Analysis of covariance is a technique that combines regression and analysis
of variance. It is often used with randomized block design to reduce the
variance of the error terms in the general linear model. Parametric and
non-parametric tests can be used with analysis of covariance to test a
null hypothesis. One example of a non-parametric test that will be discussed
is a rank transformation test. In order to check these different tests,
Monte Carlo simulation is used to generate random numbers from various
types of distributions, such as, normal, exponential, unifrom, lognormal,
and Cauchy. Finally, testing results will be presented.
Kimberly Jordan - Mathematics Anxiety
Gender Stereotypes reguarding anxiety towards mathematics will be presented.
In addition, research related to female susceptibility to math anxiety,
avoidance to math related careers as well as student's attitudes and beliefs
will be discussed. Finally, methods of identifying, reducing and preventing
this anxiety will be given.
Jerry Priddy - A Linear Programming Formulation to Optimize
Sawmill Operations
A linear programming formulation to optimize operations at a medium-sized
sawmill is presented. Results from sensitivity analysis and parametric
programming are used to analyze input data and recommendations for their
increase/decrease are given.
Alan B. Shettel - Bernoulli Numbers in Series Summations
The Bernoulli numbers first appeared in print in 1713 in Ars Conjectandi,
a posthumous work of James Bernoulli. Bernoulli used this sequence of rationals
to obtain an expression in closed form for the general sum: 1^p+2^p+...+n^p,
where n,p are integers -- a result that seems often overlooked today. Several
applications are examined.
Kendra Sinopoli - Re-marking Dice
The probability of rolling a two on a standard pair of dice is 1/36; the
probability of rolling a three is 2/36, and so on. Is it possible to re-mark
a pair of dice so that the probability of throwing each number from one
through twelve is the same?
A set of eight initial basic solutions will be derived from which all other
solutions can be obtained. The problem is then described and discussed
with a formulation in terms of modular arithmetic. Finally, abstract properties
and patterns will be presented.
Jason M. Spangler - Fault Tolerance in Parallel Processing
Parallel processing is the use of mutiple processors to perform concurrent
operations. Fault tolerance, the ability for a system to withstand faults,
is added to a parallel processor scheme because as the number of processors
increases, the mean time between failures of connections between the processors
decreases. Many fault tolerant schemes tolerate one fault on a hypercube.
My project consisted of verifying several cases of a new scheme developed
by Youngstown State University professor Dr. Shih and Kent State University
professor Dr. Batcher, which tolerates multiple faults on a hypercube network.
Christina T. Tsiaparas - A discussion of Simple Continued Fractions and
Their Applications
Continued fractions and their applications are interesting topics that
are usually covered in most Elementary Number Theory courses. In this talk
we will briefly define what a simple continued fraction is, and look at
examples od simple continued fractions and their convergents. We will also
examine how these convergents can be used to find rational approximations
to an irrational number, such as Pi and how they can be used to find integral
solutions to linear Diophantine equations in two unknowns.
Lisa White - Applications of Fractals in Geology and Geophysics
Fractals can be used to study many earth processes. One of these processes
is crustal deformation. Crustal deformation takes place at the boundaries
between surface plates as they move. Although seemingly complex, crustal
deformation will be shown to follow fractal statistics in many ways. These
include frequency-magnitude statistics of earthquakes and a fractal distribution
of faults.
