Symposium Flyer

WESTERN KENTUCKY UNIVERSITY
20th ANNUAL MATHEMATICS SYMPOSIUM

Mathematics of an Unbelievable Nature

November 17-18, 2000

Thompson Complex, Central Wing, Room 129
Bowling Green, Kentucky

INVITED SPEAKERS

Calvin T. Long
Washington State University

Dr. Long is a recipient of the Mathematical Association of America's Certificate of Meritorious Service, past president of the Fibonacci Association, author of Elementary Introduction to Number Theory, and coauthor of Mathematical Reasoning for Elementary Teachers.

Douglas Hardin
Vanderbilt University

Dr. Hardin is internationally known for his work in the field of wavelet theory. During sabbaticals, he has worked at Sandia National Laboratories and with Michael Barnsley at Iterated Systems.

Schedule of Events

All times are CST and
all sessions are in TCCW 129.

Friday evening, November 17

6:30-7:00
Registration

7:00-7:20
Mathematical Eyeglasses: Crime-Fighting, Spy Satellites, and Wavelets
Bruce Kessler, Western Kentucky University
The seemingly disjoint topics of crime-scene evidence collection, orbital imaging satellites, and the mathematics of wavelets come together in the science of image analysis. Images captured at the scene of a crime by an automated camera or witness could be pivotal pieces of evidence that lead to the arrest of a dangerous criminal, but only if their contents can be clearly seen. Likewise, satellite photos taken from space could be the key to our national security, but only if we can understand what we are seeing in the pictures. Two such examples will be examined, with hardly-
believable results. A short introduction to wavelets and how they are applied in edge detection and image analysis will be included.

7:25-7:45
Time To Touch Base
John Spraker, Western Kentucky University
Bases are an interesting topic that most people see in elementary school. There are a number of different things that one can study concerning bases. The Cantor set is one such topic. I will also discuss fractional and negative bases. Arithmetic and counting in these systems is quite unusual.

8:00-9:00
The Fascinating Fibonacci Sequence
Calvin T. Long, Washington State University
William F. White once wrote, "The beautiful has its place in mathematics, for here are triumphs of the creative imagination, beautiful theorems, proofs, and processes whose perfection of form has made them classic. He must be a practical man who can see no poetry in mathematics." The Fibonacci sequence discussed in this talk is replete with remarkable, surprising, and elegant results of the sort White spoke of. The presentation also stresses the importance of inductive reasoning in the actual doing of mathematics.

9:00-10:00
Reception in Room 368

Saturday morning, November 18

8:00-8:30
Registration
Coffee and donuts will be provided in the Lobby of TCCW.

8:30-9:30
Generalizations of Moessner's Theorem: An Exercise in Guessing
(Some Combinatorial Results That Are Hardly Believable)
Calvin T. Long, Washington State University
Mathematics tends to be taught as an accomplished fact - - a set of ideas and skills to be learned. But this does not reflect how mathematics is really done or how non-rote problems are solved. In this presentation, a series of delightful and surprising results are discussed with heavy emphasis on the role of inductive reasoning (guessing) in the actual practice of mathematics.

9:40-10:00
Billiard Ball Arithmetic
Lyn Miller, Western Kentucky University
Did you know that the path of a ricocheting billiard ball gives a surprising visual way to perform some very familiar 4th grade arithmetic? Whether you're interested in teaching or you just enjoy learning unexpected math "tricks," come find out the secret!

10:05-10:25
Magical or Mathematical?
Carroll Wells, David Lipscomb University
As part of his television specials, magician David Copperfield includes magic tricks which allow his television audiences to participate. Some of these, including "Murder on the Orient Express" and "Clock Game" will be examined in light of basic mathematical concepts.

10:35-10:55
Simpson's Paradox: Simple, Sublime, Stupendous
Barry Brunson, Western Kentucky University
The phenomenon known as Simpson's Paradox can be viewed at many levels. On being encountered for the first time, it can evoke incredulity and a near-certainty that a mistake in calculation must have occurred. In a statistical context, it can dramatically underscore the importance of looking for lurking variables. After seeing a stark, formula-based "explanation" (perhaps offered by a blasé mathematician), one may be tempted to consider it a triviality hardly worth notice. This talk will use examples both real-world and mathematical to illustrate what Simpson's Paradox is, and to suggest that a reasonable level of astonishment is appropriate at all levels.

11:00-11:20
The Generalized yet Mysteriously Different Continuum
Sherrie Serros, Western Kentucky University
By representing the continuum of real numbers in (0,1) as sequences of zeroes and ones (binary decimal representation), it is natural to generalize the continuum using binary sequences of larger ordinality. This generalization does indeed yield a linearly ordered continuum, yet despite this likeness, there are distinctively different characteristics for these new continua of higher cardinality.

