On April 23-24, 2004 Salisbury University hosted the Spring 2004
MD-DC-VA Regional Meeting of the MAA.
- On Friday afternoon, Mary Kay Abbey and Bette Daudu of Montgomery College
conducted a workshop entitled, Writing to Learn Mathematics - No
Grading Required.
- On Friday evening, Paul K. Stockmeyer of the College of William and Mary
gave our banquet address. His talk was entitled, Pascal's Rhombus and the
Stealth Fractal.
- On Saturday, Charles Seife of Science Magazine gave the invited address
Mathematics, the Press, and the Art of Storytelling (or, Why Larry King
Won't Return Your Phone Calls).
Also on Saturday, James S. Sochacki and G. Edward Parker of James Madison University
gave the invited address
Relevance of Classical Analysis in Modern Contexts: Theory
and Application of Polynomial Projection.
Invited Addresses
Mary Kay Abbey (Mathematics Department) and
Bette Daudu (English Department)
Montgomery College
Workshop: Writing to Learn Mathematics - No Grading Required
Abstract:
Would you like your students to write more? Would you add writing
activities to your syllabus if the assignments would be graded without
your input? If you answered yes to these questions, this is the workshop for
you and your students. You will learn to use Calibrated Peer Review (CPR)
- a template software program available on the web. Lessons for mathematics
do exist and you will learn to write lessons tailored to your curriculum.
Once written, lessons can be used again and again and even published on the
UCLA server for national use.
Biographical Sketch:
Dr. Mary Kay Abbey has been with Montgomery College since 1982 in the
Mathematics Department. Her dissertation at the University of Maryland
studied the effect of journal writing on student success. After doing all
the grading required, she was quite happy to find this program and wants
to share it with all. Just as Professor Daudu was involved with committees
outside the classroom, so was Dr. Abbey as she served as the chair of the
mathematics department for six years and chair of the college-wide Academic
Assembly for two years. Both Dr. Abbey and Professor Daudu learned about the
capabilities of the CPR software while attending a Chautauqua workshop at UCLA
during the summer of 2001. This September they have received an NSF grant
(0311218) to write lessons for developmental mathematics students.
Professor DauduÕs role for the NSF grant will be as editor.
Professor Bette Daudu has been with Montgomery College since 1989.
During her tenure she has taught both regular English and English as a
Second Language. She has served as the Faculty Council Chair, Chair of
the Faculty Evaluation Team, and Chair of the English Department. Her
performance in each role has gained her the respect of her colleagues.
Her desire to increase active student involvement by means of this software
has the support of her department as other faculty have agreed to beta test
the lessons. Her role in the NSF grant is crucial since she brings
knowledge of student writing - what is to be expected, what is acceptable,
and what errors should be identified by the concept questions in the calibrations.
Paul K. Stockmeyer
Professor of Computer Science, College of William and Mary
Banquet Address: Pascal's Rhombus and the Stealth Fractal
Abstract:
We are all familiar with Pascal's triangle. Further, it is fairly well
known that the positions of the odd entries in the first 2n rows
of Pascal's triangle converge to the fractal known as the Sierpinski gasket
as n grows to infinity.
Pascal's rhombus, defined and developed in [1], is a variation of Pascal's
triangle in which each term is computed as the sum of four earlier terms,
rather than two. In this talk we will see how the positions of the odd
entries of Pascal's rhombus also converge to a fractal. The natural shape of
this new fractal is not the triangle of the Sierpinski gasket, but rather an
octagon that resembles the B-2 stealth bomber aircraft. By focusing on
this stealth shape we obtain easy proofs of several results conjectured in
[1] and later proved in [2].
References:
[1] William F. Klostermeyer, Michael E. Mays, Lubomir Soltes, and George Trapp,
"A Pascal Rhombus," Fibonacci Quart. 35 (1997), 318-328.
[2] John Goldwasser, William F. Klostermeyer, Michael Mays, and George Trapp,
"The Density of Ones in Pascal's Rhombus," Discrete Math. 204 (1999), 231-236.
