# Honors in Mathematics

The department off ers mathematics majors the opportunity to graduate with honors in mathematics by completing an honors project. Of those students choosing to do so, most initiate the project during their senior year. An honors project entails an in-depth study of an area of mathematics not typically covered in the undergraduate curriculum. The choice of field is essentially left to the student and their honors advisor. The only stipulation is that the material must be of sufficient sophistication to warrant the honors designation, along with prior approval by the department faculty. Completion of an honors project requires both an expository report (the thesis) and an oral presentation to the department (the defense).

## Math Honors Processes

### Initial requirements

By the beginning of the approved honors activity, the student will:

• declare a major in mathematics.
• have a sufficiently high GPA: at least 3.0 overall and at least 3.5 in Mathematics courses numbered 122 and above and Statistics courses numbered 280 and above.
• complete at least two 400-level mathematics courses (excluding Math 499).

### How to apply

• Select a faculty member willing to supervise a directed study or undergraduate research project.
• Write a proposal with the aid of the advisor and present it to the department for approval. (View a sample proposal and suggested timeline.)
• Ask two faculty members (other than the advisor) to serve on the student’s honors committee. The advisor will be an ex officio member of the honors committee.

### Final requirements

• Major in mathematics with overall GPA at least 3.0 and at least 3.5 in Mathematics courses numbered 122 and above and Statistics courses numbered 280 and above.
• Completed directed study (three credits of Math 491 or 492) or undergraduate research project.
• An honors thesis approved by the honors committee. The thesis will contain either an exposition of known mathematics research or original student research. (View a sample honors thesis.)
• Final presentation given to the department.

## Honors Recipients:

### 2019 ~ 2020

• Abigail Bernhardt  – Markov Chain Model for the Spread of an Epidemic (under Dr. Esunge)
• Amy Creel – The $T, T^*, V_I, V_{NI}$ Model for Human Immunodeficiency Virus Type 1 (HIV-1) Dynamics (under Dr. Lee)
• Hannah Frederick – Conjugation by Circulant Matrices in Non-commutative Cryptography (under Dr. Helmstutler)
• Ashley Scurlock – Anticommutative Associative Algebras and the Binomial Theorem (under Dr. Collins)
• Stephen Tivenan – Exploration of Solvable Quintic Polynomials (under Dr. Lehman)

### 2018 ~ 2019

• Riley Anderson  – Improving Bertini 2.0: Classifying Singular Polynomials with Machine Learning (under Dr. Collins)
• Makenzie Clower – Predicting Parameters for Bertini Using Neural Networks (under Dr. Collins)
• Emily MacIndoe – Analysis of Deterministic and Stochastic HIV Models (under Dr. Lee)

### 2017 ~ 2018

• Henry Darron – An Analysis of Performance Measures of the Schooner Zodiac (under Dr. Chiang)
• Shannon Haley – Non-commutative Massey-Omura Encryption with Symmetric Groups (under Dr. Helmstutler)
• Bailey Stewart – Non-commutative Zero-Knowledge protocols (under Dr. Helmstutler)

### 2016 ~ 2017

• Rachelle Dambrose – Algorithms to Approximate Solutions of Poisson’s Equation in Two and Three Dimensions (under Dr. Lee)
• Nicholas Gabriel – Maxwell’s Equations, Gauge Fields, and Yang-Mills Theory (under Dr. Chiang)

### 2015 ~ 2016

• Chris Lloyd – The Ko-Lee Key Exchange Protocol with Generalized Dihedral Groups (under Dr. Helmstutler)
• Victoria Moore – Simultaneous Estimation of Multiple Time Series (under Dr. Hydorn)
• Pengcheng Zhang – Homogeneous, Isotropic Cosmology, Schwarzschild Solution and Applications (under Dr. Chiang)

### 2014 ~ 2015

• Michelle Craft – Eigenvectors of Interpoint Distance Matrices (under Dr. Hydorn)
• Kimberly Hildebrand – Using Independent Bernoulli Random Variables to Model Gender Hiring Practices (under Dr. Hydorn)

### 2013 ~ 2014

• Kyle Genovese – Application of Multiple Regression: A Two Case Study (under Dr. Esunge)
• Casey Howren – Computational Analysis of the SIR Epidemic model (under Dr. Lee)
• Chris Hunt – Surface Theory, Minimal surfaces, and Weierstrass Representations (under Dr. Chiang)
• Dane Lawhorne – Analogies Between the Real and Digital Lines and Circles (under Dr. Helmstutler)

### 2012 ~ 2013

• Kelly Brown – Mathematical Models of Honey Bee Populations: Rapid Population Decline (under Dr. Sumner)
• Morgan Brown – Numerical Approximations to the One- and Two-Dimensional Wave Equation (under Dr. Lee)
• Katie Dillinger – Analysis of the Heat Equation with a Heat Source Term (under Dr. Lee)
• Peter Slattery – Analytical Approaches to the Wave Equation (under Dr. Lee)