11:30-12:30
The Fractal Pizza Parlor Problem
Doug Hardin, Vanderbilt University
You have just opened a shop selling fractal pizzas. If you charge $10 for a 12 inch pizza, then how much should you charge for an 8 inch pizza? The answer lies in mathematical ideas introduced by Hausdorff in the early part of this century and then later developed by many other mathematicians including Besicovitch and Mandelbrot. In this talk we will discuss Hausdorff measure and dimension, self-affine sets, and fractal functions and surfaces.

SPECIAL ANNOUNCEMENT

Terry Wilcutt, commander of the Space Shuttle and an alumnus of the WKU Mathematics Department will speak Thursday evening, November 16, at 8:00 in Van Meter auditorium.

Parking Information

All parking areas except 10-minute spaces and those marked "handicapped" are open and no permits are required.

	Friday evening, November 17
6:30-7:00	Registration
7:00-7:20	Mathematical Eyeglasses: Crime-Fighting, Spy Satellites, and Wavelets Bruce Kessler, Western Kentucky University The seemingly disjoint topics of crime-scene evidence collection, orbital imaging satellites, and the mathematics of wavelets come together in the science of image analysis. Images captured at the scene of a crime by an automated camera or witness could be pivotal pieces of evidence that lead to the arrest of a dangerous criminal, but only if their contents can be clearly seen. Likewise, satellite photos taken from space could be the key to our national security, but only if we can understand what we are seeing in the pictures. Two such examples will be examined, with hardly- believable results. A short introduction to wavelets and how they are applied in edge detection and image analysis will be included.
7:25-7:45	Time To Touch Base John Spraker, Western Kentucky University Bases are an interesting topic that most people see in elementary school. There are a number of different things that one can study concerning bases. The Cantor set is one such topic. I will also discuss fractional and negative bases. Arithmetic and counting in these systems is quite unusual.
8:00-9:00	The Fascinating Fibonacci Sequence Calvin T. Long, Washington State University William F. White once wrote, "The beautiful has its place in mathematics, for here are triumphs of the creative imagination, beautiful theorems, proofs, and processes whose perfection of form has made them classic. He must be a practical man who can see no poetry in mathematics." The Fibonacci sequence discussed in this talk is replete with remarkable, surprising, and elegant results of the sort White spoke of. The presentation also stresses the importance of inductive reasoning in the actual doing of mathematics.
9:00-10:00	Reception in Room 368

	Saturday morning, November 18
8:00-8:30	Registration Coffee and donuts will be provided in the Lobby of TCCW.
8:30-9:30	Generalizations of Moessner's Theorem: An Exercise in Guessing (Some Combinatorial Results That Are Hardly Believable) Calvin T. Long, Washington State University Mathematics tends to be taught as an accomplished fact - - a set of ideas and skills to be learned. But this does not reflect how mathematics is really done or how non-rote problems are solved. In this presentation, a series of delightful and surprising results are discussed with heavy emphasis on the role of inductive reasoning (guessing) in the actual practice of mathematics.
9:40-10:00	Billiard Ball Arithmetic Lyn Miller, Western Kentucky University Did you know that the path of a ricocheting billiard ball gives a surprising visual way to perform some very familiar 4th grade arithmetic? Whether you're interested in teaching or you just enjoy learning unexpected math "tricks," come find out the secret!
10:05-10:25	Magical or Mathematical? Carroll Wells, David Lipscomb University As part of his television specials, magician David Copperfield includes magic tricks which allow his television audiences to participate. Some of these, including "Murder on the Orient Express" and "Clock Game" will be examined in light of basic mathematical concepts.
10:35-10:55	Simpson's Paradox: Simple, Sublime, Stupendous Barry Brunson, Western Kentucky University The phenomenon known as Simpson's Paradox can be viewed at many levels. On being encountered for the first time, it can evoke incredulity and a near-certainty that a mistake in calculation must have occurred. In a statistical context, it can dramatically underscore the importance of looking for lurking variables. After seeing a stark, formula-based "explanation" (perhaps offered by a blasé mathematician), one may be tempted to consider it a triviality hardly worth notice. This talk will use examples both real-world and mathematical to illustrate what Simpson's Paradox is, and to suggest that a reasonable level of astonishment is appropriate at all levels.
11:00-11:20	The Generalized yet Mysteriously Different Continuum Sherrie Serros, Western Kentucky University By representing the continuum of real numbers in (0,1) as sequences of zeroes and ones (binary decimal representation), it is natural to generalize the continuum using binary sequences of larger ordinality. This generalization does indeed yield a linearly ordered continuum, yet despite this likeness, there are distinctively different characteristics for these new continua of higher cardinality.
11:30-12:30	The Fractal Pizza Parlor Problem Doug Hardin, Vanderbilt University You have just opened a shop selling fractal pizzas. If you charge $10 for a 12 inch pizza, then how much should you charge for an 8 inch pizza? The answer lies in mathematical ideas introduced by Hausdorff in the early part of this century and then later developed by many other mathematicians including Besicovitch and Mandelbrot. In this talk we will discuss Hausdorff measure and dimension, self-affine sets, and fractal functions and surfaces.