Undergraduate Research

2009-2010


The Mathematics of Counter-Terrorism


brittanySSC.JPGThis project involved using graph theory and discrete mathematics to analyze the terrorist cell network in the United States.  The project pinpointed the city that would have the greatest detrimental effect on the national network if the terrorist cells in the city would be shut down.  This information would be useful to Homeland Security in order to know which city they should concentrate their resources and focus.


Student:  Brittany Fanning

Mentor:  Dr. Pam Warton



The Chaotic World of Complex Fractals

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This project involved investigating the relationship between chaos theory, complexity theory, and the beautiful fractals.  Even systems acting chaotically eventually start to form patterns that are actually fractals.  This project then focused on understanding the famous Mandelbrot set.


Student:  Kora Riding

Mentor:  Dr. Pam Warton








2008-2009


Winning Strategies of Monopoly

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This project involved setting up a Markov chain to model all of the nuances of the game of Monopoly which resulted in a large matrix.  Techniques from linear algebra were then applied to determine which properties would be landed on the most.  This project was invited to be written up and submitted for publication to the Pi Mu Epsilon Journal.


Students:  Erica Keene and Danielle Rohal

Mentor:  Dr. Pam Warton





Modeling the Population of the Round Goby in Lake Erie

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This project involved gathering data from several state and federal organizations on the invasive species Round Goby in Lake Erie, as well as data on the more desirable species in the lake.  Techniques from differential equations were used to develop two different models - one showed that the Round Goby could live in harmony with the other species, and the other showed that the Round Goby would take over the lake habitat and force the desirable fish species out.


Students:  Kora Riding and Jeremy Foster

Mentor:  Dr. Pam Warton



2007-2008


Bridging the Gap Between Algebra and Abstract Algebra

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This project investigates the connection between typical high school algebra and group theory.  It takes a historical look at how many topics in group theory were created to determine if a general quintic equation had a general solution.


Students:  Ryan McDannell and Erica Keene

Mentor:  Dr. Pam Warton







Symmetries of a Cube

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After investigating symmetries of many two-dimensional objects, it is natural to explore the group created by the symmetries of a cube.  This group along with its cyclic and non-cyclic subgroups are explored, and an isomorphic group is discovered.


Students:  Jeraco Speelman and Kendra Bruns

Mentor:  Dr. Pam Warton