Department of Mathematics

West Chester University

**Mathematics Information**

Office: Room 101

25 University Avenue

West Chester, PA 19383

Phone (610) 436-2440

Fax (610) 738-0578

Email: Department Chair

Each Thursday there will be a mathematics seminar (usually in UNA 127 from 3:15-4:15), while colloquium talks will normally be on a Wednesday (usually in UNA 158 from 3:15-4:15).

These seminars/colloquium talks may be by visiting speakers, WCU faculty, or WCU students, and are open to all interested students and faculty.

Send an e-mail to jmclaughl@wcupa.edu, if you would like to be on the e-mail list to receive advance notice of upcoming talks.

Previous Semesters: Fall 2007, Spring 2007, Fall 2006, Summer 2006, Spring 2006,

**Thursday, January 24th, 2008**

3:15 pm in 115 Anderson Hall

**James Mc Laughlin** (West Chester University)

**The AGM: an introduction to the arithmetic-geometric mean **

**Thursday, January 31st, 2008**

3:15 pm in 115 Anderson Hall

**Michael Rowell** (Pennsylvania State University)

**An introduction to q-series and Partition Theory **

We will introduce q-series notation and some classical q-series identities. We will discuss two proof methods which can aid in exploring q-series: analytic methods and combinatorial methods. Our discussion will provide examples which illustrate of the importance of each method and how the two methods relate.

**Thursday, February 7th, 2008 **

3:30 pm in 115 Anderson Hall

**Todd Drumm** (University of Pennsylvania)

**Infinity: it's not just for a single point any more **

We will look at one point compactifications of the line and the plane and extend these ideas to flat space-times. In these compactifications, or "Einstein Universes", we will find an ideal circle, the cone-at-infinity and the improper point. We will further investigate these new spaces by examining the compactifications of some standard objects.

**Tuesday, February 5th, 2008**

3:15 pm in 120 Anderson Hall

**Rosemary Sullivan** (West Chester University)

**The Boundary Distribution in Crofton's Theorem **

In the late nineteenth century M.W. Crofton stated a differential equation which relates the probability of an event involving n random points in a domain to the probability of the same event involving n-1 random points in the domain and one point on the boundary of the domain. Crofton's statement of the theorem omits specifying the distribution of the point on the boundary. A method using standard probability conditioning techniques will be given for computing the measure of the point on the boundary. An example illustrating this method will be presented.

**Thursday, February 14th, 2008 **

3:15 pm in 115 Anderson Hall

**Michael Fisher** (Fresno State University)

**Distinguishing Colorings of Cartesian Products of Complete Graphs **

We determine the values of s and t for which there is a coloring of the edges of the complete bipartite graph Ks,t which admits only the identity automorphism. In particular, this allows us to determine the distinguishing number of the Cartesian product of complete graphs.

**Thursday, February 21st, 2008**

3:15 pm in UNA 109

**Professor Peter Zimmer** (West Chester University)

**Poly-Basic Hypergeometric Identities, III**

**Thursday, October 23rd, 2008**

3:15 pm in 115 Anderson Hall

**James Mc Laughlin** (West Chester University)

**The AGM and Complete Elliptic Integrals of the First Kind: I**

**Wednesday, February 27th, 2008**

3:20 pm in 120 Anderson Hall

**Lin Tan** (West Chester University)

**Variations on a Theme by Moser**

We will present the investigation into the Moser Triangle, consisting of the numbers of lattice points of up to a fixed (taxi-cab) distance away from the origin. The presentation will emphasize its analogy with the Pascal Triangle, various recurrence relations among the entries of the Moser Triangle, and its connections with various sequences of numbers, such as the Fibonacci numbers, the ``side and diagonal numbers," among others. The main tool will be the method of generating functions. The talk is of expository nature, and is accessible to undergraduate math majors.

**Thursday, March 6th, 2008**

3:15 pm in 115 Anderson Hall

**James Mc Laughlin** (West Chester University)

**The AGM and Complete Elliptic Integrals of the First Kind: II**

**Thursday, March 27th, 2008**

3:15 pm in 115 Anderson Hall

**Ian Melbourne** (University of Surrey, UK)

**Decay of correlations for Lorentz gases**

The planar periodic Lorentz gas is a deterministic model for stochasticity. In particular, it is known that the motion of almost every gas molecule is asymptotically like a sample path for planar Brownian motion. Less well-understood is the decay of correlation (loss of memory/gain of statistical independence) for such systems. In this talk, I will describe recent, and in some cases on-going, results on decay of correlations for various continuous time Lorentz gas models, including (in)finite horizon Lorentz gases, Bunimovich stadia, and cuspoidal domains. In particular, a recent result proves that the classical infinite horizon Lorentz gas with a doubly periodic array of circular scatterers has decay of correlation rate 1/t as anticipated by physicists.

**Tuesday, April 1st, 2008**

3:15 pm in 103 Anderson Hall

**James Hamblin** (Shippensburg University)

**Alternative Voting Methods: Choosing a Winner**

There have been many controversial elections in recent history, including the infamous 2000 Presidential race in Florida. Whenever there is a close election, there seems to be an outcry for a new voting system to be used. In this talk we will discuss some of these alternative voting systems (many of which are used around the world) and the advantages and disadvantages of each. Choosing the winner of an election is not as easy as you might think... [This talk is suitable for a general audience and does not assume any advanced mathematical knowledge.]

The tactics insights have application in real life search problems where one is trying to quickly determine the location of multiple different-sized threatening (or valuable) objects.

**Thursday, April 17th, 2008**

3:15 pm in 115 Anderson Hall

**James Mc Laughlin**(West Chester University)

**The AGM and Complete Elliptic Integrals of the First Kind: III**