I am interested in working with students on a research project in applied mathematics. Students would work closely with me on the project.  This is a very attractive opportunity for you to consider and something very substantive to add to your resume.

In my project, you would consider first a mathematical equation that models natural phenomenon. Then you would try to analyze it mathematically and/or numerically so that you could make predictions about how the physical phenomenon will behave in various circumstances. In this project, you would learn a modeling process using given data and physical facts, learn how to solve a model problem using mathematical technique, learn the computer programming necessary to simulate the model problem, and eventually see how mathematicians analyze real-world problems.  This is a great opportunity for you who may be interested in seeking employment at places like Dahlgren.

If this sounds interesting to you, please do not hesitate to contact me to discuss it further. If you know someone who might be interested in this, please let him or her know this.

Undergraduate Research Projects:

    • Catherine Nguyen, Analytical and Numerical Analysis of the SIRS Model, Honors in Mathematics 2024
    • Catherine Nguyen, Analytical Solutions to a SIRS Model, UMW Summer Science Institute 2023
    • Tori Mueller, A Numerical Study of COVID-19 (SIRS Model), UMW Summer Science Institute 2023
      (Tori was the 2nd place winner for the poster presentation)
    • Caitlin Holt, A Numerical Study of the SEIQR Model for COVID-19, Honors in Mathematics 2021
    • Trevor Drinkwater, Analytical and Numerical Analysis of the SEIRP Model for COVID-19, UMW Summer Science Institute 2021
    • Caitlin Holt, A Numerical Study of COVID-19 using the SVIR Model, UMW Summer Science Institute 2021
    • Amy Creel, The $latex T, T^*, V_I, V_{NI}$ Model for Human Immunodeficiency Virus Type 1 (HIV-1) Dynamics, Honors in Mathematics 2020
    • Makayla Ferrell, Analysis of the Deterministic SIV Model for HIV, UMW Summer Science Institute 2019
    • Emily MacIndoe, Analysis of Deterministic and Stochastic HIV Models, Honors in Mathematics 2019
    • Amy Creel, A Numerical Analysis of the SIV Model for HIV Infection, UMW Summer Science Institute 2018
    • Emily MacIndoe, Analytical Solutions of the HIV Model, UMW Summer Science Institute 2018
    • Rachelle Dambrose, Algorithms to Approximate Solutions of Poisson’s Equation in Two and Three Dimensions, Honors in Mathematics 2017
    • Rachelle Dambrose, Numerical Approximations of Poisson’s Equation, UMW Summer Science Institute 2016 (Rachelle was the 1st place winner for the oral presentation)
    • Aaron Thomas, Mathematical Solution to Poisson’s Equation, UMW Summer Science Institute 2016
    • Casey Howren, The SIR Model  for Evaluating the Impact of Epidemics on a Population, Honors in Mathematics 2014
    • Casey Howren, The SIR Model  for Evaluating the Impact of Epidemics on a Population, UMW Summer Science Institute 2013
    • Morgan Brown, Numerical Approximations to the One- and Two-Dimensional Wave Equations, Honors in Mathematics 2013
    • Kathryn Dillinger, Analysis of the Heat Equation with a Heat Source Term, Honors in Mathematics 2013
    • Peter Slattery, Analytical Approaches to the Wave Equation, Honors in Mathematics 2013
    • Morgan Brown, How to Win Every Time, UMW Summer Science Institute 2012
    • Peter Slattery, Brave the Wave, UMW Summer Science Institute 2012
    • Rebecca Presor, Black-Scholes Option Pricing Model: Analysis, Approximations, and Applications, Honors in Mathematics 2012
    • Teresa Yao, The Diffusion of a Chemical Pollutant Modeled by a Fourier Series, Honors in Mathematics 2012
    • Kathryn Dillinger, Profiting with Options Using the Black-Scholes Equation, UMW Summer Science Institute 2011
    • Rebecca Presor, Mathematical Analysis of Option Pricing, UMW Summer Science Institute 2011
    • Erin Strange, Computational Models of the Diffusion Equation, Honors in Mathematics 2011
    • Kathryn Christian, Mathematical and Numerical Solutions for a Heat Conduction Model, Honors in Mathematics 2011
    • Erin Strange, On Numerical Models of Chemical Pollutant Diffusion, UMW Summer Science Institute 2010
    • Teresa Yao, Concentration of a Chemical Pollutant Modeled by a Fourier Series, UMW Summer Science Institute 2010
    • Elizabeth Bernat, Analysis of Temperature Change Using a Mathematical Model, Honors in Mathematics 2010
    • Kathryn Christian, An Exact Solution to Laplace’s Equation Inside a Rectangle, UMW Summer Science Institute 2009
    • Elizabeth Bernat, Numerical Estimates of Temperature Changes Using the Finite Difference Method, UMW Summer Science Institute 2009

