Mathematics Awareness Week
April 26 - May 2, 1998
Mathematics and Imaging
Official Description of the Theme
Mathematics is an essential element of imaging in fields as diverse as
medicine, computer science, and space exploration, and many other settings as well. For
instance, medicine benefits from the techniques of tomography, including cutting-edge
ideas like electrical impedance tomography that may greatly improve the detection of
cancerous tumors, and from level set and marching methods that can extract images of
beating hearts from MRI images.
Computer imaging depends upon a whole range of mathematical tools. Wavelet transforms
permit efficient illumination of two-dimensional representations of three-dimensional
scenes so that the images created by computer graphics are realistic and visually
pleasing. Familiar references like Microsoft's Encarta encyclopedia and its 7,000 color
images fit on a single CD-ROM because of fractal image compression.
Image compression is also one of the essential tools of space exploration. For example,
the scientists monitoring transmissions from the Mars Pathfinder will be receiving data at
a mere 40 bytes per second (about 700 times slower than a typical modem!) when the
spacecraft reaches Mars. Compression routinely increases the effective transmission rate
of image data by a factor of fifteen or twenty.
New techniques are being developed that will raise compression ratios into the hundreds
while still preserving essential features of the image. One of these new ideas, wavelet
image compression , has already enabled electronic storage and retrieval of the FBI's vast
archive of fingerprint records.
Image restoration tools can extract additional detail otherwise hidden in images from a
wide range of sources, including satellites, medical imaging devices, telescopes, and even
amateur video pictures submitted as courtroom evidence. Images from astronomical
telescopes are cleaner to begin with if they have benefited from the control strategies of
active and adaptive optics that minimize degradation from atmospheric blur and mechanical
tremors.
The Department of Mathematics is
pleased to sponsor
the following events in celebration of
National Mathematics Awareness Week 1998.
Lectures and Activities
Keep checking this page for the updated list of events.
Calendar
of events. See below for descriptions.
MONDAY, April 27th
Refreshments.
Time: 4:00 PM
Place: St. Thomas 160 - Mathematics Departmental Office
Topics on Wavelets - a new way to see and represent a signal.
Dr. Andrew Berger
Time: 4:30 PM
Place: St. Thomas 414
Dr. Berger is an Associate Professor in the Department of Physics at the University of
Scranton. The subject of wavelets is a beautiful combination of mathematical analysis and
signal processing applications. Any signal can be decomposed into a sum of these small,
overlapping waves. It offers a new way of analyzing, storing and transmitting information.
Wavelets have remarkable properties. They are localized waves. Instead of oscillating
forever, they drop to zero, and because of the repeated rescaling that produces them,
wavelets decompose a signal into details at all scales. This natural multiresolution finds
important application in representation and compression of images.
This lecture is intended for a general mathematics audience. Seating is limited.
TUESDAY, April 28th
Refreshments.
Time: 4:00 PM
Place: St. Thomas 160 - Mathematics Departmental Office
Mathematics Modelling and Cancer Research.
Dr. Mehdi Razzaghi
Time: 4:30 PM
Place: St. Thomas 414
Dr. Razzaghi is a Professor of Mathematics at Bloomsburg University. Mathematical models
designed to maximize the information obtainable from real-life experiments and to provide
the most precise quantitative risk estimates possible will be discussed.
This lecture is intended for a general audience. Seating is limited.
WEDNESDAY, April 29th
Short presentations by Mathematics Faculty on their
current mathematical pursuits.
Time: 4:00 PM
Place: St. Thomas 161 - Mathematics Department Computer Laboratory
Reception hosted by the Mathematics
Club.
Time: Following the presentations.
Place: St. Thomas 160 - Mathematics Departmental Office
Mingle with the Mathematics Department Faculty and the Mathematics
Club members.
All of the above presentations are accessible to students as well as
teachers and community. Hope to see you there!
THURSDAY, April 30th
Chaotic Attractors with Discrete Planar Symmetries.
Nathan Carter
Time: 4:00 PM
Place: St. Thomas 414
Mr. Carter is a junior with a dual mathematics and computer science major. He will be
presenting the results of his Research Experience for Undergraduates (REU) Project from
the Summer of 1997. The project involved finding, for each of the 27 distinct planar
symmetry groups, a function that generates a chaotic attractor that has the symmetry of
that group. Images of each attractor will be shown.
Using Maple to Characterize Chaotic Dynamical Systems.
Christopher L. Rogers
Time: 4:30 PM
Place: St. Thomas 414
Mr. Rogers is a graduating senior with a chemistry major/mathematics minor who will be
attending University of Pennsylvania to pursue a Ph.D. in chemistry. He will be presenting
some results of his Spring 1998 Honors Project which was under the direction of Dr. Steven T. Dougherty. Maple
can allow one to understand the behavior of chaotic dynamical systems by utilizing
graphical analysis and symbolic dynamics, with symbolic dynamics being the more powerful
method. In this talk, he will show how to use these methods with Maple to characterize the
dynamics of the family of quadratic functions Q_c(x)= x^2 + c.
The Arithmetic-Geometric Mean and Approximations of Pi.
Anatoly Shtekhman
Time: 5:00 PM
Place: St. Thomas 414
Mr. Shtekhman is a sophomore mathematics major who will be presenting some results of his
Spring 1998 Faculty Student Research Project which was under the direction of Dr. Jakub Jasinski.
Mathematics Links:
The National Mathematics
Awareness Week 1998 Homepage
The 1998 Mathematics
Awareness Theme
About this year's Mathematics
Awareness Theme Poster
The Mathematics Forum
Unsolved Mathematics Problems
Ask Dr. Math
Mathematical Quotations Server
Favorite Mathematical
Constants
Mathematics Cartoons
Other Interesting
Mathematics Sites
Do you have any questions or favorite mathematics links to share? Send
e-mail to
Professor Carroll: carrollm1@uofs.edu
