Below is a list of topics which I think
would be interesting for undergraduate research projects. For each topic I
have also included some information and possibly 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.
The picture to your right is of Dr. P. (my hubby) and me on a sunset sailing cruise off the coast of Okracoke Island on the Outer Banks, June 2010.
List of Topics (in no particular order)
|
Topic |
Information/Reference Article(s) and/or Book(s) |
Mathematics Background Needed |
| Dynamical Systems Applied to Social Justice Problems | This is a hot new field! The models are used not so much for prediction as describing behavior. Check out this recent dissertation from Alexander Gutfraind (Cornell) on Mathematical Terrorism. | MATH361 - Ordinary Differential Equations |
| Converting Ordinal Scale Measurement Data to Interval/Ration Scale |
A recent paper develops an algorithm for
this conversion. Are there better algorithms? When would it
make sense to do this? Granberg-Rademacker, J. Scott, "An Algorithm for Converting Ordinal Scale Measurement Data to Interval/Ratio Scale," Educational and Psychological Measurement, 70(1) 74-90, SAGE Publications, 2010. http://epm.sagepub.com |
Minimally MATH301: Applied Statistics. Knowing how to program would also be very useful. |
| Regression Analysis Question | It is also well known that if the sample size is too large than it is very possible to get results that are significant statistically but not significant in a practical sense. How large is "too large" for regression? | Minimally MATH301: Applied Statistics. Knowing how to program would also be very useful. |
| Fuzzy Logic | "Undecidability in Fuzzy Logic" in the UMAP Journal, 30.4 (2010) | MATH or CMSC 300 or an equivalent course on logic and reasoning. |
| Statistical Analysis of an Interesting Data Set | The data set should be part of a research project for which statistical analysis is needed. Interdisciplinary projects are great! As a "statistician" on the project you will need to learn enough about the project to analyze and interpret your results. | As much statistics as possible. Minimally MATH301: Applied Statistics |
|
Modeling Diseases (including a Zombie Apocalypse) |
1. "Epidemic Models for SARS and Measles," by Edward Rozema, in The College Mathematics Journal, Vol. 38, No. 4, Sept. 2007, p 246 - 259. 2. "When Zombies Attack!: Mathematical Modelling of an Outbreak of Zombie Infection," by Munz, Huea, Imad, and Smith, Infectious Disease Modelling Research Progress, ISBN 978-1-60741-347-9, Nova Science Publishers, 2009. |
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 Probability and Statistics (MATH171) Preferred: Calculus-based Probability and Statistics (MATH270) |
| 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. |