    Undergraduate Publications:

    • Amy Creel, Analytical Solution of the $latex T, T^*, V_I, V_{NI}$ Model for HIV-1 Dynamics, SIAM Undergraduate Research Online Journal, Vol. 14, pp 567 – 584, 2021
    • Emily MacIndoe, Analytical Solutions of the Susceptible-Infected-Virus (SIV) Model, SIAM Undergraduate Research Online Journal, Vol. 12, pp 154 – 166, 2019
    • Ray Dambrose, Algorithms to Approximate Solutions of Poisson’s Equation in Three Dimensions, Rose-Hulman Undergraduate Mathematics Journal, Vol. 20, Iss. 1, Article 2, 2019
    • Morgan M. Brown, Identifying a Coefficient Matrix for Numerical Approximations to the Wave Equation in Two Dimensions, Rose-Hulman Undergraduate Math Journal, Vol. 16, Issue 1, pp 152 – 166, 2015
    • Kathryn E. Christian, Polynomial Approximations of Laplace’s equation, in preprint
    • Erin L. Strange, On Numerical Models of the Diffusion Equation, in preprint
    • Elizabeth M. Bernat, Analysis of Temperature Change Using a Mathematical Model, in preprint

    Undergraduate Presentations:

    • Catherine Nguyen, Analytical Solutions to a SIRS Model, at UMW Summer Science Institute 2023
    • Tori Mueller, A Numerical Study of COVID-19 (SIRS Model), at UMW Summer Science Institute 2023 (Tori was the 2nd place winner for the poster presentation)
    • Caitlin Holt, A Numerical Study of the SEIQR Model for COVID-19, at the Shenandoah Undergraduate Mathematics and Statistics Conference at James Madison University (virtual), December 4, 2021
    • Trevor Drinkwater, Analytical and Numerical Analysis of the SEIRP Model for COVID-19, at UMW Summer Science Institute 2021
    • Caitlin Holt, A Numerical Study of COVID-19 using the SVIR Model (poster presentation), at UMW Summer Science Institute 2021
    • Amy Creel, Deterministic and Stochastic Models for HIV-1 Dynamics (poster presentation) , at UMW Student Research and Creativity Symposium, April 23-24, 2020
    • Makayla Ferrell, Analysis of the Deterministic SIV Model for HIV (poster presentation), at UMW Summer Science Institute 2019
    • Emily MacIndoe, Analysis of Deterministic and Stochastic HIV Models, at UMW Student Research and Creativity Symposium, April 26, 2019
    • Amy Creel, A Numerical Analysis of the SIV Model for HIV Infection, at the Shenandoah Undergraduate Mathematics and Statistics Conference at James Madison University in Harrisonburg, VA, October 13, 2018
    • Amy Creel, A Numerical Analysis of the SIV Model for HIV Infection (poster presentation), at UMW Summer Science Institute 2018
    • Emily MacIndoe, Analytical Solutions of the HIV Model, at UMW Summer Science Institute 2018
    • Rachelle Dambros, Three-Dimensional Approximations of Poisson’s Equation, at UMW Student Research and Creativity Symposium, April 28, 2017
    • Rachelle Dambrose, Numerical Approximations of Poisson’s Equation, at the Shenandoah Undergraduate Mathematics and Statistics Conference at James Madison University in Harrisonburg, VA, September 24, 2016
    • Aaron Thomas, Mathematical Solution to Poisson’s Equation, at the Shenandoah Undergraduate Mathematics and Statistics Conference at James Madison University in Harrisonburg, VA, September 24, 2016
    • Rachelle Dambrose, Numerical Approximations of Poisson’s Equation, at UMW Summer Science Institute 2016 (Rachelle was the 1st place winner for the oral presentation)
    • Casey Howren, A Numerical Analysis of the SIR Model for Modeling Epidemics, at the Joint Mathematics Meetings, Baltimore, MD, January 14, 2014
    • Casey Howren, The SIR Model  for Evaluating the Impact of Epidemics on a Population, at UMW Summer Science Institute 2013
    • Morgan Brown, Numerical Approximations to the One- and Two-Dimensional Wave Equations, at UMW Student Research and Creativity Symposium, April 26, 2013
    • Kathryn Dillinger, Analysis of the Heat Equation with a Heat Source Term, at UMW Student Research and Creativity Symposium, April 26, 2013
    • Morgan Brown, How to Win Every Time, at the Shenandoah Undergraduate Mathematics and Statistics Conference at James Madison University in Harrisonburg, VA, September 29, 2012
