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 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006, Summer 2006, Spring 2006,

**Thursday, February 4th, 2010**

3:15 - 4:15 pm in UNA 127

**Professor Michael Fisher** (West Chester University)
**The Probabilistic Method - VIII**

**Wednesday, February 17th, 2010**

3:15 - 4:15 pm in UNA 161

** Professor Dr.Neil J. A. Sloane (AT & T Fellow - Shannon Lab)**

The On-Line Encyclopedia of Integer Sequences (OEIS) is a free website that provides information about over 170,000 number sequences. Available in 49 languages, it is used by lovers of numbers, both amateurs and professionals, from all over the world. Questions such as what comes next after 1, 2, 5, 12, 29, 70, 169, ... arise in all cultures and have a universal appeal. Many users have remarked that the OEIS is one of the best examples of international cooperation on the Web. Contemplation of such wonderful discoveries as the Colombian Bernardo Recaman Santos's sequence 0, 1, 3, 6, 2, 7, 13, 20, ... (entry A5132 in the OEIS) provides a welcome escape from the troubles of our planet. The talk will discuss this sequence, the "toothpick" sequence, as well as several others that have arisen recently in connection with problems from combinatorics, graph theory, number theory and geometry. The talk will also demonstrate a new feature that has recently been added to the OEIS: the ability to listen to the sequence played on a musical instrument.

Neil Sloane is a Fellow at AT&T Shannon Labs in Florham Park, NJ. He is a member of the National Academy of Engineering, an IEEE Fellow, and recipient of the IEEE Hamming Medal and the MAA Chauvenet Prize. He is the author or co-author of numerous books, including "The Theory of Error- Correcting Codes" (with F. J. MacWilliams), "Sphere Packing, Lattices and Groups" (with J. H. Conway) and "A Climbing Guide to New Jersey" (with Paul Nick).

**For further information e-mail mfisher@wcupa.edu or sgupta@wcupa.edu**

**Wednesday, February 24th, 2010**

3:15 - 4:15 pm in UNA 158

**Lisa Driskell (Purdue University)**
**The Mathematics of a Broken Heart**

Heart disease is the leading cause of death in the United States each year. One form of heart disease is an arrhythmia which is classified as any disturbance from the normal periodicity of the heart beat. Alternans is one type of arrhythmia which can be a precursor to potentially fatal conditions of the heart. We introduce a two-variable model developed as a modification of other popular models for electrical activity in excitable cells. Our model captures major components of cardiac behavior, including alternans, while allowing for an explicit analysis of the propagation of electrical impulses in cardiac tissue.

**Friday, February 26th, 2010**

3:15 - 4:15 pm in UNA 158

**Professor Wayne Eby (Cameron University)**
**Mathematical Modeling of Wound Healing**

This presentation describes current research in modeling the progression of healing of dermal wounds using mathematical growth models. In a comparative evaluation of the hyperbolastic growth models [Tabatabai et al. 2005] with other popular models, the hyperbolastic models are shown to have a significantly greater accuracy, particularly H2 and H3. These models are used to accurately describe the time course of the wound healing in an explicit functional form. We outline some of the underlying biological issues in wound healing and present how the biological events are reflected in the time progression of the wound healing. To illustrate the use of the hyperbolastic models in giving a quantitative understanding of the wound healing, as tied to the biological processes, we analyze three data sets representing different aspects of wound healing. Each is interpreted in the context of how the underlying biology affects the rate of healing at different stages in the healing process.

**Thursday, March 4th, 2010**

3:15 - 4:15 pm in UNA 158

**Professor Allison Kolpas**

Spatially explicit stochastic models have become a popular alternative to more traditional ordinary and partial differential equation models for population dynamics. Such models can include more biological realism but at the cost of being difficult to interpret and analyze. Here, I present work on the development and analysis of two stochastic spatially explicit models for population dynamics.

The first model describes stochastic population and dispersal dynamics in advective media and can be applied to invertebrates in streams, larvae in the coastal ocean, or wind-dispersed seeds. Numerical methods are developed to simulate the model and analyze the effects of demographic stochasticity, both in reproduction and movement, on population persistence.

