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: Spring 2008, Fall 2007, Spring 2007, Fall 2006, Summer 2006, Spring 2006,

**Thursday, September 18th, 2008**

3:15 pm in UNA 109

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

**Introduction to Poly-Basic Identities**

By basic identities, we mean identities of basic hypergeometric series or q-series. A q-series has a base variable usually denoted by q. Poly-basic identities have more than one base. Bibasic have two base variable usually denoted by p and q while in the general case we denote the base variables by q_1, q_2, …,q_n. We will review some the fundamentals of q-series and introduce some poly-basic identities from the literature along with some new identities. The fundamental techniques used in poly-basic identities are quite elementary (from Calculus II) and we hope to find other techniques.

**Thursday, September 25th, 2008**

3:15 pm in UNA 109

**JJ Hennessey, Charles Mattioli, Dan Moran, Cristin Scott, Eric Werley** (West Chester University Students)

**A Fun Summer Using Math: It CAN Happen! **

Listen to five math students share their experiences on internships, research, presenting at conferences, and working to advance their careers this past summer. Focus will be placed on how to find these opportunities and encouraging more students to take advantage of the summer months. These presentations will cover a variety of topics from work with annuities to biostatistics.

**Thursday, October 2nd, 2008**

3:15 pm in UNA 109

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

**Poly-Basic Hypergeometric Identities, II **

**Wednesday, October 8th, 2008**

3:20 - 4:10 pm in UNA 125

**Professor Lin Tan** (West Chester University)

**What Are Elementary Functions?**

Discussion will be made on what are, or rather should be, the characterizing properties of the elementary functions (and their inverses).

**Thursday, October 16th, 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 UNA 109

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

**Mac Mahon's Ω Operator, I**

Let Δ (n) denote the number of incongruent triangles with integer sides and perimeter n. Can you find a closed form for the generating function for this sequence? Over the next couple of weeks we will examine Mac Mahon's Ω operator, which gives a method for finding the generating function for this and other sequences.

**Wednesday, October 29th, 2008**

3:20 - 4:10 pm in UNA 125

**Professor Michael Fisher** (West Chester University)

**The Distinguishing Number of a Graph**

In this talk, I will look at families of graphs whose distinguishing number is known and discuss some of the strategies that have been used to compute this parameter. Time permitting, I will also talk about the related concept of the distinguishing number of a group.

**Wednesday, November 5th, 2008**

3:20 - 4:10 pm in UNA 125

**Bernard McCabe** (West Chester University and Independence Advisors)

**Evaluating Tactics in the Game of Battleship **

In the game Battleship two opponents hide ships of various sizes on a grid, and take turns guessing locations of the opponents ships. The first player to sink all his opponents ships wins. We show how to evaluate three different specific kinds of search strategy for a simplified version of the game, and with heuristic approximations where necessary. We show the benefit to be obtained from the right combination of systematic, randomized, and reactive behavior. We hope to persuade you that this analysis reveals a near optimal strategy. Several open problems are identified.

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.

**Friday, November 14th, 2008**

3:00 - 4:00 pm in UNA 161

**JOHN STILLWELL**(University of San Francisco )

**"The Long Flirtation Between Logic and Combinatorics" **

In the mid-17th century, Leibniz dreamed of a "calculus ratiocinator" that would settle all disputes in logic by combinatorial computation. But little happened until the development of set theory and symbolic logic in the 19th century, and the startling discovery of Gödel incompleteness in 1930. This led to the search for natural theorems not provable by finitary methods -- a search that turned up some remarkable theorems of combinatorics in the 1970s and 1980s. Today, with the assistance of some eminent mathematicians, logic and combinatorics seem on the brink of living happily ever after.

**Thursday, November 20th, 2008**

3:15 pm in UNA 109

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

**Mac Mahon's Ω Operator, II**

Let Δ (n) denote the number of incongruent triangles with integer sides and perimeter n. Can you find a closed form for the generating function for this sequence?

In this talk we continue to examine Mac Mahon's Ω operator, which gives a method for finding the generating function for this and other sequences.

**Tuesday, December 2nd, 2008**

3:15 - 4:15 pm in UNA 109

**Professor Lin Tan** (West Chester University)

**WHAT IS THE OMEGA PROCESS AFTER ALL?**

We will show the essence of Macmahon's Omega Process in his Combinatorial Analysis in an entirely elementary fashion, inspired by results from Diophantine equations and Diophantine inequalities, for $\Omega_=$ and $\Omega_{\geq}$ respectively, by Gordan (an invariant theorist) and Dickson (a number theorist), among others. We will use Macmahon's list, Jimmy's triangle problem and some example from George Andrews and his crew as our launching pad to illustrate the idea, in particular what the denominators and numerators in the corresponding generating functions account for.

**Friday, December 5th, 2008**

3:00 - 4:00 pm in UNA 161

**ROBERT L. DEVANEY** (Boston University)

**"Chaos Games and Fractal Images"**

In this lecture we will describe some of the beautiful images that arise from the "Chaos Game." We will show how the simple steps of this game produce, when iterated millions of times, the intricate images known as fractals. We will describe some of the applications of this technique used in data compression as well as in Hollywood. We will also challenge students present to "Beat the Professor" at the chaos game and maybe win his computer.