YSU MathFest Workshops
One of the main features of MathFest is the workshops. All students
will attend 2 workshops chosen from a wide variety of topics. Workshops encourage
learning about the depth and breadth of many fields in mathematics
through group activities and demonstrations. Here students will
have the opportunity to see that mathematics is much more than
algebra, geometry, trigonometry, and calculus.
The workshops will be conducted by university faculty and are noncompetitive.
Some of the workshops will utilize the computer while some will use graphing
calculators.
YSU MathFest 2007 Workshop Titles
- Computer Vision and Image Processing by Andy Chang.
- Geometry of Gothic Design by Aimee Crabtree.
- The Cracker Barrel Puzzle by J. Douglas Faires. CLOSED
- The Mathematics of Roller Coaster Tycoon by Elizabeth Goldthwait. CLOSED
- Pyramids, Cones, and the Volume of a Sphere by Richard Goldthwait.
- Mathematics and Origami by John Hoffman. CLOSED
- Check out the group on MySpace by Frank Ingram.
- Using Math to Study the Brain by Jozsi Jalics. CLOSED
- Coordinates On A Spacetime Light Cone by Steve Kent.
- Are You In The Zone? by Jay Kerns. CLOSED
- Topology and Moebius Strips by Roy Mimna.
- "Intermediate" Ideas about Geometric Transformations by David Pollack.
- Mathematics of Sudoku by Nathan Ritchey.
- Instant Insanity by Thomas Smotzer.
- What Might You Expect From a Game Called "Chuck-A-Luck?" by Gary Stanek.
- Why Should We Hire You? by Paddy Taylor.
- Continued Fractions by Eric Wingler.
- Math in Medicine and Forensic Science by George Yates. CLOSED
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.
Geometry of Gothic Design
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.
The Cracker Barrel Puzzle
by Doug Faires, Youngstown State University
People often confuse mathematics with computation, and think that mathematicians spend their
time doing complicated arithmetic and algebra. However, for most mathematicians their basic tool is
logic rather than these computational tools, and they often think more about whether a certain problem
is possible to solve rather than actually describing the solution.
In this workshop we will look at a puzzle that is often found in "family" restaurants and other establishments
where the proprietor wants you to have something to spend your time on while you wait. We will find a
solution to the problem, and then look at a number of questions of the type a mathematician would naturally
consider.
Please CLICK HERE to see the puzzle.
The Mathematics of Roller Coaster Tycoon
by Elizabeth Goldthwait, Youngstown State University
While "riding" a roller coaster, using the videocam in Roller Coaster
Tycoon, participants will create graphical representations of their traveling speed.
These graphs will then be used for determining the
distance travelled while riding the coaster, as well as the
acceleration experienced by riders.
Pyramids, Cones, and the Volume of a Sphere
by Richard Goldthwait, Youngstown State University
A famous geometrical construction leads to the volume formula for a square pyramid.
We will discuss this construction along with another principle that connects the
volume of a pyramid and to that of a cone.
We will then see how these ideas lead to an exact formula to compute the volume of a sphere.
Mathematics and Origami
by John Hoffman and YSU Students, Youngstown State University
In this workshop we will explore relationships between Origami, the art of paper folding and
mathematics. We will learn how to create the PHIZZ unit of paper and how to use these units to make a
buckey ball (soccer ball). We will see that mathematics is necessary in order to color the ball in 3 different
colors.
Check out the group on MySpace
by Frank Ingram, Youngstown State University
Addition, subtraction, multiplication, and division are familiar
examples of operations on an appropriate set of numbers. Intuitively,
an operation on set A is a way of combining any two elements of A to
produce another element in the same set A. For example, adding two
positive integers gives another positive integer, but subtracting two
positive integers does not necessarily result in a positive integer.
Every operation is denoted by a familiar symbol, such as + or -. In this
workshop we will look at operations from a lofty perspective. We will
discover facts pertaining to operations in general rather than specific
operations about specific sets. Accordingly, we will develop
unfamiliar operations on what I call My Space and discover properties
there in.
