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


Presentations


Thomas Anderson (West Chester University Undergraduate Student)
20 minutes Expository Talk
RSA Encryption and YOU!

The presentation will discuss RSA Encryption and its ties to abstract algebra. The method of RSA Encryption will be discussed, as well as why it is so secure and common, all of which are applications of abstract algebra. An example encryption will be demonstrated using Mathematica during the presentation to illustrate these connections.



Ximena Catepillan (Millersville University Faculty)
Other Presenter: Nazli Hardy
30 minutes Panel Discussion
Women in Mathematics & Science

The main goal of leading the panel discussion is to encourage other PASSHE institutions to create a course like our pioneer Women in Mathematics and Science course at Millersville University. Many women pursuing degrees in science and mathematics face struggles (peer pressure, societal expectations, male dominance in their field of work, image associated with a field of study etc.) that detract from their intended careers in these professions. The focus on our discussion will be on how we developed a course around the personal and scientific achievements and discoveries (often in the face of great adversity) of women scientists and mathematicians.
Andy Dorsett, Wolfram Research
Demonstration
Mathematica 7 in Mathematics Education and Research

This talk illustrates capabilities in Mathematica 7 that are directly applicable for use in teaching and research on campus. Topics of this technical talk include:
* 2D and 3D visualization
* Dynamic interactivity
* Example-driven course materials
* Symbolic interface construction
* Practical and theoretical applications
* Demonstrations of Digital Image Processing and Parallelization

Current users will benefit from seeing the many improvements and new features of Mathematica 7 (http://www.wolfram.com/products/mathematica/newin7), but prior knowledge of Mathematica is not required.




K Blayne Easter (West Chester University Graduate Student)
Student Poster Presentation
Food for Thought  (A Pricing Analysis)

The presenter has conducted a comparison of inventory pricing bewteen two major grocery store chains in the Chester County region. The project sampling methodology, data gathering, data analysis, and results will be shared with conference participants.




Kevin Ferland (Bloomsburg University Faculty)
20 minutes Expository Talk
Generalizing the Pythagorean Theorem and Its Proof

Simple proofs of the Pythagorean Theorem using pictures are well-known.  We study in depth a particularly elegant one and explore how such an argument can be generalized.  This leads to the discovery a similarly elegant proof of a well-known result in trigonometry.




Serina Foehr (W.H. Freeman)
Demonstration
W.H. Freeman’s StatsPortal

StatsPortal integrates a rich suite of diagnostic, assessment, tutorial, and enrichment features into one convenient, fully-customizable learning space, enabling students to master mathematics at their own pace. It is organized around three main teaching and learning components: a fully interative eBook, the Resources Center, and the Assignment Center.




Gail M. Gallitano (West Chester University Faculty)
20 Minute Research Talk
The Attitudinal Effect of a Week Long Graphing Handheld In- Service/Pre-
service Training Institute on Mathematics Teachers

The West Chester University Teachers Teaching with Technology In-service/Pre-service
Training Program was founded in 1995. Approximately six one week all day in-service graphing handheld institutes are sponsored through this program each summer. Every summer approximately 125 mathematics teachers attend one or more institute. The purpose of these institutes is to retrain teachers on graphing handheld technology and how to effectively incorporate it into the mathematics classroom. There is strong evidence that student use of graphing handhelds increases student test performance. It also enhances their attitudes toward mathematics. It is therefore important that all mathematics teachers feel competent and comfortable using graphing handhelds to teach mathematics. This study helps to confirm that teacher in-service training plays a vital role in helping mathematics teachers to feel comfortable and competent using the graphing handheld. The study also helps to confirm that teacher in-service training significantly affects, in a positive direction, teachers' attitudes toward the use of graphing handhelds and other technology in the mathematics classroom.


Zhigang Han (Millersville University Faculty)
20 minutes Expository Talk
Euclidean Geometry and Symplectic Geometry

In this expository talk we will provide a comparison between Euclidean geometry and symplectic geometry. The talk is accessible to everyone who has some knowledge about high school geometry.




Paul Hartung (Bloomsburg University Faculty)
45 minutes Expository Talk
A Data Mining Tutorial

A brief overview of data mining will be given.  A specific mathematical procedure to produce rules from a database will be discussed.




Paul Hartung (Bloomsburg University Faculty)
45 minutes Research Talk
Arithmetic skills of preservice elementary teachers

Data from preservice elementary teachers will be presented.  Efforts at Bloomsburg to improve the situation will be discussed.




Linda W. Iseri (Mansfield University Faculty)
20 minutes Research Talk
Examining Aspects of Pre-Service Secondary Teachers' Dispositions

This presentation will briefly discuss pre-service math teacher responses to open-ended questions about how they envision themselves as math teachers.




Jonathan Keiter (East Stroudsburg University Faculty)
20 minutes Expository Talk
Can Students Teach Each Other Calculus?

I used an inquiry learning approach for many of the topics in the second semester of Calculus.  I will discuss the structure of the course, the challenges of the course, and the reaction from the students.   




Paul Loomis (Bloomsburg University Faculty)
20 minutes Expository Talk
Friendly and Solitary Numbers

Let σ(n) be the sum of the divisors of a natural number n. We say m and n are friends if σ(m)/m=σ(n)/n. So 6 and 28 are friends (as are any two perfect numbers), as σ(6)/6=2=σ(28)/28. A number is solitary if it has no friends. For most numbers, it is not known whether they are friendly or solitary. Here we find a few families of solitary numbers and show that it is not hard to reach results like "if 10 has a friend, it is an odd square not divisible by 3 with at least five distinct prime factors". (These are analogous to similar-sounding results on odd perfect numbers.) This talk is suitable for students.




