Schedule of Talks for the 2019-2020 Academic Year
Date: Wednesday, October 2, 2019
Speaker: Prof. Robert E. Bradley
Department of Mathematics and Computer Science
Adelphi University
Email: bradley AT adelphi DOT edu
Title: Series: Convergent, Divergent ... Whatever!
Abstract: A few years ago, the more mathy corners of the internet were in a tizzy over the assertion that

1 + 2 + 3 + 4 + ... = -1/12,

a result which is actually used in string theory. Of course, this series is not convergent in the usual sense, so in what sense does this identity hold?

In this talk, we investigate some of the early uses of divergent series, especially by Leonhard Euler (1707-1783). We examine the introduction of the modern definition of convergent and divergent series by Augustin-Louis Cauchy (1789-1857) in 1821. We discuss the ideas of Ernesto Cesaro (1859-1906) and Niels Heinrik Abel (1802-1829) that extend the notion of convergence. We conclude with an examination of a tour de force by Euler and Cauchy: an elementary proof of the convergence of the binomial series.

This talk will be accessible to anyone who has taken two semesters of calculus.

Date: Wednesday, November 6, 2019
Speaker: Prof. Glen Van Brummelen
Institute for Advanced Study
Quest University
Email: gvb AT questu DOT ca
Title: The Forgotten Man: Astronomy in the Transformative 15th Century
Abstract: We know a lot less than we think. The history of mathematics is partly a record of what happened, but uncomfortably more than we might expect, over the decades it has also been a record of what we care about. We will explore one episode that illustrates the "forgotten" history of mathematics, in early 15th-century mathematical astronomy. The forgotten man is Giovanni Bianchini, the CFO from Ferrara who turned his eye away from bookkeeping and toward the heavens. His unusual path to academia provoked a number of revolutions, including among others the birth of the European tangent function. Overlooked in the shadow cast by his now more illustrious successor Regiomontanus, Bianchini's role in the history of mathematics and science fully deserves a resurrection.
Date: Wednesday, December 4, 2019
Speaker: Prof. Josh Hiller
Department of Mathematics and Computer Science
Adelphi University
johiller AT adelphi DOT edu
Title: A historical and axiomatic look at the Armitage and Doll multistage model of carcinogenesis
Abstract: In 1954, Armitage and Doll published one of the most influential papers in the history of mathematical epidemiology. However, when one examines the literature one finds that there are in fact several distinct mathematical models attributed to the 1954 paper. In thistalk, we examine this important paper and the mathematical derivation of the model. We find, very surprisingly, that no stochastic process can account for all the assumptions of the model and that many of the models in the literature use a consistent subset of the assumptions used in Armitage and Doll's paper.
Date: Wednesday, March 4, 2020
Speaker: TBA


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Date: Wednesday, April 1, 2020
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Date: Wednesday, May 6, 2020
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