### 2011 ~ 2012

• Hannah Baumgardner – The Gauss-Bonnet Theorem and its Applications on Manifolds (under Dr. Chiang)
• Marianne Dubinsky – Methods for Solving the Basel Problem (under Dr. Esunge)
• Alan Liddel – Generalized Functions of Schwartz Type (under Dr. Collier)
• Catherin O’Doherty – Explorations of Stable Distributions (under Dr. Esugne)
• Rebecca Presor – Black-Scholes Option Pricing Model: Analysis, Approximations, and Applications (under Dr. Lee)
• Kelly Scott – Anti-Blocking Sets (under Dr. Mellinger)
• Teresa Yao – The Diffusion of a Chemical Pollutant Modeled by a Fourier Series (under Dr. Lee)

### 2010 ~ 2011

• Kathryn Christian Mathematical and Numerical Solutions for a Heat Conduction Model (under Dr. Lee)
• Kevin DoubledayApplication of Markov Chains to Stock Trends (under Dr. Esunge)
• Geoff DriskellA Comparison of Two Derivations of the Black-Scholes Option Pricing Model (under Dr. Esunge)
• Kelsie Snyderc-Dominating Sets for Families of Graphs (under Dr. Mellinger)
• Andrew Snyder-Beattie Dissecting Two Approaches to Energy Prices (under Dr. Esunge)
• Erin StangeComputational Models of the Diffusion Equation (under Dr. Lee)

### 2009 ~ 2010

• Sarah BallEvaluating Mean Willingness to Pay for the Success of the Blue Crab in the Chesapeake Bay (under Dr. Hydorn)
• Elizabeth BernatAnalysis of Temperature Change Using a Mathematical Model (under Dr. Lee)
• Barbara BrownGeneralized Dihedral Groups of Small Order (under Dr. Helmstutler)
• Katie HunsburgerThe Weight Enumerator for a Class of LDPC Codes Generated by Hyperovals (under Dr. Mellinger)
• Thomas WolfeStatistical Analysis of Genetic Mutations in SMS Patients and Resulting Phenotypes (under Dr. Hydorn)

### 2008 ~ 2009

• William EllaRetracts in Category Theory (under Dr. Helmstutler)
• Christine ExleyCryptography Based on Determining Sets (under Dr. Mellinger)
• Jacob Farinholt Designing Codes to Fit Your Needs: a closer look at BCH codes (under Dr. Mellinger)
• Jonathan StallingsImproved Covariance Eigenvalue Estimates and Line Estimation (under Dr. Hydorn)
• Christopher TriolaSpecial Orthogonal Groups and Rotations (under Dr. Helmstutler)

### 2007 ~ 2008

• Elizabeth Liskom Teaching Geometry with The Geometer’s Sketchpad (under Dr. Mellinger)
• Katherine Mulrey Differential Geometry and its Applications to Einstein’s Equations (under Dr. Chiang)
• Roberto PalombaSn-Normal Semigroups of Partial Transformations (under Dr. Konieczny)
• Juliette Zerick Computational Characterizations of Basin Boundaries (under Drs. Edmunds and Ackermann)

### 2006 ~ 2007

• Robert CarricoEstimating the Eigenvalues of Covariance Matrices using Confidence Intervals (under Dr. Hydorn)
• Sean DromsPartial Linear Transformations of a Vector Space (under Dr. Konieczny)
• Ryan Johnson Investigation of a Min-Max Scheduling Problem (under Dr. Mellinger)
• Gardner MarshallA Lie-Theoretic Approach to the Spin Groups (under Dr. Helmstutler)

### 2005 ~ 2006

• Chris MeyerCodes Generated by Matrix Expansions (under Dr. Mellinger)
• Allison PiccoloThe Effect of Stage Structure on Basins of Attraction (under Dr. Edmunds)

### 2004 ~ 2005

• Daniel Bowers Elliptic Curves and Their Applications in Cryptography (under Dr. Lehman)
• Amanda Passmore An Elementary Solution to the Menage Problem (under Dr. Mellinger)
• Lisa Yuhui SongApplication of Transition Matrix Theory and Stochastic Modeling to Aeschynomene virginica Population Dynamics, a Threatened Species (under Drs. Edmunds and Griffith)
• Jennifer Stovall A New Class of Codes from Finite Geometry (under Dr. Mellinger)

### 2003 ~ 2004

• Damian Watson Fractional Analysis and its Applications (under Dr. Chiang)

### 2002 ~ 2003

• Jaime Ann Miller Differential Geometry and its Applications to Minimal Surfaces (under Dr. Chiang)
• Matthew WelzExtension Fields and Geometric Constructions (under Dr. Konieczny)

### 2001 ~ 2002

• Mohamed ChakhadDifferential Geometry and its Applications to Relativity (under Dr. Chiang)

### 2000 ~ 2001

• Wendi Cook Fourier Analysis and its Musical Applications (under Dr. Chiang)