Undergraduate Research Opportunities


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Below is a list of topics which I think would be interesting for undergraduate research projects.   For each topic I have also included an article or book as a starting point.  Please contact me if you would like to do research on any of these topics or if you have another topic of interest!   Click here for a list of presentations and papers from students who have done undergraduate research with me.

List of Topics (in no particular order)

Topic

Reference Article(s) and/or Book(s)

Mathematics Background Needed

Modeling Diseases

"Epidemic Models for SARS and Measles," by Edward Rozema, in The College Mathematics Journal, Vol. 38, No. 4, Sept. 2007, p 246 - 259.

Minimal:  Calculus II

Preferred:  Differential Equations

Counterintuitive Probabilities in Coin Tossing (and other games?)

"Penney Ante:  Counterintuitive Probabilities in Coin Tossing," The UMAP Journal, Winter 2007, Vol. 28, No. 4, p 503 - 528.

Minimal:  Basic probability concepts (such as those in MATH270).  It would also be nice to be able to program in order to estimate probabilities empirically.

Preferred:  Calculus-based Probability and Statistics

Fractals

1.  Fractals Everywhere, Michael Barnsley, Academic Press, Inc., 1988

2.  “Using Fractals to Motivate Linear Algebra,” UMAP Module 787, in the ILAP Modules 2004-05, published by COMAP

3.  "A Fractal Made of Golden Sets," Mathematics Magazine, Vol. 82, No. 4, October, 2009, pp. 243 - 254.

Minimal:  Linear Algebra and Foundations of Mathematics

Preferred:  Multivariable Calculus and Advanced Calculus (aka Real Analysis)

Math History:  The Normal Distribution "The Evolution of the Normal Distribution," Saul Stahl, Mathematics Magazine, Vol. 79, No. 2, April 2006.

Minimal:  Introductory Level Statistics

Preferred:  Calculus-based Probability and Statistics

Genomics: Data Analysis of DNA Microarrays Exploration and Analysis of DNA Microarray and Protein Array Data,
Dhammika Amaratunga, Javier Cabrera, John Wiley & Sons, Inc, 2003
ISBN: 0-471-27398-8

Statistics (preferably a calculus-based probability and statistics sequence), ability to quickly learn and use software.

Variational Inequalities (Finite Dimensional)

1.  “Variational Inequalities: One-Stop Shopping for Optima and Equilibria,” by Steve McKelvey, in the On Jargon section of The UMAP Journal Vol. 27, No. 1, 2006

2.  Existence Results for Generalized Variational Inequalities, M. Leigh Lunsford, Ph.D. Dissertation, University of Alabama in Huntsville, 1995.

Familiarity with vectors and matrices as covered in an introductory linear algebra class and vector fields and gradients as covered in multivariable calculus.


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