Math Colloquia

FLC Mathematics Colloquia are a series of talks given by FLC Math faculty, FLC Math students, and math researchers from outside the college. Usually the talks are about interesting mathematical topics, which we always try to make sure are accessible to everyone. Sometimes we change things up a bit and and talk about some more practical matters like what math class you should take next or careers in math.

Here are the recent/upcoming talks:

Thursday, October 30 at 4:30 pm in EBH 118

Speaker: Kathy Merrill

Title: Continued Fractions

Abstract: Mathematical applications regularly require that we make simple rational approximations to messy numbers. For example, building the scale used in western music requires reconciling fifths and octaves, and thus making a simple approximation to the log (base 2) of 3. Developing a calendar based on both lunar and solar cycles requires a simple approximation to (365.242199)/(29.350588). Continued fractions provide the best way of approximating irrationals and messy fractions with simple fractions. This talk will describe the continued fraction algorithm both numerically and geometrically, and discuss applications that make use of it, such as those mentioned above. We will also explore continued fraction approximations for old friends like e, pi, the square root of 2, and the golden mean.

Thursday, October 16 at 4:30 pm in EBH 118

Speaker: Mike Johnson (Swarthmore College)

Title: Relating Dynamical Systems to Arithmetic Progressions

Abstract: Given finitely many colors, we assign a color to each positive
integer. Given any such coloring of the integers, van der Waerden's
Theorem states that we can find arithmetic progressions of any length,
where each term has the same color. More recently, Furstenberg showed that
finding arithmetic progressions in subsets of the integers has connections
to the field of dynamical systems. In dynamical systems, we study the
behavior of functions that transform a space while preserving volume. We
describe how recurrence properties of such functions can be used to prove
theorems like van der Waerden's.

Tuesday, September 30 at 4:30 pm in EBH 118

Speaker: Laura Scull (University of British Columbia/Future FLC Faculty)

Title: Counting votes in an election: How hard can that be?

Abstract: Counting up the votes cast in an election and determining the winner seems like it should be the easy part of democracy. Surprisingly, as soon as there are more than two candidates, this becomes delicate. I will discuss various vote-counting methods in use from a mathematical standpoint, and show some of the pitfalls of the process.

Thursday, September 25 at 4:30 pm in EBH 118

Speaker: Hilary Smallwood (FLC Student)

Title: Rings, Graphs and Irreducible Divisors: A Summer REU at Wabash College

Abstract: This summer I attended a Research Experience for Undergraduates in Indiana. This was a great experience and I would recommend it to anyone interested in math research and higher math. I will share some of my results regarding irreducible divisor graphs of ring elements. Background on ring theory and graph theory will be provided prior to the presentation of research results.

A list of colloquia from the 2007 - 2008 school year can be found here.