeling.**Revised a stochastic model for cancer progression to include new growth functions. Student: Sarah Taylor; Advisor: Jason Rose

**Statistical Prediction Methods.**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

**Complex Analysis.** 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

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

**Game Theory.** Studied the topic of Game Theory - which built off the student’s background of economics. Student: Sam Clyde; Advisor: Ben Woodruff

**Abstract Algebra.** Studied homological algebra which would assist in graduate school. Student: Tara Fife; Advisor: Ben Woodruff

**Encryption Schemes.** 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

**Potential Areas for senior projects:**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