Schedule of Talks for the 2015-2016 Academic Year

Date: Wednesday, October 14, 2015 Speaker: Prof. Sloan Despeaux Matheamtics and Computer Science Department Western Carolina University Email: despeaux AT email DOT wcu DOT edu Title: Augustus De Morgan's Budget of Paradoxes Abstract: De Morgan's often-quoted and highly entertaining work, A Budget of Paradoxes, was an natural outgrowth of his anonymous book reviews for the weekly London-based literary magazine, The Athenaeum. This talk will give a sample some of the Budget's most enjoyable excerpts, discuss De Morgan's motivations for writing them, and consider why the work enjoyed such wide-ranging appeal.

Date: Wednesday, November 4, 2015 Speaker: Prof. Laura Turner Department of Mathematics SUNY New Palz Email: turnerl AT newpaltz DOT edu Title: Analytic representations and generality in mathematics in the late 19th century Abstract: "Analytic representations" of functions were widely employed and studied during the late 19th century. They appear in countless papers from this period, sometimes serving as helpful tools and other times as the focal point of an exposition. In spite of their popularity, however, the task of uncovering the the reasons for their widespread use is largely uncharted territory. What is more, their very definition represents shaky ground, highlighting both the fluidity of these objects and the benefit to be gained from closer historical consideration. In my talk we will explore precisely why studies of analytic representations were so widespread and the roles they served for different individuals, devoting particular attention to the circles of Hermite and Weierstrass and the reception of the body of results which together are known as the Mittag-Leffler Theorem. As we will see, analytic representations of functions were seen as foundational precisely because their applications, some examples of which we will consider. What is more, by virtue of this foundational character, they forged a crucial bridge between analytic and developing synthetic methods by rooting new set-theoretic concepts in older, established fields.

Date: Wednesday, December 2, 2015 Speaker: Title: [Postponed to March 2016] Abstract:

Date: Wednesday, March 2, 2016 Speaker: Prof. Alan Gluchoff Department of Mathematical and Statistics Villanova University Email: alan DOT gluchoff AT villanova DOT edu Title: The Spread of Nomography in America from 1900 to 1925: Perspectives from Mathematics, Engineering, and Education Abstract: Nomography - loosely defined as the use of geometric ideas and constructions to build computational diagrams - is a mathematical discipline of French origin dating from the mid nineteenth century. Its absorption by the United States, beginning around 1900, is an interesting story of the diffusion of a mathematical discipline into a new environment, a story involving several communities in that environment. We will examine its influence on the engineering, mathematical, and school communities and see how the embrace of nomography affected and was affected by these parties. Societal trends favoring the use of nomography will be mentioned. Along the way we will meet some familiar figures in American mathematical history: E.H. Moore, Frank Morley, O. D. Kellogg, and T.H. Gronwall all played a role in the propagation of nomography.

Date: Wednesday, April 6, 2016 Speaker: Prof. Robert E. Bradley Dept. of Mathematics and Computer Science Adelphi University Email: bradley AT adelphi DOT edu Title: Polar Ordinates in L'Hôpital's Analyse Abstract: Priority of publication for polar coordinates is usually given to Jakob Bernoulli (1691), although priority for the invention seems to belong to Newton, whose results were only published posthumously, more than forty years later. However, it was not until the middle of the 18th century that polar coordinates took on a form that would be recognized by today's readers. Earlier versions all featured ordinates emanating from a single point or pole, with some geometric construction playing the role that now belongs to an angular coordinate. The largest and most accessible collection of these early schemes of polar ordinates is to be found in the Marquis de l'Hôpital's Analyse des infiniment petits (1696), based on the lessons given to the Marquis by Johann Bernoulli. In this presentation, we will examine Bernoulli's approaches to polar ordinates, as presented in l'Hôpital's textbook.

Date: Wednesday, May 4, 2016 Speaker: Prof. V. Frederick Rickey Dept. of Mathematics USMA (emeritus) fred DOT rickey AT me DOT com Title: E228 Abstract: How's that for the shortest title ever? How can you decide if a number is the sum of two squares? Euler begins with the dumbest possible algorithm you can think of: Take the number, subtract a square, and check if the remainder is a square. If not, repeat, repeat, repeat. But Euler, being Euler, finds a way of converting all those subtractions into additions. Then he does several things to speed up the computation even more (but, sadly, does not explain himself very well). He applies this to 1,000,009, and - in less than a page - finds that there are two ways to express this as a sum of squares. Hence, by earlier work in E228, it is not a prime. Amusingly, when he later described how to prepare a table of primes "ad milionem et ultra" (E467), he includes this number as prime. So he then feels obliged to write another paper, E699, using another refinement of his method, to show that 1,000,009 is not prime.