2000 Mathfest: UCLA
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YSU PME Student Presentations:
Katie Fleming - What Does a 40% Chance of Rain Really Mean?
Weather is around us every day. Rain, in
particular, affects many aspects of our lives. In this talk I will look
at the different aspects of weather and translate the percentage of rain
into what it really means to find out if the weathermen and -women are
100% right.
David Gerberry - Mark McGwire Meets Mathematicians
In recent past seasons of major league baseball, the outburst of offense
has definitely added excitement to the national pastime. However, many
"old school" fans have been left to wonder what happened to the days of
the pitchers duel. Using statistical methods to examine the offensive trend,
we can hope to shed some light on the phenomenon and its possible causes.
Sarah Grove - The Best Seat in the House
Movies, plays, and concerts are wonderful to see. The better
your seat, however, the more you enjoy the experience. No one likes to
watch movies at an awkward viewing angle. Logically, the maximized viewing
angle should encompass the entire screen or stage. Mathematical techniques
will be presented to determine which seat is the best in the house.
Sara LaLumia - Convergence of Infinite Series
~~ Best Talk Award ~~
In 1743, Leonhard Euler announced that he had
found the sum of the series 1 + (1/4)+ (1/9) +...+(1/k^2)+...
This problem had baffled mathematicians for over a hundred years,
and Euler's solution, (Pi2)/6, was quite a surprise. Euler went
on to find the sums of similar series with k raised to different even powers.
However he was unable to solve the problem with k raised to an odd power.
Even today this remains an unsolved problem. I will discuss the methods
used by Euler to find the sum of (1/k2) and present some approximations
for the sum of (1/k3).
Joel Lepak - Searching for a Perfect Voting System
~~ Best Talk Award ~~
We have all been taught that the best way to decide things
is to let everyone vote, but how fair is voting? Our voting methods all
have many flaws, some of which allow election results to be altered by
devious politicians. Is there a better way for society to make choices?
Specific examples, including this year's London mayoral election, will
be used to illustrate various flaws and a voting system that avoids some
of the major flaws will be derived.
Jodie Matulja - Statistical Analysis of Mastery Learning
Mastery Learning is a teaching technique that promotes
student learning by letting each student rework tests to reclaim missed
points. There is a considerable amount of extra grading involved for teachers
who implement Mastery Learning. This project will compare information from
two linear algebra classes that were taught using Mastery Learning to ascertain
if it is a worthwhile classroom technique.
Teresa Selee - Stolz' Theorem: L'Hopital's Rule for Sequences
Approximately 100 years ago, Otto Stolz proved
an interesting theorem that says that for any two sequences an and
bn, such that bn increases to infinity,
limn->infinity(an/bn)
= limn->infinity(an-an-1)/(bn-bn-1),
provided the limit on the right side exists or equals infinity. A brief
introduction to the origin of the theorem will be given. Applications and
examples will be shown to illustrate the usefulness of this simple, yet
often forgotten theorem.
Robert Shuttleworth - Virtual Visualizations
The spread of smog and other airborne contaminants is a growing problem
in the world. To effectively analyze these problems, scientists create
visualizations as an easy means to three dimensionally organize and view
the data in question. This presentation will showcase the mathematics behind
creating these visualizations as well as how these visualizations are used
in the work of both Oak Ridge National Labs (ORNL) and the Defense Intelligence
Agency (DIA).
Ryan Siskind - Separated at Birth?
Two equations walking down the street bump into each other. As
the two equations look each other over, they don't notice very much in
common, but there is an eerie connection between the two. It is almost
as if they are the same. Visually the two equations look very different,
but they are both used to determine differentiability in multivariable
calculus. I will prove that they are both in fact equivalent, and explain
why different definitions are given.
John Slanina - A Risky Algorithm: The Relative
Risk vs. the Odds Ratio
In medical statistical analysis, the odds ratio is most often used to predict
the risk for health outcomes given exposure to a disease. Because the odds
ratio and its respective confidence intervals are easy to compute, statistical
software packages such as SPSS and SAS use this indicator as their method
to compute risk. In some health studies however, the incidence of disease
is high and the odds ratio's estimate of risk is erroneous, sometimes by
several magnitudes. This presentation will focus on creating an algorithm
to calculate the correct relative risk values and computationally challenging
confidence intervals from the given statistical data.
Tom Wakefield - The Irrationality of e and Pi
~~ Best Talk Award ~~
In various areas of mathematics, engineering,
and the physical sciences, e and Pi are important physical constants. Because
of this, the nature of e and Pi interest mathematicians. The irrationality
of these numbers has been verified by various methods of proof. Two such
proofs are examined in this presentation.