Schedule of Talks for the 2000-2001 Academic Year
Date: Wednesday, October 4, 2000
Speaker: Prof. Amy E. Shell
Department of Mathematics
United States Military Academy
Title: Mina Rees and Her Influence on Mathematical Research
Abstract: Mina Spiegel Rees (1902-1997) had a profound effect on mathematics and mathematical research during the middle years of the twentieth century, which is still felt today. Her tenure at the head of the Mathematical Sciences Division of the Office of Naval Research during its inception after World War II shaped much of academic research in mathematics and computers. Her leadership in establishing the Graduate School and University Center of the City University of New York during the 1960s influenced graduate education in the United States.
Date: Thursday, November 9, 2000
Speaker: Prof. Francine Abeles
Department of Mathematics
Kean University
Title: Lewis Carroll's "Game" of Voting
Abstract: In the 1870s, Charles L. Dodgson (Lewis Carroll) wrote three pamphlets applying his mathematical skills to the political procedures at work in the committees that were then, and remain, ubiquitous in academic life. These pamphlets, grounded in issues of fairness like minority representation, reflect his thinking about how a committee should select the best candidate or proposal. On the strength of these pamphlets, Dodgson is now considered as a voting theorist second only to the great eighteenth century French social scientist and philosopher, the Marquis de Condorcet.

In this talk, I will discuss the circumstances that motivated Dodgson to write these pamphlets, and I will sketch some later developments, for example in social choice theory, game theory, and computational complexity that illustrate the modern relevance of his work.

Date: Wednesday, December 6, 2000
Speaker: Prof. Rob Bradley
Department of Mathematics & Computer Science
Adelphi University
Title: Leonard Euler and the Genoese Lottery
Abstract: Most States in the USA sponsor lotteries of the following type: k numbers are randomly chosen from among the first n positive integers, and players are paid off at various rates if they have correctly guessed some of the k winning numbers. In New York's Lotto, for example, n=51 and k=6.

Lotteries like this took Europe by storm in the 18th century. When Frederick the Great of Prussia was approached with a scheme to begin such a lottery in Berlin, he called upon Leonard Euler (1707-1783), the leading mathematician of his day and a member of the Berlin Academy, for a mathematical analysis of the proposal. Euler devoted a substantial portion of his writings in probability theory to the analysis of games of chance. In this talk, I will survey Euler's writings about lotteries, beginning with the royal charge of Frederick the Great, and summarize his findings.

Date: Wednesday, January 24, 2001
Speaker: Prof. Rudiger Thiele
Department of the History of Science
University of Leipzig
Title: The Brachistochrone Problem
Abstract: The Brachistochrone problem posed by John Bernoulli in 1696 served as a starting point for many important mathematical developments. Firstly, it stimulated a cascade of related problems, thereby establishing a new branch of mathematics: the Calculus of Variations. Secondly, it gave rise to a mathematical formulation linking such disparate branches as Geometry, Mechanics, Optics (and even Philosophy by extremal principles). Thirdly, it resulted in the concept of function changing to that of an analytic function. In addition to these cornerstones in the history of mathematics, the famous quarrels between the Bernoulli brothers give an insight into personal and social conditions of the learned world three centuries ago.
Date: Wednesday, February 7, 2001
Speaker: Prof. Glen van Brummelen
Department of Mathematics
Bennington College
Title: A Millennial Journey, Y1K: Episodes in the Renaissance of Islamic Mathematical Astronomy
Abstract: Although Islamic mathematical astronomy owed a great debt to its Ptolemaic ancestry, it transformed into a unique and creative discipline between the 11th and 15th centuries. The turn of the millennium (in our calendar) may be seen as the birthdate of a distinct astronomical science. We explore two episodes: firstly, the beginnings of the establishment of spherical trigonometry as a discipline independent of astronomy as seen through the eyes of Abu Sahl al-Kuhi, a pure geometer and methodological conservative. Secondly, we derive the reasonings behind Kushyar ibn Labban's tables for computing planetary positions, one of the first attempts to improve on Ptolemaic procedures.
Date: Wednesday, March 7, 2001
Speaker: Prof. Jack Winn
Department of Mathematics
SUNY Farmingdale
Title: Fifty Years of Mathematics Curriculum Reform - Common Problems and Connecting Themes
Abstract: It is generally agreed that at the end of World War II the mathematics curriculum was antiquated. It did not reflect the applied mathematical advances made during the war and was devoid of the "modern point of view" that could be traced to such masters as Riemann, Lobachevski, Hilbert, and Hamilton, etc. Mathematicians returning from the war were prepared to address this state of affairs. In the second half of the twentieth century a very rich body of curriculum innovation emerged due in part to some of the most creative mathematical minds of the time. One might even detect a cycle of frustration generated by seemingly under-prepared students followed by a reform effort, that has continued over the years. The speaker will present the highlights of these reform efforts pointing out common themes and the controversies that ensued. Examples of curriculum materials will be provided.
Date: Wednesday, April 4, 2001
Speaker: Prof. Agnes Kalemaris
Department of Mathematics
SUNY Farmingdale
Title: Could You Pass the Entrance Examination?
Abstract: This paper will look at some questions asked in "arithmetic," "algebra," and "geometry" sections of the mathematics examinations for college entrance in the USA between 1878 and 1884. The topics seem familiar: finding roots, solving systems of equations, factoring, and verbal problems. However, many of the questions will have some interesting surprises for faculty and students at the beginning of the twenty-first century.
Date: Wednesday, May 2, 2001
Speaker: Prof. Karen Parshall
Department of Mathematics/Department of History
University of Virginia
Title: Entering the International Arena: The Impact of Hilbert's Grundlagen der Geometrie on the American Mathematical Community
Video Stream: Click here
Abstract: This talk will focus on the reception in the United States of Hilbert's 1899 text Grundlagen der Geometrie. In particular, it will analyze both the rise of postulational mathematics in America and the role of University of Chicago mathematicians and others in those developments.