Schedule of Talks for the 2008-2009 Academic Year
Date: Wednesday, October 15, 2008
Speaker: Patricia R. Allaire
Department of Mathematics and Computer Science
Queensborough Community College, CUNY
Email: PatAllaire at gmail dot com
Title: Yours truly, D. F. Gregory
Abstract: Duncan F. Gregory (1813-1844) was a proponent of the Calculus of Operations and a founding editor of the Cambridge Mathematical Journal. Extant is a series of five letters that Gregory wrote to a friend in 1839. This correspondence provides a glimpse into life at early-Victorian Cambridge, reveals something of the character of Gregory and his dedication to the CMJ, and shows some of the mathematical problems he pondered. In this talk, we will look briefly at Cambridge, Gregory and the CMJ, and will examine several of the problems.
Date: Wednesday, November 5, 2008
Speaker: Harold M. Edwards
Courant Institute
New York University
Email: edwards at cims dot nyu dot edu
Title: Kronecker's Lost Theorem: An Insight into the Solvability of Algebraic Equations that Goes Beyond Galois
Abstract: Leopold Kronecker's first published paper sketches a construction that purports to find the most general polynomial of prime degree with coefficients in a given field that can be solved by radicals. The theorem is not even stated in detail, and there is no indication whatever of a proof. Moreover, it has been overshadowed by another theorem in the paper that is of secondary importance to the paper but that has fascinated number theorists ever since, the so-called Kronecker-Weber theorem. A reconstruction of the theorem on solvable equations of prime degree will be given, along with some reflections on how the theorem was lost and why it deserves to be found.
Date: Wednesday, December 3, 2008
Speaker: Prof. Herbert C. Kranzer
Department of Mathematics & Computer Science
Adelphi University
Title: Two Centuries of Shock Wave Theory and Applications
(A lecture dedicated to the memory of my friend and colleague Robert G. Payton)
Abstract: A shock wave is fundamentally a mathematical anomaly: a discontinuous solution of a system of differential equations. Yet shock waves do occur in many natural phenomena and man-made situations, from thunderclaps to sonic booms, from traffic flow on highways to water flow in rivers and canals, from the explosion of an atomic bomb to the progress of Earth's magnetosphere through the the solar wind. A consistent mathematical treatment of these waves has become a valuable resource of humankind.

We first trace the development of shock wave theory from its beginnings with Stokes and Riemann through its aeronautical engineering and chemical combustion applications in the early 20th century to its spectacular growth in the World War II era. We next describe the influence of the seminal book by Courant and Friedrichs (1948) and the major theoretical breakthroughs of Peter Lax in the 1950's. Finally, we discuss some of the new ideas arising from shock wave theory which have enriched the mathematics of the later 20th century. Among these are the treatment of wave interactions by Glimm, the concept of a viscosity solution introduced by Crandall & Evans, the Lax-Wendroff finite difference scheme, and the notion of compensated compactness developed by Tartar.

Date: Wednesday, February 4, 2009
Speaker: Prof. Salvatore J. Petrilli
Department of Mathematics & Computer Science
Adelphi University
Email: pertilli at adelphi dot edu
Title: Monsieur François-Joseph Servois: His Life and Work on Differential Calculus.
Abstract: Born on July 19th, 1767, François-Joseph Servois was a mathematician who would remain relatively unknown until the beginning of the 21st century. Near the beginning of the French Revolution, Servois was ordained a priest, and if it had not been for the revolution, he would probably have been a successful priest and mathematician. With the outbreak of the revolution, he joined the armed forces and followed a military career while also pursuing mathematics during his leisure time.

Servois was a great admirer of Lagrange and considered his work to be truly "brilliant." Within his 1814 work, Essai sur un nouveau mode d'exposition des principes du calcul differential, he continued the work of Lagrange by placing calculus on a foundation of algebraic analysis without the need of infinitesimals. Servois' main contribution to the development of symbolic analysis was recognizing the distributive and commutative property of functions, terms which he coined, and the method of separating symbols and their operators.

In this presentation, we will explore the life of Servois, his contributions to mathematics, and will examine several aspects of his differential calculus, located within the Essai.

Date: Wednesday, March 4, 2009
Speaker: Prof. Dominic Klyve
Department of Mathematics
Carthage College
Email: dklyve at carthage dot edu
Title: An Embarrassment of Riches: Euler's Choice of Number Theory Problems Near the End of his Life
Abstract: The last ten years of his life were, by most measures, Euler's most productive. He had been freed of most of his administrative duties, and had become widely regarded as the leading mathematician and physicist in the world. This situation left him with total freedom to choose the problems that he worked on. From this viewpoint, many of Euler's researches, including many of his number theory problems, seem odd; it's not always clear why these problems in particular attract his attention. This talk will give some preliminary insights into the motivations for some of Euler's mathematics, with particular focus on his number theory.
Date: Wednesday, April 1, 2009
Speaker: Prof. Judy Green
Department of Mathematics
Marymount University
Email: judy dot green at marymount dot edu
Title: New Yorkers Among the Pioneering American Women in Mathematics
Abstract: Among the 228 women who earned PhD's in mathematics before 1940 are many with connections to New York. In this talk we will look at those born, raised, educated, or employed there as well as the New York institutions important to women in mathematics.
Date: Wednesday, May 6, 2009
Speaker: Prof. Hugh McCague
Institute for Social Research
York University
Email: hmccague at yorku dot ca
Title: The Method of Equal Altitudes or the Indian Circle in the History of Mathematics, Cosmology and Architecture
Abstract: The method of equal altitudes, also known as the Indian Circle, is a procedure for the determination of the meridian, the North-South line formed by the great circle of the Earth that passes through the observer's position. This simple procedure involves the observation of the shadow of a vertical rod, a gnomon, at two crucial times during the morning and afternoon. The bisection of an angle and the construction of a perpendicular bisector, basic geometric constructions described in Euclid's Elements, are performed as part of this method. The method of equal altitudes is described in wide-ranging influential ancient and medieval manuscripts on practical geometry, astronomy, architecture, land surveying and town planning from both Eastern and Western civilizations. The practically-oriented historic texts provide only the method and no indication of why it works. Other, more theoretically-informed historic texts, show knowledge of why the method is approximate. They make some suggestions for increased accuracy including the use of repeated measurements, trigonometry and the sun's declination, the angle of the sun above or below the celestial equator. There are several variations on the Indian Circle. An extension is a more elaborate method involving the observation of 3 shadows accompanied by a proof in 3-dimensional geometry. The shadow curve is approximately a conic section depending on the latitude and sun's declination. In various epochs and cultures, the method of equal altitudes was a central part of the extensive work that was done with gnomons and shadows for sundials, calendars, and the determination of the meridian and the equinoxes and solstices. The procedure was often part of the initial stage of the ritualized surveying, orienting and geometric laying out, of mandalas, altars, temples and towns. The method of equal altitudes was deemed to re-enact, on a smaller scale, the larger dynamic creation and structure of the universe, and thereby applied the law of the correspondence of the microcosm and macrocosm. The Indian Circle is a pervasive example of the central and profound importance of mathematics to art, architecture, cosmology and philosophy.