2009 Hendrix-Rhodes-Sewanee Undergraduate Symposium

32nd annual conference, April 17–18, 2009, at Hendrix College

One of the longest-running undergraduate research conferences in mathematics or computer science, the H-R-S Symposium rotates annually between three liberal arts colleges: Rhodes, Hendrix, and Sewanee. Hendrix College is the host in 2009. [History]


(click for larger map)

Friday, April 17

5:00pm-6:30pm

Dinner in Murphy House (#16 on map)

(best parking is behind Bailey Library (#2))

6:30pm-7:30pm

Welcoming address and invited lecture in Mills Center B (#13)

Journeys Down Short Paths
Kevin Hutson, Asst Professor, Furman University, South Carolina
(Hendrix alum and H-R-S student presenter in 1993 and 1994)

In the field of optimization, the problem of finding shortest paths in a network has been well-studied due to the abundance of applications that either rely on the shortest path problem directly or as a subproblem of a larger problem. In this talk, we discuss the shortest path problem, its optimality conditions, and some methods for finding such a path. We then focus on some non-standard applications that rely on finding shortest paths in order to achieve a solution efficiently. Two of these applications have come up in the context of some of my experiences with undergraduates doing research, and we highlight these. We end the talk by discussing finding short paths in the context of stochastic networks. Specifically, we study the problem of finding a path P that combines in a reasonable way the mean m(P) and variance v(P) of its length.

7:30pm–Activities for student guests

Saturday, April 18

7:30am-8:30am Breakfast for students in Hulen Cafeteria (#17)
8:30am-11:30am

Student talks in M C Reynolds 315 (#14)

8:30am Four-Dimensional Tetris
Don Bennett, Hendrix College
8:55am Mathematically Generated Fife Tunes
Annie Tracy, University of the South
9:20am Adaptive Artificial Intelligence for the Game of Checkers
Justin Whorton, Hendrix College
9:45am Discrete Complex Analysis on Triangular Graphs
Henry Wang, Hendrix College
refreshment break as time allows
10:15am Creating Fuzzy Logic Programs for Robot Controllers
Brett Geren and Whitney Maguffee, Hendrix College
10:40am Cantor Sets of Julia Sets
John Schulte, Rhodes College
11:05am Simulation and Comparison of Traffic Control Algorithms
Christopher Schulze, Hendrix College
11:30am-12:30pm Lunch available in Hulen Cafeteria (#17)

Selected student abstracts

Four-Dimensional Tetris, Don Bennett

The goal of this project is to provide a tool that any person, with or without a strong mathematical background, could use to quickly gain an understanding of what the fourth dimension is and how it works. The theory is that people learn complex sets of rules much faster when they are associated with goals. The programming portion of my project is a game that requires the player to play by the rules of linear algebra in four dimensions, thus teaching the player to learn to predict how an object in this space will behave.

Creating Fuzzy Logic Programs for Robot Controllers, Brett Geren and Whitney Maguffee

In fuzzy logic, as opposed to boolean logic, a variable can take on a range of truth values as opposed to just true and false. How "true" a variable is can then be used to determine the action of a device. The application of fuzzy logic to robotics can produce pleasing results since the robot's actions seem intuitive to humans. An excellent example of this is turning a corner with a smooth parabolic motion as opposed to a sharp right turn.

The goal of this project was to develop a program that allowed a basic user to input information and have a fuzzy logic based program for a robot controller be output. The program should preferably use a GUI for the sake of simplicity and usability. The program should also be capable of loading the programs it creates onto the robot.

Simulation and Comparison of Traffic Control Algorithms, Christopher Schulze

In order to test the efficiencies of a variety of traffic control algorithms, I have created a simulation of a city block, populated with simulated automobiles following randomly determined routes. Utilizing this simulation, I simulated the traffic control algorithms in question for predetermined metrics in order to gauge efficiency.

Mathematically Generated Fife Tunes, Annie Tracy

Trying completely to reduce musical composition to a simple mathematical algorithm may be impossible, but mathematics undeniably plays a major role in writing music. To investigate the role of mathematics in musical composition, we created a model that randomly generates music predominantly using a Markov chain. A Markov chain is a set of possible states and the probabilities that a given state will lead to any of the others. For this model, the states were a particular note (or sequence of notes) extracted from a data set of about 200 fife tunes. Using the probabilities as weights, the model then randomly generates a new, fife-tune-like song.

Adaptive Artificial Intelligence for the Game of Checkers, Justin Whorton

With the proper programming, computers can often play board games such as chess or checkers at a skill level beyond the average human player. So, the question arises: How can an artificial intelligence be adapted to seem to naturally match the skill level of its current opponent? Using an artificial intelligence designed to play checkers, this project explores three methods to adapt such an artificial intelligence to the skill of its current opponent.

Back to conference description and history.