YSU MathFest 2005 Workshop Titles
- Computer Vision and Image Processing by Andy Chang.
- Some Problem Solving Principles by Jacek Fabyrkowki.
- How to get Poor Quick(ly) by J. Douglas Faires.
- Some "Stressful" Applications of Algebra by Richard Goldthwait.
- Are You In The Zone? by Jay Kerns.
- Moebius Strips and Topology by Roy Mimna.
- Incredible Distances by Zbigniew Piotrowski.
- Iteration of Functions by David Pollack.
- Game Theory by Nathan Ritchey.
- Instant Insanity by Thomas Smotzer.
- Let's Make Deal! by Gary Stanek.
- Continued Fractions by Eric Wingler.
- Growth, Decay and Forensic Science by George Yates.
Descriptions of Workshops
Computer Vision and Image Processing
by Andy Chang, Youngstown State University
How can a computer see things?
Mathematics! Statistics! Matrix! Algebra! That's
right. In fact, with mathematics and statistics, a computer can do lots of
wonderful things that humans cannot do. In this workshop, basic ideas of
computer vision will be introduced, and the spreadsheet software EXCEL will be
used to simulate Computer Vision and Image Processing.
Pre-Workshop Activities
for Computer Vision and Image Processing.
Some Problem Solving Principles
by Jacek Fabrykowski, Youngstown State University
In this workshop we will describe some commonly used heuristic principles,
which offer a variety of potentially successful strategies for solving many
unconventional, nonstandard mathematical problems. Competition level examples will be
provided to illustrate a powerful action of the Invariant Principle, the Box (Pigeonhole)
Principle, and the Extremal Principle. These strategies often reveal the real nature of a problem.
The workshop will be suitable for those students interested in learning challenging problem-solving
strategies.
Warm-up example: Five points are inside a 3 by 4 rectangle. Show that two of them
are at a distance of at most, the square root of 5.
How to get Poor Quick(ly)
by Doug Faires, Youngstown State University
Casinos are popping up everywhere, millions of people are
playing internet poker, and states throughout the country are into
lotteries in a big way. Is there a way for a clever person to make a
quick buck on all this gambling? We will look at a few games and see how
likely you are to get rich in the process. I can't guarantee that you will
make money, but I think I can show you how to lose less!
Some "Stressful" Applications of Algebra
by Richard Goldthwait, Youngstown State University
This workshop is a brief introduction to engineering mechanics.
After discussing Archimede's principle of "moment balance," we will see how this principle
applies to calculating the stress and strain distribution in a beam that is subject to loads
that cause a beam to bend.
After developing an algebraic formula for computing the stresses in a beam that is being
bent under various types of loads, we will test the theory by loading up some simple balsa
wood structures and seeing when they break!
Are You In The Zone?
by Jay Kerns, Youngstown State University
Any American sports fan is likely to have heard a basketball player referred to as a "streak shooter"
or a baseball player referred to as a "streak hitter". Such people are sometimes said to have the
"hot hand" or be "in the zone". Is this phenomenon real? Or could these long streaky sequences be
happening by chance alone? In this workshop, we will investigate some of the models and methods
statisticians use to distinguish
between streaky and random sequences, and we will finally be able to decide: are you in the zone?
Moebius Strips and Topology
by Roy Mimna, Youngstown State University
A Moebius strip is a unilateral surface which also has a single edge.
A fly could crawl over the whole of it without crossing its edge.
There are many exotic surfaces which are studied in the mathematical subject known as topology.
The Moebius strip is known as a two-dimensional manifold.
There are other manifolds which exist in four or more dimensions.
Incredible Distances
by Zbigniew Piotrowksi, Youngstown State University
In this workshop, we will study properties of the distance between points on a
line and in the plane. We will use common-sense to derive some constraints on the notion of distance.
Time permitting, some "exotic" distances in the plane will be introduced.
Iteration of Functions
by David Pollack, Youngstown State University
Please CLICK HERE
for more information.
Game Theory
by Nathan P. Ritchey, Youngstown State University
Although the branch of mathematics known as Game theory was first introduced by John von
Neumann in 1928, it took the movie, “A Beautiful Mind,” which is a story about Nobel Prize
winner John Nash, to bring this powerful subject into public view. Applications of game theory
are quite extensive and can be found in anthropology, communications, social psychology,
economics, politics, business, biology, and philosophy.
In this workshop students will be introduced to game theory and its uses.
In particular, students
will study and play matrix games, develop winning strategies using the ideas of dominance,
saddle points, and the “minimax” principle. Students will also be introduced to
non-cooperative
games and the ideas of John Nash and his “Nash Equilibria,” for which he won
the Nobel Prize
for in 1994.
Pre-Workshop Activities
for Game Theory.
Instant Insanity
by Thomas Smotzer, Youngstown State University
In 1736 Euler proved that the Konigsberg bridge problem had no solution. The citizens of
Konigsberg wanted to know if a person could cross each of the 7 bridges over the Pregal
River exactly once, before returning where they started.
We will also see how the Konigsberg bridge problem relates to the game instant insanity.
Let's Make Deal!
by Gary Stanek, Youngstown State University
In a 1991 edition of her popular newspaper column "Ask Marilyn,"
Marilyn vos Savant responded to a question regarding the probability of
winning the grand prize on the television game show "Let's Make a Deal."
Her answer sparked a nationwide controversy that resulted in hundreds of responses
from readers, some of them mathematicians and other "self-proclaimed experts."
In this workshop we will look at this problem and related probability topics.
Continued Fractions
by Eric Wingler, Youngstown State University
Continued fractions can be used to provide us with good rational approximations
to real numbers. In this workshop we will see how to find the continued fraction
expansion of a rational number and how to approximate a real number with a rational number.
We will also consider infinite continued fractions and periodic continued fractions.
A calculator may be useful for some parts of the workshop, but it is not absolutely necessary.
Growth, Decay and Forensic Science
by George Yates, Youngstown State University
Mathematics has played an important role in advancing epidemiology, genetics, ecology,
physiology and other areas of biology. Workshop participants will explore the dynamics of
population growth and the spread of deadly diseases.
Several activities will be performed to measure the growth of a population and the spread of a disease.
The participants will also develop models for these populations and compare their models to data observed
during the workshop.
Finally, the mathematical models discussed will be used to determine if a murder suspect’s alibi
assures that he could not have committed the crime.
A graphing calculator is not required but may be useful for this workshop.
Pre-Workshop Activities
for Growth, Decay and Forensic Science.
MathFest
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