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


Spring 2007 Colloquium/Seminar Schedule

Each Thursday during the semester there is a mathematics seminar (usually in Anderson 120 from 3:15-4:15). Over perhaps one or two semesters, we consider a selected topic and, beginning with basic definitions, work up to the point where we can discuss current research in the area and present research discoveries by department faculty members in the area. This seminar is open to all interested students and faculty at West Chester.

Occasionally outside speakers or WCU mathematics faculty present a talk in the mathematics colloquium, which may be on a different topic (check this page for times and locations).

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

This Semester our topic is Integer Partitions.

Thursday, January 25th, 2007
3:15 pm in 120 Anderson Hall
James Mc Laughlin (West Chester University)
Introduction to Integer Partitions and Overview of Upcoming Seminars

Thursday, February 1st, 2007
3:15 pm in 120 Anderson Hall
Greg Sternschuss (student) (West Chester University)
Stanley's Theorem

Thursday, February 8th, 2007
3:15 pm in 120 Anderson Hall
James Mc Laughlin (West Chester University)
Introduction to Generating Functions

Thursday, February 22nd, 2007
3:15 pm in 120 Anderson Hall
James Mc Laughlin (West Chester University)
The Analytic Version of the Rogers-Ramanujan Identities

Thursday, March 1st, 2007
3:15 pm in 120 Anderson Hall
James Mc Laughlin (West Chester University)
Partition Interpretations of the Rogers-Ramanujan Identities

Thursday, March 8th, 2007
3:15 pm in 120 Anderson Hall
James Mc Laughlin (West Chester University)
Ferrer's Diagrams and Euler's Pentagonal Number Theorem

Thursday, March 22nd, 2007
3:15 pm in 120 Anderson Hall
James Mc Laughlin (West Chester University)
Introduction to q-Series and a Theorem of N. J. Fine

Wednesday, March 28th, 2007 (Colloquium Talk)
3:15 pm in 120 Anderson Hall
Lin Tan (West Chester University)
An Mat 103 in China

My experience of teaching a pilot class of Mathematics for the Liberal-arts Students in China in Fall of 2006 will be shared, with a comparision with similar classes taught at universities in the U.S.
Some of the difficulties the Chinese students had, the exam problems, and some of the technologies employed in the course will also be discussed.

Wednesday, April 4th, 2007 (Colloquium Talk)
3:15 pm in 120 Anderson Hall
James Mc Laughlin (West Chester University)
Continued Fractions, and Generalizations, with Many Limits.

Consider the following two examples of infinite processes:
(1) Let the sequence {xn}n ³ 0 be defined by

x0 = 3

2
,             xn+1 = 3

2
- 1

xn
,            n ³ 1.

What can be said about the sequence {xn}n ³ 0 ?
(2) Let a and b be points on the unit circle, let |q| < 1, and define the continued fraction

G(q,a, b): = - ab

a+b+q+
  -ab

a+b+q2+
  ¼ -ab

a+b+qn+
¼.

What can be said about the convergence or divergence of G(q,a,b)? What difference, if any, does it make if a and b are roots of unity? It turns out that both the sequence and the continued fraction diverge, but diverge in quite interesting ways. There are several infinite processes (matrix products, continued fractions, (r,s)-matrix continued fractions, recurrence sequences) which, under certain circumstances, do not converge but instead diverge in a very predictable way. This talk will present a survey of results in the area, concentrating on recent results by Douglas Bowman and the speaker.

Monday, April 16th, 2007 (Mathematics Education Colloquium)
3:15 pm in 120 Anderson Hall
Steven Soltys (Manheim Central High School)
Correlation and Simple Linear Regression.

Though mandated by most state standards and frequently assessed on state assessments, the topics of correlation and simple linear regression are often taught in a cursory disconnected manner. The concepts and ideas underlying correlation and regression do not need to be sacrificed due to a lack of time, computational skill, or mathematical maturity. Various tools and illustrations are available that will foster a deeper understanding of these topics as well as emphasize the interpretation of correlation and regression in the context of the problem.

Light refreshments are available following the colloquium.

Tuesday, April 17th, 2007 (Mathematics Education Colloquium)
3:15 pm in 120 Anderson Hall
Geoffrey Birky (University of Maryland)
Implementing Eighth-Grade Mathematics Problems in Six Countries:
A Secondary Analysis of the TIMSS 1999 Video Data

The 1999 Video Survey of the Third International Mathematics and Science Study (TIMSS) videotaped hundreds of randomly selected, representative eighth-grade mathematics classrooms in the U.S. and six "high performing" countries. The goal was to understand the differences among teaching in those countries. One of the study's striking findings was that U.S. teachers, unlike their peers in the other countries, rarely discussed mathematics problems in ways that promoted conceptual understanding and mathematical reasoning. This occurred in spite of the fact that they assigned problems with the potential to promote such thinking roughly as often as teachers did in the other countries. I will present preliminary results of a study which is examining the videotaped lessons more closely in order to describe how teachers outside the U.S. discuss problems in ways that promote higher order thinking, and how teachers in all of the countries, to varying degrees, miss opportunities to address such thinking.

Light refreshments are available following the colloquium.

Monday, April 23rd, 2007 (Mathematics Colloquium)
3:15 pm in 120 Anderson Hall
Miranda Morehead (West Chester University)
Normal Operators in Euclidean Spaces
(A Master's Thesis Presentation)

Results of research regarding normal operators (commuting with their adjoints) in Euclidean spaces (finite-dimensional vector spaces with inner product) will be presented.
First, eight equivalent conditions which summarize the essence of a normal operator will be discussed. Then the commutant of a normal operator will be described.

Wednesday, April 25th, 2007 (Mathematics Colloquium)
3:15 pm in 120 Anderson Hall
Peter Zimmer (West Chester University)
Some Variations of the Bailey Transform

Ramanujan stated many identities, but gave little in formal proofs. In 1913, Ramanujan found a proof for two of his identities (now known as the Rogers-Ramanujan Identities) in a paper written by L. Rogers in 1894. Rogers' proof was rather difficult, and the literature is filled with alternative proofs of the same identities.
In particular, W. Bailey (in the 1940s) closely analyzed Rogers' proof and illuminated the critical technique of Rogers' proof in what is now known as the Bailey's Transform. We in turn analyzed the Bailey's Transform and found some variations that has produced many interesting identities and basic hypergeometric transforms that we believe to be new. In particular, we have yet another proof of the Rogers-Ramanujan Identities.

Wednesday, May 2nd, 2007 (Mathematics Colloquium)
3:15 pm in 120 Anderson Hall
Lin Tan (West Chester University)
VIVA EULER!

In commemoration of the great Euler's tricentennial birthday, we showcase his work by presenting his top ten hits, a very subjective selection of course, from Euler's opus through his life. Proofs or outlines of proofs will be given. Yet the emphasis will be on the mathematical ideas involved and the later mathematical developments out of these amazing results of Euler.

Thursday, May 3rd, 2007
3:15 pm in 120 Anderson Hall
James Mc Laughlin (West Chester University)
Binary Partitions