    • Peter Slattery, The Wave Equation in One Dimension (poster presentation), at the Shenandoah Undergraduate Mathematics and Statistics Conference at James Madison University in Harrisonburg, VA, September 29, 2012
    • Morgan Brown, How to Win Every Time, at UMW Summer Science Institute 2012
    • Peter Slattery, Brave the Wave (poster presentation), at UMW Summer Science Institute 2012
    • Rebecca Presor, Black-Scholes Option Pricing Model: Analysis, Approximations, and Applications, at UMW Student Research and Creativity Symposium, April 17, 2012
    • Kathryn Dillinger and Rebecca Presor, Black-Scholes Option Pricing Model: Analysis, Approximations, and Applications (poster presentation), at the Joint Mathematics Meetings, Boston, MA, January 6, 2012
    • Kathryn Dillinger, Profiting with Options Using the Black-Scholes Equation (poster presentation), at the Shenandoah Undergraduate Mathematics and Statistics Conference at James Madison University in Harrisonburg, VA, October 22, 2011 (Katie won second place for her poster at this conference)
    • Rebecca Presor, Black-Scholes Option Pricing Model: Analysis, Approximations, and Applications at the Shenandoah Undergraduate Mathematics and Statistics Conference at James Madison University in Harrisonburg, VA, October 22, 2011
    • Kathryn Dillinger, Profiting with Options Using the Black-Scholes Equation (poster presentation), at UMW Summer Science Institute 2011
    • Rebecca Presor, Mathematical Analysis of Option Pricing, at UMW Summer Science Institute 2011
    • Kathryn Christian, Mathematical and Numerical Solutions for a Heat Conduction Model, at UMW Student Research and Creativity Symposium, April 19, 2011
    • Kathryn Christian, Mathematical and Numerical Solutions for a Heat Conduction Model, at the MD-DC-VA Section Meeting of the Mathematical Association of America at Randolph-Macon College, April 16, 2011
    • Erin Strange and Teresa Yao, Chemical Pollutant Diffusion Model: Analysis and Approximations (poster presentation), at the Joint Mathematics Meetings, New Orleans, LA, January 8, 2011
    • Kathryn Christian, Polynomial Approximations of a Heat Conduction Model (poster presentation), at the Joint Mathematics Meetings, New Orleans, LA, January 8, 2011
    • Erin Strange, On Numerical Models of Chemical Pollutant Diffusion (poster presentation), at the Shenandoah Undergraduate Mathematics and Statistics Conference at James Madison University in Harrisonburg, VA, October 23, 2010
    • Teresa Yao, Concentration of a Chemical Pollutant Modeled by a Fourier Series, at the Shenandoah Undergraduate Mathematics and Statistics Conference at James Madison University in Harrisonburg, VA, October 23, 2010
    • Erin Strange, On Numerical Models of Chemical Pollutant Diffusion (poster presentation), at UMW Summer Science Institute, July 2010
    • Teresa Yao, Concentration of a Chemical Pollutant Modeled by a Fourier Series, at  UMW Summer Science Institute, July 2010
    • Elizabeth Bernat, Analysis of Temperature Change Using a Mathematical Model, at UMW Student Research and Creative Day, April 2010
    • Kathryn Christian, Solution to Laplace’s Equation in Modeling Heat Conduction (poster presentation), at the Shenandoah Undergraduate Mathematics and Statistics Conference at James Madison University in Harrisonburg, VA, October 3, 2009
    • Elizabeth Bernat, Numerical Estimates of Temperature Changes Using the Finite Difference Method, at the Shenandoah Undergraduate Mathematics and Statistics Conference at James Madison University in Harrisonburg, VA, October 3, 2009
    • Elizabeth Bernat and Kathryn Christian, Laplace’s Equation: A Mathematical and Computational Analysis,  at the Annual Meeting of the Mathematical Association of America in Portland, OR, August 6, 2009
    • Kathryn Christian, An Exact Solution to Laplace’s Equation Inside a Rectangle (poster presentation), at UMW Summer Science Institute, July 2009
    • Elizabeth Bernat, Numerical Estimates of Temperature Changes Using the Finite Difference Method, at UMW Summer Science Institute, July 2009