Mathematics

Presentation by T. Christine Stevens Professor Emerita, Saint Louis University, Associate Executive Director of American Mathematical Society Operatic bass Jerome Hines, who died in 2003, sang at the New York Metropolitan Opera for over forty years. He was also a math major who retained a lifelong interest in mathematics. In the 1950’s he published several papers based on work that he had done as a student. Our speaker will focus on the first of these papers, which describes a new method for finding the solutions of an equation.

Professor Peter Schumer will present a mathematics seminar talk on “The Bernoulli Family and Some of their Mathematical Creations.” The Swiss Bernoulli family included at least eight prominent mathematicians and scientists. He will discuss a bit of their family history - especially brothers Jakob (1654 - 1705) and Johann (1667 - 1748) and Johann’s son Daniel (1700 - 1782). He will then give a brief overview of some of their interesting mathematics such as the brachistochrone problem (curve of quickest descent) and the gambling problem known as the St. Petersburg Paradox.

Senior mathematics majors will speak about their theses: 3:00 pm: Kate Stewart: “Modeling Vermont’s Heroin Epidemic” 3:30 pm: Jillian Green: “A Technology Based Rumor Spreading Model for College Campuses” 4:00 pm; Jordan DuBeau: “Inaccessible Cardinals: How Big Can Infinity Be?”

Senior mathematics majors will speak on the topics of their theses. 3;00 pm: Calvin Kim “The Four Color Theorem” 3:30 pm: Eliot Van Valkenberg “Nonperiodic Tilings of the Plane” 4:00 pm: Tiffany Hau “The AKS Primality Test” There will be a second round of presentations on Thursday, May 12

Lecture by Kathryn Montovan of Bennington College . Mathematical modeling, simulation, and analysis are valuable tools for answering biological questions about evolution, self-organization, and complex ecosystem interactions. For each biological question the appropriate mathematical tools must be carefully employed in order to produce meaningful results. This talk will present several recent projects to illustrate the process of taking a biological problem and making it into a mathematical one, the mathematics used to answer the question, and the biological meaning of the results.

Lecture by Donna Beers of Simmons College Just as you can alter pictures to make yourself look more attractive, so, too, politicians, advertisers, and others with particular agendas are using digital imaging tools to manipulate photos to create false impressions. Determining whether a photo has been doctored is just one of the many questions that photo forensics tries to answer. The good news is that linear algebra offers powerful tools for carrying out digital photo forensics.

A New Proof of the Generalized Wilson’s Theorem Wilson’s Theorem is a staple of elementary number theory: for a prime number p, (p-1)! is congruent to -1 modulo p. Suppose we would like to generalize Wilson’s theorem. Why? Well, the title says so: in fact it is, verbatim, the title of a 1903 paper by the American group theorist G.A. Miller. But more fundamentally: why not? Shouldn’t we be trying to generalize all the theorems we meet? I think so. In this talk we will contemplate several possible generalizations and then hit upon two that are discussed in Miller’s paper.

Exploring the Gompertz Curve as a Mathematical Model Michael Olinick Many dynamic processes exhibit continuous growth in some quantity of special interest. The growth frequently follows a pattern of initial rapid expansion eventually transitioning through an inflection point to an approach toward a limiting value. The graph of the size of the quantity over time is often an S-shaped curve. The logistic curve is the most common model for such growth, but the Gompertz curve often does a more accurate job in mirroring the real world.

Navajo Math Circles is a one-hour film that documents the meeting of two worlds: that of some of the country’s most accomplished mathematicians and mathematics educators, with the children and teachers in the underserved, largely rural Navajo educational system. Hundreds of Navajo children in recent years have found themselves at the center of a lively collaboration with mathematicians from around the world.

Pierre de Fermat and the Method of Infinite Descent Peter Schumer, Middlebury College Pierre de Fermat (1601 – 1665) is known as the “prince of amateurs” for his many important independent contributions to mathematics including his creation of analytic geometry, the beginnings of probability theory, and many key concepts and techniques that led to the development of calculus. We will discuss some of his imaginative number-theoretic observations and suggest how he may have discovered them. In particular, we will focus mainly on his method of infinite descent.