# Undergrad Colloquium Fall 2015

McHenry Building - Room 4130

For further information please contact Richard Gottesman or call the Mathematics Department at 459-2969

**Monday, October 5, 2015
TBA
**

**Monday, October 12, 2015
** The notion of an integral is sometimes intuitively explained as the area formed by an infinite number of infinitesimal strips. But what do we mean when we say 'infinitesimal'? A number bigger than 0 and yet smaller than any positive decimal expansion? And yet infinitesimal numbers played quite an important role in mathematical history before falling out of favor due to their philosophically unsettling behavior. In this talk, we will show one formal construction of the 'infinitesimal' or 'hyperreal' numbers that eradicates that unsettling behavior and replaces it with better logical footing. With time permitting, we will introduce the notion of galaxies, monads, and discuss the importance of Robinson's Transfer Principle.

*"A "small" introduction to infinitesimals."*Bob Hingtgen, University of California, Santa Cruz

**Monday, October 19, 2015
No Colloquium**

**Monday, October 26, 2015
** We discuss the beginnings of billiard dynamics. At a minimum we aim to give a rather complete sketch of how two one-dimensional billiards moving according to the standard laws of elastic collision in physics can count the digits of pi.

*"Billiards."*Richard Montgomery, University of California, Santa Cruz

(Reference: Tabachnikov: Geometry and Billiards.)

**Monday, November 2, 2015
** Did you know that a math major can open the door to careers in mathematics education research? Work at research and development centers includes designing curriculum, piloting assessments, and more. This presentation provides an overview of career opportunities for students interested in mathematics education. Although you may be familiar with teaching as an option, there are other possible paths, including a PhD in mathematics education for those interested in college and university level positions. Currently there is a shortage of qualified applicants for such positions, so pursuing a graduate degree in mathematics education can prove intellectually stimulating, practical and rewarding.

*"Careers in Math Education."*Dr. Judit Moschkovich, University of California, Santa Cruz Education Department

**Monday, November 9, 2015**

**TBA**

**Monday, November 16, 2015
TBA
**

**Monday, November 23, 2015
**In this talk I will pose to the audience a few problems in integral calculus (at the level of Math 11a/19b). The solutions to these problems will lead us to some surprising realizations about the torus. Afterward I will demonstrate how one may deduce these results by visual inspection and an appeal to Pappus’ theorem. Audience participation will be encouraged.

*"Surprising Properties of the Torus Arising from Basic Integral Calculus."*Richard Kelvan, University of California, Santa Cruz

**Monday, November 30, 2015**

**TBA**