Biographical Sketch:
Paul K. Stockmeyer (stockmeyer@cs.wm.edu) received his BA degree from Earlham
College, and his graduate degrees from the University of Michigan, all
in Mathematics. He has been teaching at the College of William and Mary
since 1971, where he has been masquerading as a computer scientist for the
past 20 years. Now officially retired, he is finding time to rediscover the
joys of mathematics. His interests lie mainly in combinatorics and recreational
mathematics, including all aspects of the Tower of Hanoi.
Charles Seife
Journalist Science Magazine
Invited Address: Mathematics, the Press, and the Art of Storytelling (or, Why Larry King Won't Return Your Phone Calls)
Abstract:
The public seems to have an enormous appetite for stories about science and
medicine. There are science magazines on the newsstands and science shows
on several television networks; every Tuesday, the New York Times devotes
an entire section to science and health. Late last year, PBS spent three
primetime hours explaining string theory. So, with all the demand for
scientific storytelling, why are articles and documentaries and films about
math so rare?
It's not because the typical mathematician is perceived as being
"fat, scruffy, [having] no friends ... a badly dressed, middle-aged nerd
with no social life." (The Times of London, 3 January 2001.) It's not because
Hollywood's mathematicians run the gamut from eccentric to sociopathic.
It's because there is an inherent conflict between good mathematics and
good storytelling.
In this talk, I will explain the nature of that conflict, and why the craft
of storytelling makes it so difficult to get a math story past an editor or
a producer -- and I will show how to overcome those hurdles when you try to
tell your story to the public.
Biographical Sketch:
Charles Seife is a journalist with Science magazine and the author of two books.
His first book, Zero: The Biography of a Dangerous Idea, received the Martha
Albrand/PEN award. He has also written for New Scientist, Scientific
American, The Economist, Science, Wired, Wired UK, The Sciences, and numerous
other publications. Seife holds an M.S. in mathematics from Yale University.
He lives in Washington D.C.
James S. Sochacki and G. Edgar Parker
James Madison University
Invited Address: Relevance of Classical Analysis in Modern Contexts: Theory and Application of Polynomial Projection
Abstract:
In classical analysis, MacLaurin series play a seminal role. In this
talk, we discuss a sub-algebra of the convergent MacLaurin series,
that we call the projectively polynomial functions and denote by P. We
offer some structural properties of P, of both topological and algebraic nature,
including the denseness of P in spaces of functions of both applied and
theoretical interest. A theorem on modification of the Picard iteration
links this theory of P to numerical generation of solutions for ordinary
and partial differential equations. These methods are suitable for both
numeric and symbolic computing environments and are highly adaptable and
elementary to implement. An a priori estimate for functions in P, that is
independent of the derivatives, gives the proximity of MacLaurin polynomials
to their MacLaurin series. Posing and solving classical problems from physics
within P is illustrated. These examples, which include the n-body problem
and cavitation of a solid under pressure, show the wide applicability of the
theory. Problems under investigation are also offered.
Biographical Sketch:
Jim Sochacki, Associate Professor of Mathematics, has both teaching and
research interest in using computer technology to do applied mathematics.
He teaches courses that address solving ordinary and partial differential
equations and that address solving linear and nonlinear systems of equations.
Equations of these types arise in the modeling of such phenomena as population
dynamics, newtonian dynamics, wave propagation, fluid mechanics and diffusion.
In his courses Dr. Sochacki discusses both the advantages and disadvantages
associated with using computers to do the symbolic and numeric calculations
involved in solving equations.
His current research includes using picard iteration to solve systems of
ordinary and partial differential equations and using mathematical
software packages to develop programs that students and faculty can use to
solve problems. Dr. Sochacki is currently the director of the Center for
Computational Mathematics and Modeling.
Ed Parker is currently Professor of Mathematics at James Madison University.
He received his baccalaureate degree from Guilford College in 1969 with a
major in Mathematics and a minor in Philosophy and Religion. He was granted
the PhD in mathematics by Emory University in 1977 where his thesis on
nonlinear semigroups was directed by John W. Neuberger. He has taught
mathematics at Bayside High School in Virginia Beach, Virginia and as a
member of the faculties of Pan American University and James Madison University,
and remains strongly committed to discovery techniques in teaching mathematics,
using Moore method whenever feasible. His research has been primarily in
nonlinear analysis (with the last decade and a half being largely spent
on developing a theory for generating and using MacLaurin polynomials)
and application of mathematics to competitive sports.