Using Math to Study the Brain
by Jozsi Jalics, Youngstown State University
About a trillion neurons in the human brain interact in complicated ways
to perform innumerable complex functions each moment. Neuronal
disorders such as schizophrenia, Parkinson's disease, and epilepsy are
caused by the abnormal firing activity of certain neurons. We will
discuss the vital role that mathematical modeling is playing in
understanding the complex patterns of activity present in the brain and
explore a neuronal model that employs the unit circle.
Coordinates On A Spacetime Light Cone
by Steve Kent, Youngstown State University
Light rays, or more generally electromagnetic radiation, form light cones in
4-dimensional spacetime and are important in studying areas of mathematical
physics such as Yang-Mills theory (a mathematical generalization of electricity
and magnetism) and Einstein's relativity. The sphere is often used to mathematically
model directions of this radiation emanating from a point, and form cross-sections of these light cones.
Simpler coordinates allow for simpler study of these objects. We will investigate how to
put complex number coordinates on a sphere using "stereographic projection" onto the complex plane.
This workshop will be accessible to students familiar with geometry and trigonometry.
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.
"Intermediate" Ideas about Geometric Transformations
by David Pollack, Youngstown State University
You have heard about Geometric Transformations many times - you know, they were called flips,
slides and turns in elementary school and reflections, translations, and rotations in middle school.
Unfortunately, you were probably shown only the most basic ideas about these transformations,
namely what are they, but not much more. In fact, they are very useful for many purposes.
One purpose has to do with the most important concept in geometry: congruence of figures.
In this workshop we will explore the relationship between geometric transformations and the concept of congruence.
We will also show you a few "intermediate" ideas about reflections, translations, and rotations.
Mathematics of Sudoku
by Nathan P. Ritchey, Youngstown State University
The Sudoku is a logic puzzle that has become extremely popular over the past two years.
The objective of the puzzle is to use the whole numbers 1 through 9 to fill in a 9 x 9 matrix
in such a way that each of the numbers appears exactly one time in each row, in each column and
in each of the nine 3 x 3 dominant sub-matrices or blocks.
The game is quite fun and can be very challenging.
It is also filled with an immense amount of mathematics.
In this workshop, we will explore some of the mathematics that lies just under the surface of this marvelous game.
As a pre-workshop activity, students should practice solving some Sudoku puzzles. There are many free
ones available on-line. For example,
Web Sudoku has billions
of free puzzles.
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.
What Might You Expect From a Game Called "Chuck-A-Luck?
by Gary Stanek, Youngstown State University
We introduce the probability concept of mathematical expectation and
apply it to analyze the fairness of a particular game of chance that
is often called "Chuck-A-Luck." The game originated as a dice game,
but a version using a large Roulette-type wheel can often be found at festivals.
We plan to also examine other games, such as state lottery games.
Why Should We Hire You?
by Paddy Taylor, Youngstown State University
Regardless of the job, employers want to hire a candidate who can
make sense out of problems, both expected and unexpected, that may
arise. In their attempt to find problem solvers, many employers
pose challenging questions during job interviews to test the
reasoning abilities of applicants.
In this workshop, students will be presented with questions (from
actual companies including Google) that have been asked during job
interviews or used in the applicant screening process.
An example of one such question is: 10 machines produce gold
coins of a uniform weight. Unfortunately, one of the machines is
broken and produces coins that are x grams too heavy. Assuming we
know what the correct weight of the coins should be, can we locate
the broken machine if the only tool at our disposal is a scale with
a digital read-out, and we are only allowed to use the scale once?
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.
Math in Medicine 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 Math in Medicine and Forensic Science
2006 Workshops titles and abstracts.
2005 Workshops titles and abstracts.
2004 Workshops titles and abstracts.
2003 Workshop titles and abstracts.
MathFest
mathfest@math.ysu.edu