The second model describes self-organized collective patterns of motion displayed by animal groups such as schooling fish and flocking birds. This model evolves over much shorter time scales and therefore includes only movement dynamics. Mathematical methods are developed to perform bifurcation analysis on the model allowing direct quantification of how parameters related to individual-level behaviors translate to population-level dynamics.

**Wednesday, March 24th, 2010**

3:15 - 4:15 pm in UNA 161

**Professor Jenny Quinn (University of Washington (Tacoma))**

Positive sums count. Alternating sums match. So which is "easier" to consider mathematically?

From the analysis of infinite series, we know that if a positive sum converges, then its alternating sum must also converge but the converse is not true. From linear algebra, we knowthat the permanent of an n x n matrix is usually hard to calculate, whereas its alternating sum, the determinant, can be computed efficiently and it has many nice theoretical properties.

In this talk, we will visit a variety of positive and alternating sums as two mathematical techniques (direct counting versus matching) compete one-on-one for the title of "Most Superior." You will be the judge and jury. I ask you to consider how the terms in each sum are concretely interpreted. What is being counted? What is being matched? Which leads to simpler results? Which is most elegant? The outcome is not predetermined. You decide!

Jennifer Quinn earned her BA, MS, and PhD from Williams College, the University of Illinois at Chicago, and the University of Wisconsin, respectively. She recently joined the faculty at the University of Washington, Tacoma where she is a Professor of Interdisciplinary Arts & Sciences working to build a mathematics curriculum on the expanding campus. Prior to joining UWT, she served as Executive Director of the Association for Women in Mathematics and before that, spent more than a decade as a faculty member at Occidental College in Los Angeles.

Professor Quinn has received regional and national awards as a teacher, scholar, and author -- most recently being recognized as one of three who received the 2007 MAA Deborah and Franklin Tepper Haimo National Award for Distinguished College or University Teaching of Mathematics. Her book 'Proofs That Really Count: The Art of Combinatorial Proof', coauthored with Arthur T. Benjamin, was lauded as distinguished and innovative by the 2006 Beckenbach Book Prize.

**For further information e-mail mfisher@wcupa.edu or sgupta@wcupa.edu**

**Thursday, April 8th, 2010**

3:15 - 4:15 pm in UNA TBA

**Professor Glenn Herbert (Arizona State University)**

Graph pebbling was born in number theory but has grown to become a new kind of network transportation model. A significant difference compared to traditional models is that finding pebbling numbers is harder than NPcomplete. Thus one cannot expect exact answers except for a few wellstructured classes of graphs. In this talk we will describe a new discovery, the weight function lemma, that yields upper bounds derived from linear optimization, thereby giving succinct proofs of sometimes exact and often tight results for many classes of graphs.

Glenn Hurlbert received his PhD from Rutgers University under the direction of Ronald Graham. He has written 50 papers on universal cycles, graph pebbling, extremal set theory, and other topics in graph theory, combinatorics, and optimization, one of which was recognized by Discrete Mathematics as one of the best research papers of 2003. He is the author of 'Linear Optimization: the Simplex Workbook' (Springer 2010), and was awarded the 2007 Southwestern Section of the MAA Award for Distinguished Teaching.

**For further information e-mail mfisher@wcupa.edu or sgupta@wcupa.edu**

**Wednesday, April 21st, 2010**

3:15 - 4:15 pm in UNA 161

**Professor Steve Weintraub (Lehigh University)**

(The above cartoon is reproduced with the permission of xkcd.)

Unique factorization (the fact that every positive integer can be factored into a product of primes in a unique way) is a very important property of the integers. We will investigate the question of whether unique factorization continues to hold in a more general situation, in rings of integers of quadratic fields. We will be able to prove that in some cases unique factorization does hold, while in other cases it does not. Indeed, we will see that unique factorization is the exception, rather than the rule! Our constructions, methods and results will be quite explicit.

Steven H. Weintraub is Professor of Mathematics at Lehigh University. His research spans a broad area of algebra, geometry, and topology. He is the author of over 50 research papers and 8 books, with a ninth one on the way.

**For further information e-mail mfisher@wcupa.edu or sgupta@wcupa.edu**