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 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006, Summer 2006, Spring 2006,

**Thursday, September 23rd, 2010**

3:15 - 4:15 pm in UNA 161

**Professor James Mc Laughlin** (West Chester University)
**Elliptic Functions - I**

**Thursday, September 30th, 2010**

3:15 - 4:15 pm in UNA 161

**Professor James Mc Laughlin** (West Chester University)
**The Weierstrass P-function - I**

**Wednesday, October 6th, 2010** Mathematics Department Colloquium Talk

3:15 - 4:15 pm in UNA 155

**Bernie McCabe** (West Chester University)
**"Mean – Median as a Measure of Non-normality"**

**The difference between the mean x̄ and the median m for a sample from a normal distribution will tend to be small because the underlying mean µ and median µ0 are equal. How large need a value be to indicate non-normality?**

We first investigate for any distribution how large can |x̄-m| or µ - µ0 be.

We will find that for any distribution |x̄-m| < s and |µ - µ0| < σ where s and σ are the sample and theoretical standard deviations, respectively.

We will give the original very clever proof by Harold Hotelling, the mathematician and economist, dating to 1932. Two other elegant proofs will be given. Along the way we will need and prove several probabilistic lemmas which should interest the students: Jensen's inequalities (one for convex functions and one for concave functions), the one-sided Chebychev inequality due to Cantelli and a bit more trouble to prove than the two-sided version, and the fact that the function E[[X- α]] is minimized for α = µ0 the median.

We show that if the underlying distribution is normal then the variance of |x̄-m| is approximately (π/2-1)/n. That fact can be used to indicate that if |x̄-m|/(s/√n) is much bigger than 1.5 or 2, the distribution is unlikely to be normal.

**The latter conclusion is based on some simulation results which can be described using Minitab, and that might be an interesting excursion for the students.**

**Thursday, October 7th, 2010**

3:15 - 4:15 pm in UNA 161

**Professor James Mc Laughlin** (West Chester University)
**The Weierstrass P-function - II**

**Wednesday, October 20th, 2010** Mathematics Department Colloquium Talk

3:15 - 4:15 pm in UNA 155

**JIM COYKENDALL** (North Dakota State University)
**"Large Numbers, Elementary Probability, Goats, and Poker"**

The aim of this talk will be to give some interesting results that come from elementary probability, counting, and large numbers.

We will begin by looking at some "large numbers". For example, the number of combinations on the Rubik's cube is roughly 43 quintillion. But how big is this really? We will produce some examples throughout the talk to illustrate the fact that the mere size of these numbers renders them a bit more abstract than you might think.

We will then look at some interesting "real life" questions and compute some odds. We will look at some elementary problems in counting and probability (most with absolutely astounding answers).

This talk will be quite accessible to ALL students. Time permitting, we will have a trial game show (to test some probability) and we will learn at least a little bit about being a better poker player. I will leave you with an upcoming teaser: "If you spill some ink in the ocean what is the chance that you will ever encounter any of the original ink again?" The answer may surprise you.

Jim Coykendall grew up in Gatlinburg, Tennessee (where he attended Sevier County High School...the Alma Mater of Dolly Parton). He got his B.S. in Mathematics at the California Institute of Technology (where he won the E.T. Bell Prize for undergraduate research) and his Ph.D. in Mathematics at Cornell University. Since the time of his Ph.D., he has worked at Lehigh University as the C.C. Hsiung Visiting Professor of Mathematics and has been at North Dakota State University since 1996. His research area is commutative algebra and algebraic number theory and he has published about 40 papers in these areas. He is also the recipient of the NDSU College of Science and Mathematics Teaching Award, the NDSU College of Science and Mathematics Research Award, the Odney Teaching Award, and is the James A. Meier Professor.

