Schedule of Talks for the 2006-2007 Academic Year
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Date: |
Wednesday, October 4, 2006 |
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Speaker: |
Prof. James Tattersall
Department of Mathematics & Computer Science
Providence College
Email: tat at providence dot edu
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Title: |
The Early Lucasians
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Abstract: |
In 1663, Henry Lucas, the long-time secretary to the Chancellor of the
University of Cambridge, made a bequest, subsequently granted by Charles
II, to endow a chair in mathematics. A number of severe conditions were
attached to the Chair. Among the more prominent early Lucasian
professors were Barrow and Newton. In this talk we focus attention on
two very intriguing characters Nicholas Sanderson and John Colson. Many
early Lucasians were very diligent in carrying out their
responsibilities but as we shall see that was not always the case. In
the process, we uncover several untold stories and some very interesting
mathematical results.
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Date: |
Wednesday, November 1, 2006 |
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Speaker: |
Prof. Shawnee McMurran
Department of Mathematics
Cal State, San Bernardino (USMA, 2006-07)
Email: smcmurra at csusb dot edu
Prof. Fred Rickey
Department of Mathematical Sciences
United States Military Academy
Email: fred-rickey at usma dot edu
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Title: |
The Impact of Ballistics on Mathematics
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Abstract: |
In 1742 Benjamin Robins published New Principles of Gunnery, the first
book to deal extensively with external ballistics. Subsequently,
Frederick the Great asked Euler for a translation of the best manuscript
on gunnery. Euler chose Robins' book and, being true to form, tripled
the length of the work with annotations. The annotated text was
translated back into English, which, two and a half centuries later,
brings us to the theme of this lecture.
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Date: |
Wednesday, December 6, 2006 |
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Speaker: |
Prof. Robert E. Bradley
Department of Mathematics & Computer Science
Adelphi University
Email: bradley at adelphi dot edu
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Title: |
Theory of Equations from Leonhard Euler to Etienne Bézout
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Abstract: |
On the eve of Leonhard Euler's tercentenary, we consider some of his
contributions to the theory of equations.
Euler published his Introductio in analysin infinitorum in 1748.
It is almost impossible to overstate the importance of the first volume
of this book, in which Euler advocated for the centrality of the notion
of function in analysis, among other significant innovations. Less well
remembered is the second volume, which concerned the "application of
analysis to geometry." Although this volume was in many ways the
definitive summary of analytic geometry in the 1740s, it also amounted
to something of a research agenda for Euler in the theory of equations.
In this talk we will survey the Introductio and consider some
of the problems in the theory of equations which occupied Euler's
attention in the years following its publication. These include
questions about cusps, the resolution of Cramer's Paradox and Euler's
attempts to prove the proposition which we know as Bézout's Theorem.
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Date: |
Wednesday, February 7, 2007 |
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Speaker: |
Prof. Jeff Suzuki
Department of Mathematics & Computer Science
Brooklyn College, CUNY
Email: jeff_suzuki at yahoo dot com
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Title: |
Euler and Number Theory
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Abstract: |
Number theory began with the Pythagoreans and made up
a significant fraction of Euclid's Elements,
while Diophantus solved a great many problems
involving indeterminate second degree equations. But
few mathematicians considered it to be a subject worth
pursuing. Fermat made a valiant effort to interest
his contemporaries, but the first noteworthy
mathematician interested in number theory was Euler,
encouraged by Goldbach. Euler began with Fermat's
conjectures, but added new tools and in the process
created not only elementary number theory, but also
analytic and additive number theory as well. We will
see how Euler created the essential components of
modern number theory from Fermat's work, and left the
further development of the science in the hands of his
successors, Lagrange, Legendre, and Gauss.
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Date: |
Wednesday, March 7, 2007 |
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Speaker: |
Prof. Haishen Yao
Department of Mathematics and Computer Science
Queensborough Community College, CUNY
Email: hyao at qcc dot cuny dot edu
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Title: |
A few Mathematical Problems and Methods in Ancient China
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Abstract: |
In ancient China, people developed many mathematical concepts and
methods, which are still very impressive from a modern mathematical
viewpoint. How could they compute so quickly? They never defined prime
numbers; without prime numbers, how could they do fractional
computations? How could they get such an accurate approximation for π?
How could they solve complicated equations without calculators? What
did they emphasize in solving mathematical problems? They obtained some
deep results as early as 100 BC. But why did the Chinese mathematical
development suddenly become very slow? Why did they never develop an
axiomatic system, even though they obtained most geometric results
before Europeans? In this talk, we will discuss these issues.
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Date: |
Wednesday, April 11, 2007 |
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Speaker: |
Prof. Richard Jardine
Department of Mathematics
Keene State College
Email: rjardine at keene dot edu
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Title: |
Linking Euler to Taylor: Connecting Discrete and Continuous Mathematics
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Abstract: |
In his mathematical writings, Leonhard Euler acknowledged the impact and
importance of the earlier work of Brook Taylor. Euler credited Taylor
with first producing the famous series bearing Taylor's name, and
Euler's proof of that result mirrored that of Taylor. This talk
highlights this and other connections between the "master of us all"
(Euler) and Newton's disciple (Taylor).
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Date: |
Wednesday, May 2, 2007 |
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Speaker: |
Prof. Joel Silverberg
Department of Mathematics
Roger Williams University
Email: joels at alpha dot rwu dot edu
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Title:
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Mathematics in the service of Transoceanic Navigation:
From Eastings to Lunars and Lines of Position
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Abstract: |
European navigation before Columbus was primarily restricted to
coastal cruising or traveling across the Mediterranean Sea.
With the discovery of the New World and the opening of the age
of exploration, the demands of transoceanic travel required a
fresh approach to navigation. That approach involved maintaining
an accurate dead reckonning of the ship's position, periodically
verified by increasing sophisticated celestial observations.
A study of surviving manuscript and printed sources details how
such techniques evolved over the course of more than three centuries.
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