## Faculty Reference

Faculty and Topics of Interest

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, Electro-Magnetism, 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

*

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, Electro-Magnetism, 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

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

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

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

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

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

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

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

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

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

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 Espli

Advisor: Larry Chilton

Students: Pierce Kamstra, Chris Fitzgerald, Mark Miller, Travis Loebs, Michael Espli

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

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

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

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

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

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

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

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

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

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

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

Student: Sam Clyde

Advisor: Ben Woodruff

Abstract Algebra

Studied homological algebra which would assist in graduate school.

Student: Tara Fife

Advisor: Ben Woodruff

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

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