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

**Thurssday, October 21st, 2010** Mathematics Department Seminar Talk

3:15 - 4:15 pm in UNA 161

**JIM COYKENDALL** (North Dakota State University)
**"On Cohen-Kaplansky Domains"**

- Every nonzero nonunit can be factored into a finite number of irreducible elements, and
- There are only finitely many irreducible elements (up to associates). These types of domains were first studied in 1946 by Cohen and Kaplansky and since that time have generated interest in the commutative algebra/factorization community. It is natural to ask if it is possible to "build" a nontrivial CK-domain with precisely n (nonprime) irreducible factors up to associates. This question has remained open for over 60 years, and in this talk we will show that the answer is "yes" if one can accept a modified version of the Goldbach conjecture.

Jim Coykendall grew up in Gatlinburg, Tennessee (where he attended Sevier County High School...the Alma Mater of Dolly Parton). He got his B.S. in Mathematics at the California Institute of Technology (where he won the E.T. Bell Prize for undergraduate research) and his Ph.D. in Mathematics at Cornell University. Since the time of his Ph.D., he has worked at Lehigh University as the C.C. Hsiung Visiting Professor of Mathematics and has been at North Dakota State University since 1996. His research area is commutative algebra and algebraic number theory and he has published about 40 papers in these areas. He is also the recipient of the NDSU College of Science and Mathematics Teaching Award, the NDSU College of Science and Mathematics Research Award, the Odney Teaching Award, and is the James A. Meier Professor.

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

**Wednesday, October 27th, 2010** Mathematics Department Colloquium Talk

3:15 - 4:15 pm in UNA 155

**DORIS SCHATTSCHNEIDER** (Moravian College)
**"M.C. Escher, a most mathematical artist"**

**The imagery in M.C. Escher's graphic works not only makes obvious use of geometry, but often provides visual metaphors for abstract mathematical concepts. This slide lecture will reveal mathematical concepts implicit in several of Escher's works, explain the transformational geometry that he used to create his interlocking figures, and show how this "math anxious" artist actually did pioneering mathematical research in order to accomplish his artistic goals. Escher's mathematical curiosity and insight has been the inspiration for many mathematicians, scientists, and artists of today who seek solutions to problems (both mathematical and artistic) first posed by Escher himself.**

Doris Schattschneider holds a Ph.D. in mathematics from Yale University and is Professor Emerita of Mathematics at Moravian College in Bethlehem, Pennsylvania. Her dual interest in geometry and art led naturally to her study of the work of the Dutch artist M.C. Escher. She is author of the book M.C. Escher: Visions of Symmetry, coauthor of a book and collection of geometry models, M. C. Escher Kaleidocycles, and editor of a book with CD Rom, M.C. Escher's Legacy, that contains 40 contributions by contemporary artists and others whose work has been deeply influenced by Escher. She has lectured widely on Escher's work, and has published both research and expository articles in journals and in Scientific American.

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

**Thursday, October 28th, 2010**

3:15 - 4:15 pm in UNA 161

**Professor James Mc Laughlin** (West Chester University)
**Introduction to the Modular group**

**Thursday, November 4th, 2010**

3:15 - 4:15 pm in UNA 161

**Professor James Mc Laughlin** (West Chester University)
**The Hardy-Ramanujan-Rademacher Partition Function - I**

**Thursday, November 11th, 2010**

3:15 - 4:15 pm in UNA 161

**Professor James Mc Laughlin** (West Chester University)
**The Hardy-Ramanujan-Rademacher Partition Function - II**

**Thursday, November 18th, 2010**

3:15 - 4:15 pm in UNA 161

**Professor James Mc Laughlin** (West Chester University)
**The Hardy-Ramanujan-Rademacher Partition Function - II**

**Wednesday, December 1st, 2010**

3:20 - 4:10 pm in UNA 155

**Professor Joe Moser** (West Chester University)
**Counting Peasant, Royal, Fibonacci and (even) Godly Paths in Discrete n-Space.**

**Thursday, December 2nd, 2010**

3:15 - 4:15 pm in UNA 161

**Professor James Mc Laughlin **(West Chester University)
**The Hardy-Ramanujan-Rademacher Partition Function - III**

**Thursday, December 9th, 2010**

3:15 - 4:15 pm in UNA 161

**Professor James Mc Laughlin **(West Chester University)
**The Hardy-Ramanujan-Rademacher Partition Function - IV**