October 20, 2011. Patricia Allaire, Queensborough Community College, City University of New York
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 six 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.
November 17, 2011. Chris Rorres, University of Pennsylvania
Title: "The Turn of the Screw: The History and Optimal Design of an Archimedes Screw"
Abstract: The Archimedes Screw is one of the oldest machines still in use today. It is now enjoying renewed popularity because of its proven trouble-free design, its ability to lift wastewater and debris-laden water effectively, and its gentle treatment of aquatic life. Within the last decade it has also found a new application in the generation of electricity by being run backwards. In this presentation I will give a history of this device from Archimedes' time (3rd century BC) to the present day and also discuss my past and proposed research on the design of the Screw that maximizes the amount of water lifted or lowered in each turn of the screw.
December 8, 2011. Brittany Shields, University of Pennsylvania
Title: “The Architecture of Mathematical Institutes: A Comparative Study of Göttingen and NYU’s Mathematical Institutes under the Leadership of Richard Courant”
Abstract: In this study of the cultural history of mathematics, I consider the architecture of mathematical institutes as historical artifacts. The buildings in which mathematical research and teaching take place offer incredible insight into the work practices, as well as social and cultural identities, of the mathematicians who inhabit these spaces. As a case study, I consider the career of the mathematician Richard Courant (1888-1972), who served as director during the construction of two world-class mathematical institutes – the first, in the late 1920s at the University of Göttingen (where he was exiled in 1933), and then in the 1960s at New York University. In both cases, I consider the buildings’ planning, development, construction, and habitation processes, examining blueprints, committee meeting minutes, and correspondence between the mathematicians, university administrators, government officials and philanthropy representatives. Ultimately, I hope to explore how the built environment mattered to those whose work required a certain type of private workspace, desk, and chalkboard –situated in the right relationship to shared workspaces, a mathematics library, classrooms, and other scientific departments. What can the physical environment of mathematical institutes tell the historian about the work practices and social identities of mathematicians?
January 19, 2012. Thomas L. Bartlow, Villanova University
Title: “A Tentative Look at American Postulate Theory”
Abstract: American postulate theory is the body of work of several American mathematicians in the first few decades of the twentieth century, concerned with studying the structure of established mathematical theories by examining fundamental assumptions. They examined alternative postulational formulations and considered desirable features of a postulate system: consistency, independence, completeness, categoricity, brevity. John Corcoran, “On Definitional Equivalence and Related Topics,” History of Symbolic Logic 1 (1980), 231—234, introduced the term “American postulate theory,” identified some of its practitioners and suggested a need for historical study of their work. Michael Scanlan “Who Were the American Postulate Theorists?,” The Journal of Symbolic Logic 56 (1991), 981—1002 and “American Postulate Theorists and Alfred Tarski,”History and Philosophy of Logic 24 (2003), 307-325 identified others, compared two American postulate theorists to European contemporaries, and analyzed their influence on mathematical logicians. I will undertake a broader review, attempting at least partial answers to the following questions: Who contributed to American Postulate Theory? What were the characteristics of their research? Who or what influenced them? Were there mutual influences or rivalries among them? What influence did they have on other lines of mathematical research? Did a theory of postulation develop?
February 16, 2012. Marina Vulis, Fordham University
Title: "Tales of Nineteenth Century Russian Mathematics"
Abstract: The Moscow Mathematical Society, which grew out of a math circle, had its first meeting on September 27, 1864. It was founded with the purpose of promoting mathematical sciences in Russia. In a few years, it started the publication of the "Mathematichekij Sbornik, " the first Russian Mathematics Journal. The Moscow Society reflected the philosophy of the Moscow School of Mathematics which rejected the importance of applied mathematics and emphasized mysticism and spirituality, whereas the St. Petersburg School of Mathematics, influenced by the French school, saw the importance of practical applications in development of mathematical ideas.
