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)
|
| 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.