Date: 
Wednesday, October 3, 2001 
Speaker: 
Prof. John McCleary
Department of Mathematics
Vassar College
mccleary@vassar.edu

Title: 
The Porism of Poncelet: Jacobi , Poncelet, Abel, Steiner

Video Stream: 
Click
here 

Abstract: 
This talk is a part of my investigations of Jacobi's geometrical
works. In his paper, Ueber die Anwendung der elliptischen
Transcendenten auf ein bekanntes Problem der Elementargeometrie,
Jacobi describes a proof of the Porism of Poncelet using his
then newly developed elliptic functions to prove a remarkable
geometric result. In this talk I will describe how this result
drew the attention of Jacobi, and how it fits the theory of elliptic
functions into an older tradition of analysis.


Date: 
Wednesday, November 7, 2001 
Speaker: 
John Glaus
Unaffiliated Scholar
Rumford, Maine
restinn@exploremaine.com

Title: 
Euler: Mathematician and Diligent Bureaucrat 
The Great Balancing Act

Video Stream: 
Click
here 

Abstract: 
Euler was the quintessential mathematician, but he also proved his
worth to the Russian and Prussian imperial courts as an evenhanded,
competent and tightfisted official.
The intention of this paper is to show the human armor Euler developed
to circumvent the complications caused by outrageous administrators and
belligerent autocrats. The information contained in this talk has been
taken from newly translated letters written between 1748 and 1763 to
Kiril Razumovsky and Grigory Teplov while Euler was in Berlin.


Date: 
Wednesday, December 5, 2001 
Speaker: 
Prof. Paul C. Pasles
Department of Mathematical Sciences
Villanova University
paul.pasles@villanova.edu

Title: 
The Lost Squares of Dr. Franklin

Abstract: 
In colonial times, America was hardly the hotbed of frenzied
mathematical activity it would later become. One Philadelphian, however,
was an avid builder of magic squares, those numerical novelties that
entertained early mathematicians from China to India to Islam. Until
recently, only two of Benjamin Franklin's squares were well known to
mathematicians. Since Franklin had little formal schooling, it might be
assumed that he stumbled upon his discoveries. However, it turns out
that a few more examples survived, and these show a more varied set of
tricks. Today, see the lost squares of Dr. Franklin in this colloquium.
I will also describe Franklin's procedure for constructing "magic
circles" reminiscent of the traditional Chinese and Japanese varieties.
This talk will be accessible to mathematicians and historians, from
undergraduate to faculty.


Date: 
Wednesday, February 6, 2002 
Speaker: 
William Dunham
Koehler Professor of Mathematics
Muhlenberg College
wdunham@muhlenberg.edu

Title: 
Volterra and the Limits of Pathology

Video Stream: 
Click
here 

Abstract: 
This talk describes the rise of "pathological functions" in nineteenth
century analysis, citing examples from Dirichlet (1829), Riemann (1854),
and Weierstrass (1872). Their work seemed to suggest that functions
could be arbitrarily bizarre. Such a suggestion was countered by the
young Vito Volterra in 1881. In an elegant and relatively simple proof,
Volterra established the nonexistence of a function continuous on the
rationals and discontinuous on the irrationals. We examine his
argument, which is not only of historical interest but also of
pedagogical value in the analysis classroom.

Title: 
Newton's (Original) Method  or  Though this be Method,
yet there is madness in't
(a special lecture, suitable for undergraduates, given earlier the
same day by Professor Dunham)

Video Stream: 
Click
here 

Abstract: 
This talk sketches the life and career of Isaac Newton  including his
nasty skirmishes with Leibniz over the creation of the calculus  before
considering in greater detail the method he advocated for approximating
solutions to equations. We examine his lone example of this
approximation technique and compare it to what is now called "Newton's
Method." The presentations features roughly equal doses of history,
biography, and mathematics and is accessible to anyone acquainted with
calculus.


Date: 
Wednesday, March 6, 2002 
Speaker: 
Prof. Antonella Cupillari
School of Science
Penn State Erie, The Behrend College
axc5@psu.edu

Title: 
Maria Gaetana Agnesi: Myths and Mathematics

Abstract: 
Most mathematicians are familiar with the "witch of Agnesi." To the
mistranslation of the name of this curve, Agnesi (17181799) might owe
some of her fame. But what is the truth about the woman who authored the
Instituzion Matematiche, the first calculus book in Italian?
Some answers can be found in the Elogio Storico di Donna Maria
Gaetana Agnesi, a biography written only five months after her death
by a family friend and wellknown historian of the time, Canon Antonio
Francesco Frisi. This biography mentions explicitly only one
mathematical problem about conics, taken from Agnesi's extensive
correspondence, and not related to the "witch." The solution is given,
but her work, which can be found in the original letter, is not
included.


Date: 
Wednesday, April 3, 2002 
Speaker: 
Prof. Steven Gimbel
Department of Philosophy
Gettysburg College
sgimbel@gettysburg.edu

Title: 
Poincaré, the Language of Mathematics, and the
Intuitionist/Formalist Debate

Abstract: 
Jules Henri Poincaré was simultaneously claimed as a forefather for
both sides of the intuitionist/formalist debate. He explicitly opposed the
analytic axiomatic approach to mathematics which was beginning to
blossom at the end of the 19th century, but the conventional approach to
geometry that emerges from his writings on the conceptual foundations of
mathematics are generally cited as a great influence on the acceptance
of the axiomatic approach. This discussion considers the work that
Poincaré does in order to separate his view from that of Immanuel Kant,
arguments that are mistakenly taken to be directed against empiricism.
In pointing out what he sees as Kant's conceptual misunderstandings,
Poincaré is led to view geometry as a branch of group theory and oppose
considering the general treatment of manifolds by Bernhard Riemann to be
geometry at all. The rationale for this restrictive definition of
geometry leads to the conclusion that Poincaré is to be labeled as
neither a protointuitionist nor a protoformalist, but rather posits a
deep mathematical linguistic faculty in the human mind of the sort Noam
Chomsky would champion over half a century later.


Date: 
Thursday, May 2, 2002 
Speaker: 
Prof. Walter Meyer
Department of Mathematics and Computer Science
Adelphi University
meyer@adelphi.edu
Prof. Joseph Malkevitch
Department of Mathematics
York College (CUNY)
joeyc@cunyvm.cuny.edu
Prof. Jack Winn
Department of Mathematics
SUNY at Farmingdale
winnja@farmingdale.edu

Title:

Theory and Applications in the teaching of Linear Algebra:
Evolution During 19481999

Abstract: 
Although some mathematics courses are relatively timeless, some have been
newly created in recent decades or had their contents substantially
changed (at times because new mathematics or new applications were
discovered). Studying the evolution of curriculum can be intellectually
interesting and may offer lessons so that future efforts at curriculum
change can be more effective.
As a particular example, the history of the teaching of linear algebra
has been eventful in the last halfcentury. We will present an outline
of some of the developments, with special attention to the applied versus
pure issue. Many questions are still unresolved and we hope for useful
input from the audience.

