Undergraduate Math Club

Abstract: Many people believe that mathematics consists of two disjoint halves: the continuous part such as stuff we learned from a calculus class and the discrete part such as counting learned from our childhood. This talk discusses the connection between these two. In particular, we will talk about the Mobius inversion in number theory, its history and how to use it to recover the foundamental theorem of calculus, Newton-Leibnitz formula.

Twenty years ago the study of projective geometry would have seemed somewhat like the study of Latin: good for the brain and a means to keep in contact with the ancients. Today, however, projective geometry is a popular subject with mathematicians and computer scientists. This is due to the new applications to computer vision and to the fact that geometry and geometric thinking are again on the upswing. Moreover, computer science has returned the favor by providing powerful tools for the visualization and diffusion of mathematics. Java applets, animated GIF images, and linked HTML pages allow us to present mathematics and, most particularly, geometry in a way that was unthinkable twenty years ago.

In this talk we will give a short introduction to projective geometry using PyGeo, a powerful and freely available visualization tool written in Python and developed by Arthur Siegel (who may come and participate in the talk.)