YSU MathFest 2006 Workshop Titles
- Computer Vision and Image Processing by Andy Chang.
- The Geometry of Gothic Architecture
by Aimee Crabtree.
- Games of Pure Strategy by J. Douglas Faires.
- Constructing a Cube from Pyramids by Richard Goldthwait.
- Fun with Counting by Frank Ingram.
- The Math in your Brain by Jozsi Jalics.
- Beating Las Vegas by Jay Kerns.
- Topology and Moebius Strips by Roy Mimna.
- The Fixed Point form of a Linear Function by David Pollack.
- Crazy Dice by Thomas Smotzer.
- Let's Make Deal! by Gary Stanek.
- The Golden Rabbits by Paddy Taylor.
- Continued Fractions by Eric Wingler.
- Birds, Bees, Flowers and Trees - Mathematics in the Environment 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.
The Geometry of Gothic Architecture
by Aimee Crabtree, Youngstown State University
The ancient Greek's transformed geometry from an estimation &
measurement skill into a philosophical art; their tools of reasoning:
the unmarked compass and straight edge. With these humble instruments,
they developed almost the entirety of Euclidean Geometry that you learned
in your high school geometry class. We will explore how architects refined these
techniques to an art in Gothic Cathedrals.
Games of Pure Strategy
by Doug Faires, Youngstown State University
The general public appears to think that higher mathematics involves
simply more involved arithmetic and algebra computations. In fact,
most mathematician seldom do calculations in their work, relying
much more frequently on logical problem-solving techniques. This
workshop will introduce a few games that will permit you to test
your logical skills to see if you have (mathematically) what it takes.
Fun with Counting
by Frank Ingram, Youngstown State University
This will be an introduction to the most often used counting
techniques. Consider the following. The YSU math department must choose
four new freshman to receive scholarships. They can choose from 20
incoming freshman, half of whom are female, and half of whom are male.
The department can award the scholarships in any way, as long as at
least one female and at least one male receive a scholarship. How many
possibilities does the department have?
Constructing a Cube from Pyramids
by Richard Goldthwait, Youngstown State University
The problem of volume calculation has always been of interest in mathematics.
In particular, how did mathematicians learn how to find the volume of a pyramid that has a square base long before the methods of the calculus were available?
The above question will be answered as we construct a cube from 3 congruent pyramids.
In order to make each pyramid, we first need a "template". That is, we need an accurate drawing on
paper (or cardstock) to show where to cut and where to fold in order to produce a pyramid with edges
of the correct lengths. Such a template is called a net.
The challenge is to produce the net for this activity as a compass and straightedge construction.
Students will discuss ways to perform the ruler and straightedge construction before a solution is demonstrated..
The Math in Your Brain
by Joszi Jalics, Youngstown State University
Did you know that there are about 1012 neurons in the human
brain? As you might expect, the interactions among these neurons can be
quite complicated, and it is difficult to find the causes of
pathological activity. We will discuss the vital role that mathematics
is playing in understanding the complex patterns of activity present in
the brain.
Beating Las Vegas
by Jay Kerns, Youngstown State University
We have all heard about the casinos of Las Vegas, the "Eye in the Sky", and the
House that can't be beaten. However, not long ago a team of clever MIT students
figured out a mathematical system that would beat Las Vegas at its own game.
In this workshop, we will investigate the MIT strategy and other competing betting systems using
principles of probabilistic reasoning. Can you beat Las Vegas? Come and find out!
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.
The Fixed Point form of a Linear Function
by David Pollack, Youngstown State University
This presentation is for students (and teachers) who want to
learn some new mathematics related to an old topic.
The old topic is linear functions, like f(x) = 3x + 4, with f
written in the familiar slope-intercept form.
What will probably be new to most people is another way to write f called the fixed-point form.
The fixed-point form for this function is f(x) = 3(x + 2)-2, where the constant term 4 has been
split up in such a way that there is a +2 in the parentheses and a -2 outside of them.
Even though this seems like a very slight rearrangement of the numbers from the slope-intercept form,
it turns out that this fixed-point form is very useful in solving some tricky problems in finance.
For example, suppose that your parents simultaneously bump their heads on a rock and decide to buy you a car.
The car costs $15,000 and the interest rate is 6% per year.
If you pay $300 per month, how much will you owe at the end of three years?
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.
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.
The Golden Rabbits
by Paddy Taylor, Youngstown State University
In this workshop we will take a look at the famous multiplying
rabbit problem proposed by Leonardo of Pisa. We will analyze this
problem using difference equations and explore some of the
"mystical" connections to art, architecture, and mathematics that
Leonardo and his rabbits have to offer! No prior knowledge of
difference equations is assumed, so any student comfortable with
algebra should be able to come for the ride.
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.
Birds, Bees, Flowers and Trees - Mathematics in the Environment
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 these
biodiversity indexes 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.
2005 Workshops titles and abstracts
2004 Workshops titles and abstracts
2003 Workshop titles and abstracts.
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