For the faculty members whose main focus is teaching undergraduate students, PCMI offers the opportunity to renew excitement about mathematics, talk with peers about new teaching approaches, address some challenging research questions, and interact with the broader mathematical community. Each year the theme of the UFP bridges the research and education themes of the Summer Session.
The 27th Annual PCMI Summer Session will be held June 25 – July 15, 2017.
Click HERE to apply to the Undergraduate Faculty Program.
Victor Moll, Tulane University
There is a richness and a beauty in the study of special functions that is appealing to almost all mathematicians (despite the fact that most mathematicians only have a hazy view as to what special functions are). With Experimental Mathematics and the use of modern software such as Mathematica, this richness can be shared with undergraduates. Various special functions, under the general name `hypergeometric functions', and their special values appear throughout mathematics, in areas ranging from number theory to combinatorics to physics. Most of the elementary functions of Calculus appear in this form.
The Undergraduate Faculty Program will explore properties of these functions using Mathematica. The data collected from these experiments will be used to generate conjectures about arithmetic properties of the coefficients of these special functions. Given that these functions have been around for a long time, it is surprising that these type of questions have not been decided. Many of these lead to beautiful pictures that await for an explanation.
The participants will be given a variety of projects at the beginning of the program. These will be flexible to match personal interests. By the end of the three weeks, ideally people will have the questions and the tools needed to work on research in special functions, both on their own and with students.
No particular knowledge of special functions is required, as the background material will be covered during the program.