Undergraduate
Student Papers
Session I - Room 205
5:30-5:42 High
Order Approximation of the Soliton Solution of the
Traffic Equation
Jack
Dalton, UMass Dartmouth
Abstract:
The flow of traffic on a one-lane, one-directional highway can be
modeled using a quasilinear partial differential
equation in terms of the density of cars and their speed. In this project, we
use a continuum traffic model to investigate the soliton
solution. Traditionally lower order finite difference approaches have been used
but in this project, we use the spectral method, a high order method. The
numerical results will be compared with the analytic condition for the
existence of the soliton solution.
5:45-5:57 Radial
Basis Function Neural Network Model for Discontinuous Signals
Vincent
Durante, UMass Dartmouth
Abstract: Radial
Basis Functions (RBFs) are widely used for modeling
neural networks as the approximation with RBFs is
flexible for neuron distribution. In this research, RBFs are used to approximate discontinuous input data
points and the empirical relations among the parameters and convergence have
been derived. Correspondingly, an adaptive RBF method has been developed so
that the convergence near the discontinuity is enhanced with the
adaptation.
6:00-6:12 Numerical Analysis
of Difference Equations from
Jessica
Rosen, UMass Dartmouth
Abstract:
The project attempts to solve, numerically, "difference
equations" that arise as a result of quantum theory being applied to
models of cosmology and black holes. The stability and convergence of
difference equations have been analyzed using von Neumann analysis. In
addition, the recently developed high order approximation methods are applied
to the difference equation systems to properly deal with the instabilities
which occur noticeably over time. The evolution of the wave function is
investigated through this analysis.
Session II - Room 202
5:30-5:42 A Scheduling Problem
Candace
Selneck,
Abstract:
This presentation focuses on a common scheduling problem faced by many
colleges every Fall - specifically, how to assign
incoming freshmen to first year seminars according to their preferences and
class size limitations given by the college.
This problem can be formulated as a maximum flow problem from Operations
Research, where the objective is to maximize the number of freshmen assigned to
seminars. We present an algorithm
implemented in MATLAB that constructs an optimal solution to this scheduling
problem. We present numerical results on
real world data
and
conclude the presentation with opportunities for future work.
5:45-5:57 The Game of Go
Benjamin
Harshfield,
Abstract:
In the game of Go, players take turns placing
stones on a 19x19 grid, aiming to surround the largest amount of
territory. Empirical evidence has shown
that the player who moves first, "black",
has a distinct advantage. To balance the
game, white receives "komi" compensation
which is usually between 3 and 7 points.
However, debates still rage about how many points it takes for black and
white to compete on equal footing. By
analyzing over 30,000 professional games, we will ascertain the optimal level
of compensation and any dependence on the skill levels of the players.
6:00-6:12 The Effect of Harvesting on the Peregrine
Falcon Population.
Richard
Ryan,
Abstract: We examined the maximum possible
percentage of harvest for one case study, peregrine falcons. US Fish and Wildlife Services have recently
begun to allow minimal harvesting to peregrine falcons as they are no longer on
the endangered species list. We create a
population projection matrix model that takes into account the fact that the
population date is highly uncertain and analyze the effect of harvesting on the
population taking into account these uncertainties.
6:15-6:25 A Java applet to explain and
demonstrate Markov Chains
William
Day and Joshua Sawyer,
Abstract:
Understanding Markov Chains analytically does not necessarily expose the
behaviors of chains, nor show the fit and elegance of different models.
Moreover, it can be difficult to develop an intuitive understanding of Markov
Chains. In order to develop intuition, demonstrate the efficacy as models, and
to develop understanding of short and long term properties of Markov Chains, we
present a Java applet allowing exploration both visually and numerically. We
present background and some results in an associated website.
Session III - Room 201
5:30-5:42 Fiction and Higher Dimensions
Jessica
Belanger,
Abstract:
Edwin A. Abbott's book, Flatland, reaches far beyond the geometric
perspective of "
5:45-5:57 Olga Alexandrovna Ladyzhenskaya
(1922-2004)
Ruth
Hibbard,
Abstract:
In my recent Differential Equations course I had the opportunity to study the life and
times of Russian mathematician Olga Alexandrovna Ladyzhenskaya. What was life like for an aspiring woman
mathematician during the Stalinist regime from the 1920's - 1950's? What was it like to experience first-hand the fall of the
Iron Curtain? Come and hear of the extraordinary contributions this woman made
in the area of partial differential equations.
Learn more about her
social views, her world-renowned supporters and acquaintances,
and also her broad interests in life.
Perhaps you will be inspired as I was by this woman who continued her
study of higher mathematics until the end of her life at the age of eighty-one.
6:00-6:12 The
Importance of Cantor's Diagonal Argument and Implications for Education
Lucas
Roesler,
Abstract: In this thesis we show the
importance of Georg Cantor's diagonal argument using
the requirement found in Michael Hallett's 'Towards a
Theory of Mathematical Research Programmes.' We will show that Cantor's diagonal argument
was used in the solutions for both Gödel's incompleteness theorem and the
solution of Hilbert's tenth problem.
Thus exhibiting the power and flexibility of Cantor's diagonal argument
and satisfying Hallett's requirement. We also suggest
that because of the importance and innovative nature of Cantor's diagonal
argument the topic should be taught in high school. The counter intuitive and innovative nature
of the diagonal argument would help to stimulate creative thought towards
problem solving and general interest in mathematics.