Mathematics & Computer Science
'14 Fall Semester
On October 24, Math/CS Colloquium at 2:00PM in Shankweiler 440s.
Dr. Lindsey Nagy, Assistant Professor of Economics of Muhlenberg College, will present:
How Price Discounts Can Thwart Sniping on eBay.
"This talk will discuss a commonly used late bidding strategy on eBay called sniping. We will explore why some bidders use it, why it hurts sellers' profits, and a way in which we can mitigate it. I will present a theoretical model of an eBay-like auction and show that sniping, under some conditions, can emerge as a symmetric equilibrium strategy. To incentivize bidders to deviate from this behavior, I propose a credit mechanism, which awards an early bidder with a price discount. Relative to the surplus generated by the sniping equilibrium, implementing the credit increases seller surplus and improves welfare. If time permits, I will also present results from a controlled experiment that was designed to test the effectiveness of the credit mechanism at thwarting sniping."
On October 25, two Muhlenberg College mathematics majors will be speaking at the Eastern Pennsylvania and Delaware Section of the Mathematical Association of America meeting held at the University of the Sciences in Philadelphia.
Benjamin Nassau, Muhlenberg College
The Local to Global Principle of Apollonian Circle Packings: What It Is and How to Show It
Integral Apollonian packings nested fractals of tangent circles display interesting properties, especially when considering the curvatures of the circles in a packing. We are interested in the arithmetic properties of the set of curvatures in an integral packing. We know that no matter how far we "zoom in" on a packing, we will only achieve curvatures equivalent to certain values modulo 24. It has been conjectured that while these local obstructions exist, only finitely many curvatures that satisfy these equivalence classes do not show up in the entire packing. While some headway has been made experimentally to prove this conjecture and to determine at what integer these curvatures begin appearing consistently, no definite answer has been found. We will discuss a computational approach to determining at what integer these curvatures begin appearing consistently.
Myles Dworkin, Muhlenberg College
Pythagorean Theorem in Spherical Geometry
The Pythagorean Theorem is one of the most well-known and widespread theorems in mathematics. Its existence in Euclidean Geometry is a corner stone of the model and marks one of the first major differences between it and neutral geometry. Its beauty lies in its simplicity as it relates geometric objects to one another. Although we typically focus on the relationship between squares, the same relationship holds for all regularly constructed figures including circles. As we explore these relationships in non-Euclidean geometries we must first reevaluate our idea of a right triangle before investigating the connection between various geometric figures. Work by Paolo Maraner in 2010 explores how to generalize these concepts in spherical geometry. In this talk I will explain his work and suggest further areas of study. Emphasis will be given to the relationship between equilateral, equiangular quadrilaterals constructed on the sides of triangles.
On November 14, Math/CS Colloquium at 2:00PM in Ettinger 108
Student Summer Experiences
Five math and computer science majors describe how they spent their summers, as well as how they got their summer position. The speakers are Macauley Breault, Ben Burwell, Katie Casty, Ryan Moran, and Andrew Trautmann.