Welcome to the M³ Webpage!!!

M³: Mentoring for Minorities in Mathematics is part of the National Research Experience for Undergraduates Program (NREUP) funded by the Mathematical Association of America (MAA), the National Science Foundation Division of Mathematical Sciences (NSF-DMS), the National Security Agency (NSA), and the Moody's Foundation (they ceased funding this project in 2009). We have also received internal funding from the College of Science and Math, Department of Mathematics and Statistics, and the Office for Diversity at James Madison University.

The topic for Summer 2009 is Mancala-like games.  We will be in session from May 11^th to June 19^th.  Drs. Thelwell and Tongen will mentor the following four students  for this research project:

• Rex Ford
• David Melendez
• Juan Carlos Ortega
• Zurisadai Pena
• Melinda Vergara

Project Summary:
The focus of the research project is Mancala, an ancient family of board games popular in Africa and Asia. While there are many possible rule variants, this 'sowing' type game is based on moving stone seeds from one container to others according to prescribed deterministic rules. Play can be surprisingly involved, with a large number of legal moves possible each turn. Surprisingly, there has been little published mathematical research of this very interesting game. John Conway developed his own variant, 'Sowing,' which led to some simple mathematical language and structure which could be further developed. The primary research question for this project is "Is there an optimal strategy, against which no other competing strategy can win." Mancala has been played for more than ten thousand years, suggesting that no obvious optimal strategy exists. However, with M³ mathematicians, we propose to do the following:

• Change the number of containers and number of seeds to see when an optimal strategy exists. For instance, with four total containers and one seed initially in each container, the first player has an optimal strategy, against which the other player cannot win.
• Explore and implement various rule sets and strategies numerically to build intuition.
• Use a combinatorial approach to discuss the number of possible moves and strategies.
• Consider the game as a discrete dynamical system. What type of analysis is possible using this abstraction?

Final Presentation - Friday, June 19^th, 2009 at 2:30 pm  in Roop 103


The topic for Summer 2008 was Dynamical Systems and Chaos.  We will be in session from May 5^th to June 13^th.  Drs. Thelwell and Tongen will mentor the following four students  for this research project:

• Jan Herburt-Hewell (hand in pocket)
• Michael Dankwa (baseball cap)
• Lianne Louizou (long hair)
• Juan Carlos Ortega (colorful shirt)

Project Summary:
During the first two days of the summer program, the students built a chaotic waterwheel (see picture to the right).  They then proceeded to learn dynamical systems so they could better understand, mathematically, the behavior of the wheel they built.  They are next going to build the first ever choatic sandwheel (at least to our knowledge) and derive the equations that govern the behavior of the new system and answer questions like:
Do you still see chaotic behavior?
Do you still see periodic behavior?
What is the qualitative behavior of the sand wheel?
What is the quantitative behavior the sand wheel?

Final Presentation - Friday, June 13^th, 2008 at 1:30 pm  in Roop 103

You can see the experimental progress that was made by examining the following two movies: Water and Sand (you will need quicktime to view these movies).


The topic for Summer 2007 was Discrete Mathematics with applications to Biology.  We were in session from May 14^th to June 22^nd.  The following four students were the primary investigators for this research:

• Charell Wingfield (left of James Madison)
• Michael Frempong (right of James Madison
• Jan Herburt-Hewell (behind James Madison)
• Michael Dankwa (in front of  James Madison)

Project Summary:

During the first two weeks of the M³ program, the participants will be introduced to discrete equations focusing on both analysis and numerical simulation. The director will present numerous open questions and ask the students to choose a couple on which to concentrate. The entire program (participants and director) will work together to solve the open questions pertaining to two-gender population models.

During the third and fourth week of this research experience, the students will perform a biological investigation of mate choice by male Betta splendens fish using video playback of females.  In this experiment, the students will determine whether males spend more time with and direct more courtship behaviors to a female with vertical lines than to a female without vertical lines.  This experiment will be in addition to the open questions started during the first two weeks.

During the final two weeks of this research experience, the students will conclude their research along with developing a mathematical model of mate choice in Betta splendens. The students will give a 50 minute presentation of their research results on the last day of the program.  After the conclusion of the research experience, the students will disseminate their results in July at the JMU Biology REU poster session, a poster and oral presentation in October at the Shenandoah Undergraduate Mathematics and Statistics Conference, and the director will be giving an oral presentation of the results in August at the Society for Mathematical Biology's annual meeting.

Final Presentation - Friday, June 22^nd, 2007 at 1:30 pm in Roop 103

• The influence of Female-Male Interactions on Offspring Sex Selection, Michael Dankwa and Jan Herburt-Hewell
• Infectious Disease Modeling of Human Papillomavirus, Michael Fremprong and Charell Wingfield

Click here to go to Anthony Tongen's webpage.

Thanks again to MAA, NSF-DMS, NSA, and Moody for their generous support of this project!! 

edited on 5/24/07