Friday, February 17, 2012. Dr. Jesse Frey, Villanova University
Title: "Data-Driven Nonparametric Prediction Intervals"
Abstract: Prediction involves using one sample to make inference on some aspect of a future sample. In this talk, I’ll consider the problem of using a simple random sample of size n to create a prediction interval for an independent future observation from the same distribution. Prediction intervals may be parametric or nonparametric, but I’ll focus on nonparametric intervals. I’ll describe the standard nonparametric prediction intervals, and I’ll also describe new data-driven prediction intervals that outperform the standard intervals. Specifically, the new intervals are much shorter than the standard intervals when the distribution is skewed, and they are only slightly longer than the standard intervals when the distribution is symmetric. Coverage probabilities for the new intervals are determined by using a combination of new theoretical results, Monte Carlo simulations, and known results about Brownian motion and Brownian bridges. All needed background material will be provided.
Friday, March 16, 2012. Dr. Martha Yip, University of Pennsylvania
Title: "Counting Upper-Triangular Nilpotent Matrices of a Given Jordan Type"
Abstract: The Jordan forms of upper triangular nilpotent matrices are indexed by paritions. Over a finite field of q elements, the number of matrices with Jordan form corresponding to a given parition is a polynomial in q. In this talk, I will explain how these polynomials can be calculated recursively. These polynomials are connected to certain q-rook polynomials, and I will show how the recursive formula gives a refinement of q-rook polynomials.
March 22, 2012. Robert E. Bradley, Adelphi University
Title: “The Origins and Contents of de l’Hôpital’s Analyse”
Abstract: Guillaume François Antoine de l’Hôpital’s Analyse des infiniment petits(1696) was the first ever calculus textbook. It was also something of an enigma. For one thing, it was published anonymously, although de L’Hôpital’s authorship was no secret. Also, it made no mention of the integral calculus: instead, its introduction to the differential calculus was followed by what can only be described as an advanced text on differential geometry, motivated by what were then cutting-edge problems in mechanics and optics.
However, the oddest aspect of this book is its genesis. The introductory chapters were based on Johann Bernoulli’s Lectiones de calculo differentialium, lessons that only ever existed in manuscript form and were unknown to the scholarly community until 1921. De l’Hôpital received his copy when he hired Bernoulli to tutor him in 1691-92. Subsequently, he “purchased” the advanced material of the later chapters, in an arrangement under which he supported Bernoulli with a stipend in 1694-95.
In this talk, we will consider both the mathematics that was presented in theAnalyse and the process by which in came into being. We will compare de l’Hôpital’s exposition of the elements of the differential calculus with that of Bernoulli and examine some of the more advanced results presented in the Analyse.
April 13, 2012. Dr. Mohammed Yahdi, Ursinus College
Title: “Mathematical modeling, transmission dynamics and control of antibiotic-resistant infections”
Abstract: The emergence and spread of antibiotic-resistant bacteria is considered to be one of the biggest threats to human health in the 21st century. In the last decade, mathematical models have been increasingly used as tools to identify factors responsible for observed patterns of antimicrobial resistance, to predict the effect of various factors on the prevalence of antimicrobial resistance, and to help design effective control and intervention programs. This talk focuses on the emergence of Vancomycin-Resistant Enterococci (VRE) infections that have been linked to increased mortality and costs in intensive care units (ICU). A new mathematical model is introduced, key factors are determined and simulations are produced. Optimal Control Theory is used to determine efficient and economically favorable strategies to prevent outbreaks and to control the emergence of VRE. Key controls included combinations of the levels of special preventive care, healthcare workers' complicance rates, and health and economical costs.
April 19, 2012. Francine F. Abeles, Kean University
Title: "Hypotheticals, Conditionals, and Implication in Nineteenth Century Britain"
Abstract. Modern logicians ordinarily do not distinguish between the terms hypothetical and conditional. Yet in the late nineteenth century their meanings were quite different.and their tie to implication unclear. In this paper, I will explore the views of four prominent British logicians of the period, W. E. Johnson, J.N. Keynes, H. MacColl, and J. Venn on these issues.
May 1, 2012. John Hessler; Library of Congress, Geography and Map division
Title: "Complexity and Chaos in Medieval Cartography"
Abstract: The source of the peculiar accuracy of certain medieval maps known as Portolan charts has been a mystery that has stumped scholars for hundreds of years. In this presentation I will describe the surprising accuracy of these maps, produced from 1250-1550, using mathematical models based on stochastic processes, like Brownian bridges, and transformational geometry. I will also show how the geometry of these charts develops out of the non-systematic nature of early navigational measurements and the chaotic shifting of the secular part of the earth's geomagnetic field, hints of which are encoded in the data used to make the charts themselves.