Schedule of Talks for the 2006-2007 Academic Year
Date: Wednesday, October 4, 2006
Speaker: Prof. James Tattersall
Department of Mathematics & Computer Science
Providence College
Email: tat at providence dot edu
Title: The Early Lucasians
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.
Date: Wednesday, November 1, 2006
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
Title: The Impact of Ballistics on Mathematics
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.
Date: Wednesday, December 6, 2006
Speaker: Prof. Robert E. Bradley
Department of Mathematics & Computer Science
Adelphi University
Email: bradley at adelphi dot edu
Title: Theory of Equations from Leonhard Euler to Etienne Bézout
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.

Date: Wednesday, February 7, 2007
Speaker: Prof. Jeff Suzuki
Department of Mathematics & Computer Science
Brooklyn College, CUNY
Email: jeff_suzuki at yahoo dot com
Title: Euler and Number Theory
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.
Date: Wednesday, March 7, 2007
Speaker: Prof. Haishen Yao
Department of Mathematics and Computer Science
Queensborough Community College, CUNY
Email: hyao at qcc dot cuny dot edu
Title: A few Mathematical Problems and Methods in Ancient China
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.
Date: Wednesday, April 11, 2007
Speaker: Prof. Richard Jardine
Department of Mathematics
Keene State College
Email: rjardine at keene dot edu
Title: Linking Euler to Taylor: Connecting Discrete and Continuous Mathematics
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).
Date: Wednesday, May 2, 2007
Speaker: Prof. Joel Silverberg
Department of Mathematics
Roger Williams University
Email: joels at alpha dot rwu dot edu
Title: Mathematics in the service of Transoceanic Navigation: From Eastings to Lunars and Lines of Position
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.