Cornelia Van Cott is a professor of mathematics at the University of San Francisco. A native of Indiana, Cornelia earned her bachelor's degree in mathematics from Wheaton College and her PhD in mathematics from Indiana University. Most of Cornelia's research focuses on topology, specifically knots and surfaces in 3 and 4 dimensions. She also likes the challenge of working with undergraduate students on research projects unrelated to topology. Cornelia enjoys teaching courses throughout the math curriculum during the school year. In the summertime, she enjoys teaching courses on fun, non-standard math topics at MathPath, a national residential summer camp for middle schoolers who love mathematics.

Title: The Change-Making Problem

Abstract: when cashiers give us change, we prefer to receive it in as few bills and coins as possible. In the United States, cashiers get this done using the so-called greedy algorithm. But will the greedy algorithm work with a different coin system? This leads to a question in discrete mathematics called the change-making problem. Over the last 50 years, mathematicians have laid the groundwork for understanding this problem, but lots of opportunities for new investigation remain.

Victor H. Moll was born in Santiago, Chile on Halloween 1956. His father was a doctor in a small mining town, Cabildo. He moved to Valparaiso, the main port city after his father early death. There he studied in a British school, where he learned the language and discovered his love for mathematics. After graduation from Universidad Santa Maria in 1978, he enrolled in graduate school at the Courant Institute in New York City. There he met his (future) wife Lisa Fauci, also a graduate student. In 1986 both moved to New Orleans for a job at Tulane University. The plan was to be there for a short time before going back to the northeast. We never moved from the Big Easy.

He has many mathematical interests, most of them concerning the question how to evaluate integrals and what does one learn from that? He specially enjoys working with students at all levels (undergraduate, graduate, colleagues, amateur and retired mathematicians). He is a strong believer in the unity of Mathematics.

Title: Integral Tales: Some Unexpected Connections

Abstract: during the process of learning Calculus one observes that there is a well-defined list of rules to compute derivatives: product, quotient and chain rules are among the first taught in every class. On the other hand, when one tries to compute integrals, the student is left with a feeling that now there is simply a collection of tricks. There is no clear reason of why one can integrate \(e^{x}\) is a simple manner, but the integral of \(e^{x^{2}}\) is more complicated. One learns these tricks from the instructor, by talking to older classmates or by searching for them online. At the end, there seems to be no systematic way of doing this.

It is remarkable that, in the search of producing closed-forms of definite integrals, one finds many interesting connections with apparently disjoint parts of mathematics. Examples will include (1) properties of a collection of positive integers appearing in the evaluation of a rational functions, (2) a planar dynamical system connected with a variation of the arithmetic-geometric mean and (3) a list of definite integrals involving the gamma function.

The lecture will be suitable for undergraduates and it will include stories about how the speaker got involved in such projects.