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 topics for Summer 2012 are one-player and two-player sowing games. We will be in session from May 14th to June 29th. John Johnson and Anthony Tongen mentored the following students:Picture of Summer 2012 students

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:
Final Presentation - Thursday, June 21st, 2012 at 10:00 am in Roop 103

The topic for Summer 2011 is single player Mancala-type games. We will be in session from May 16th to June 24th. John Johnson and Anthony Tongen mentored the following students:Picture of Summer 2011 students

Project Summary:

Single player Mancala-type games
Mancala is an ancient family of board games popular in Africa and Asia.While there are many 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; in fact, last summer's M3 students created an annotated bibliography of only 11 articles dealing with Mancala-type games, including computer science articles which were exhaustive in more than one way. Therefore, with M3 mathematicians, we propose to do the following:
Final Presentation - Friday, June 24th, 2011 at 1:30 pm in Roop 103


The two topics for Summer 2010 are single player Mancala-type games and PS (Parker-Sochacki/Power Series) method. We will be in session from May 17th to June 25th. Drs. Warne and Tongen will mentor the first two students in developing a Matlab GUI that solves differential equations using the PS method and Drs. Taalman and Tongen will lead the next three students in studying single player Mancala-type games:Picture of Summer 2009 students

Project Summaries:

PS Method
About 45 years ago, Fehlberg (1964) speculated that the power series method could be used to solve initial valued ordinary differential equation (IV ODE) problems with a level of accuracy that could not be achieved by other methods. About 13 years ago, a team of researchers at JMU took the first steps toward demonstrating that this is, indeed, true. Specifically, Parker and Sochacki (1996) demonstrated that power series can be used in a modified version of Picard's method and that this Parker-Sochacki/Power Series (PS) method is a practical, efficient and accurate algorithm for solving IV ODE problems.

The PS method, in addition to solving IV ODEs, has been used to solve integral-differential equations, find roots, and solve numerous application-oriented problems. Nonetheless, to date, the full potential of the PS method has not been realized because of the lack of a software tool that is accessible to the broader research community interested in these kinds of problems. Co-PI Warne has been a part of the JMU team using the PS method for the last ten years and he is at the forefront of innovation with the method. The second research group proposes to do the following:

Single player Mancala-type games
Mancala is an ancient family of board games popular in Africa and Asia. While there are many 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; in fact, last summer's M3 students created an annotated bibliography of only 11 articles dealing with Mancala-type games, including computer science articles which were exhaustive in more than one way. Therefore, with M3 mathematicians, we propose to do the following:
Final Presentation - Friday, June 25th, 2010 at 1:30 pm in Roop 103

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

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:
Final Presentation - Friday, June 19th, 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 5th to June 13th.  Drs. Thelwell and Tongen will mentor the following four students  for this research project:Picture of Summer 2008 students

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 13th, 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 14th to June 22nd.  The following four students were the primary investigators for this research:Picture of the four students 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 22nd, 2007 at 1:30 pm in Roop 103


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