MathFest 2004 Workshop Titles
- Breaking Sticks-A Game with Whole Numbers by Floyd Barger.
- Parallel Knockouts by Anita Burris.
- Computer Vision and Image Processing by Andy Chang.
- Some Elementary Methods of Solving Diophantine Equations by Jacek Fabyrkowki.
- Puzzles are Us by J. Douglas Faires.
- Voting Theory and Fair Division by Jay Kerns and Angela Spalsbury.
- Beyond Google: Paradoxes of the Infinite by Roy Mimna.
- Taking the Mystery out of i by David Pollack.
- The Mathematics of Kicking a Football by Richard Rappach.
- Game Theory by Nathan Ritchey.
- Crazy Dice by Thomas Smotzer.
- Smart Numbers, Coding, and Check Digits by Jamal Tartir.
- Geometry Logo Style by Eric Wingler.
- The Mathematics of Bio-Diversity by George Yates.
Descriptions of Workshops
Breaking Sticks-A Game with Whole Numbers
Floyd Barger, Youngstown State University
Two players named Alice and Bob play the
following game. A stick of length L (a whole number), is
given to Alice, who breaks the stick into two pieces of different
lengths. Bob then breaks one of the two pieces into two pieces of
different lengths. Playing alternates until all the the
pieces are of lengths one and two. If there are more 1's than 2's then
the last player to play wins. If there are more 2's than 1's, then
other player wins. Otherwise the game is a draw.
Assuming both players play the best possible game at all times,
we want to determine what the outcome will be, given L.
Pre-Workshop Activities
for Breaking Sticks-A Game with Whole Numbers.
Parallel Knockouts
by Anita Burris, Youngstown State University
In this Graph Theory talk we consider a situation where at each stage of the
experiment every vertex of a graph randomly knocks out an adjacent vertex. We
will compute the expected number of surviving vertices, and discuss some unsolved
problems. Bungee cords and dart guns will be provided for audience participation.
Pre-Workshop Activities
for Parallel Knockouts.
Complete the "Introduction to Graph Theory" tutorial found at this site.
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 Elementary Methods of Solving Diophantine Equations
by Jacek Fabrykowski, Youngstown State University
In this talk we will describe some elementary treatments of Diophantine equations.
A Diophantine equation is an equation in one or more unknowns that is to be solved in
integers or sometimes in rational numbers. The name honors the Greek mathematician Diophantus,
who was the first mathematician who studied such equations systematically.
Many typical math competition problems ask for a proof that a given Diophantine equation has no
solution in the integers. This workshop will discuss various tools used to solve these
equations.
Pre-Workshop Activities
for Some Elementary Methods of Solving Diophantine Equations.
Puzzles are Us
by Doug Faires, Youngstown State University
There are some interesting puzzles on the market that provide a test ingenuity.
On the surface these puzzles may not appear to involved mathematics, at least not
mathematics as the public sees it. We will see, however, that there can be quite a
lot of clever problem solving behind the solution of some of these puzzles, and this is the true spirit of mathematics.
Pre-Workshop Activities
for Puzzles are Us.
Voting Theory and Fair Division
by Jay Kerns and Angela Spalsbury, Youngstown State University
What could be easier than "voting?" After all, to vote we just count how many people favor
each candidate. What could go wrong? It turns out that lots of things can go wrong if there are more
than 2 candidates. The winner need not be whom voters really want. Mathematicians have been studying
these voting problems for the past few centuries. In this workshop we will examine various voting systems
such as those used
to elect our president, to select Oscar winners, and to select the site for the Olympic Games. In
addition, we will consider "fair division" problems. Many disputes all over the world-on international,
national, local, and even personal levels-involve the division of items for which 2 parties have
equal claim. We will work on mathematical solutions to these types of problems.
Beyond Google: Paradoxes of the Infinite
by Roy Mimna, Youngstown State University
If a finite set has n elements, then it has 2 to the power of n subsets.
A famous mathematician named Cantor discovered a similar result for infinite sets.
Later, some mathematicians and philosophers thought about
"the set of all sets that are not members of themselves." This, and other aspects of infinite sets,
have led to some interesting paradoxes, which are the subject of this workshop.
The origins of ideas of infinite sets can be traced to the ancient Greeks,
who discovered incommensurable lengths and irrational numbers.
If possible, students should consult their school libraries or internet
resources to read about "countably infinite sets."
Taking the Mystery out of i
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.
The Mathematics of Kicking a Football
by Richard Rappach
Mathematics can be found in almost everything in life, especially sports.
This activity helps determine the best angle to kick a football in order to achieve its maximum distance.
How do we find this "ideal" angle? What formulas do we use? Where do these formulas come from?
hese questions will all be answered through mathematics by using some basic trigonometry and
parametric equations. This presentation is ideal for the algebra II or pre-calculus student.
Attending students will need a TI-83+ calculator to track the flight of the football and
do some additional explorations involving sports.
Pre-Workshop Activities
for The Mathematics of Kicking a Football.
Crazy Dice
by Thomas Smotzer, Youngstown State University
When you roll a standard pair of 6-sided dice, there are 11 possible outcomes,
with a certain probability of occurrence for each possible result.
This is called the probability distribution. Now it turns out that
you can take two 6-sided dice and put different positive integers on
them in such a way that the probability distribution is the same as for two standard dice.
We will solve this problem by considering generating functions.
Smart Numbers, Coding, and Check Digits
Jamal Tartir, Youngstown State University
Virtually every product we purchase comes with a number on
the label. Two common examples of numbers found on merchandise
are universal product codes (UPC) and international
standard book numbers (ISBN). How are these numbers created and
what are their meanings? When UPC numbers are entered
incorrectly, the error is usually detected immediately.
How is this accomplished? The purpose of this workshop is
explore how these numbers are generated to be both
descriptive and self-checking.
Geometry Logo Style
by Eric Wingler, Youngstown State University
Several theorems from geometry will be examined using the
Logo programming language. If time permits, students will
also see a demonstration of how to produce a fractal curve
using recursion. A prior knowledge of Logo is not required
as the few commands that are necessary will be presented.
Pre-Workshop Activities
for Geometry Logo Style.
The Mathematics of Bio-Diversity
by George Yates, Youngstown State University
The general health of an environment is often assessed by the diversity of
plants and animals living in it. This workshop will define several mathematical
definitions of biodiversity, and we will evaluate the biodiversity index for the
environment inside a bag of candy. We will also explore the meaning of the
biodiversity index and suggest alternatives. In this exploration, we will use
the Cauchy-Schwarz and Jensen’s inequality to find upper and lower bounds on the
biodiversity indices.
MathFest
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