|
Topic |
Information/Reference Article(s) and/or
Book(s) |
Mathematics Background Needed |
|
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 MATH271: Applied Statistics |
|
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 (MATH270)
Preferred: Calculus-based Probability and Statistics (MATH371) |
|
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. |