Youmin Lu (Bloomsburg University Faculty)
45 minutes Research Talk
Oscillation Theorems for Second Order Forced Nonlinear Ordinary Differential Equation

We study a second order forced nonlinear ordinary differential equation  and obtain some oscillation theorems that extend the related existing results.




Scott McClintock (West Chester University Faculty)
45 minute expository talk
A Survey of the Fundamental Theory of Asset Pricing

The Fundamental Theorem of Asset Pricing (FTAP) is a pivotal result in mathematical
finance. At its heart it states that an equivalent martingale measure, with respect to the
price process of a collection of innancial assets, exists if and only if arbitrage holds. This talk will begin with an introduction to arbitrage theory and the FTAP. We will initially discuss
these ideas using a basic model accessible to interested beginners. We will then discuss
various generalizations and extensions of personal research interest. The talk will conclude
by showcasing how recent results of the FTAP can be utilized to study the properties of
pricing bubbles like those seen, most recently, in the housing market.



James Mc Laughlin (West Chester University Faculty)
20 minutes Research Talk
An Identity Motivated by an Amazing Identity of Ramanujan






Andrew Miranda (West Chester University Undergraduate Student)
20 minutes Expository Talk
An Introduction to Stochastic Calculus

 We will introduce Stochastic Calculus, which takes a random or "noise" component into consideration. We will define probability spaces, Brownian motion, and noise. We will describe a stochastic calculus on functions of Brownian motion and time, X (t) = f (t, B), called Ito's Calculus. We will define the Ito Integral. We will then use Ito's Isometry to derive a derivative rule, called Ito's Rule, to show, using a variation of parameters technique, how to solve Ito's integrals. We will then show several examples.




Joseph Moser (West Chester University Faculty)
20 minutes Expository Talk
Neither K(5) nor K(3,3) are Planar - Kuratowski for Liberal Arts Students.

We give an "elementary" proof of the non-planar nature of both K(5) and K(3,3). Hopefully, this argument reveals as much about the "nature of Mathematics" as the fact itself.




Reza Noubary (Bloomsburg University Faculty)
45 minutes Research Talk
RISK AND INVESTMENT

Abstract: Investors in today's global market use risk analysis to compare different investment options.  This presentation will focus on basic mathematics involved in defining and quantifying risk. We plan to discuss risk reduction methods such as diversification and their limitations. The presentation is accessible to students.



Scott Parsell (West Chester University Faculty)
20 minutes Research Talk
The underlying congruences in Waring's problem

A famous theorem of Lagrange states that every positive integer can be expressed as the sum of four squares.  Moreover, an examination of congruences mod 8 reveals that this is best possible in the sense that three squares do not suffice.  Waring proposed generalizations of Lagrange's Theorem to sums of higher powers, and it is easy to show that the number of $k$th powers required to establish such a conclusion tends to infinity with $k$.  One expects such a phenomenon for solutions of the underlying congruences as well, but in the current state of knowledge it is conceivable that the required number of $k$th powers is as small as three for infinitely many valeus of $k$.  We will discuss some recent computational progress on this question and establish a connection with the distribution of primes in arithmetic progressions.




Deivy Petrescu (Cheyney University Faculty)
20 minutes Expository Talk
Are you happily married? There is a Math for that.

Mathematical modeling has been successful in many areas, however, what is its limits.
Apparently there are none. Some researches have used mathematical modeling to predict failure or success in marriages. Can this be pushed a step further. Can we use mathematical modeling to predict other behaviors?  More to the point can mathematical modeling be used to predict outcome of psychiatric/psychological therapy?
Dr. Phillip Ray (Indiana University Faculty)
45 minutes Research Talk
Ulam's 3n + 1 Problem

An investigation of Ulam's 3n + 1 Problem including associated k values.





Mehdi Razzaghi (Bloomsburg University Faculty)
20 minutes Expository Talk
Mathematical Modeling as Capstone Course in Mathematics Curriculum and a Statistical Analysis of the MFT Test

Capstone courses are offered in many different institutions of higher learning. They are generally designed to provide the students with opportunity to demonstrate that they have achieved the learning goals set by the institution. Some capstone courses are offered at the university/college level while many are discipline specific. In this note, we discuss the experience of using a course in mathematical modeling as a capstone course. Not only the course is a way for the students to apply their abilities and learn about for the necessary tools they need in order to apply their knowledge in mathematics after graduation, the course also provides an excellent avenue for the department to evaluate its curriculum.




Carol Rehn (Lock Haven University Faculty)
45 minutes Panel Discussion
Department Chairs' Colloquium

A sharing session for chairs and others interested in department issues.  Those in attendance will determine topics for discussion.




Marc Renault (Shippensburg University Faculty)
70 minutes Workshop
Using GeoGebra for Classroom Demonstrations and Activities

This will be a workshop on using the computer program GeoGebra.  GeoGebra is free dynamic mathematics software joining algebra, geometry, and calculus.  I use GeoGebra frequently in my pre-calculus, calculus(I and III), geometry, and linear algebra courses, for both in-class demonstrations and student activities.  This workshop will introduce participants to all the fundamental features of GeoGebra, and time will be available for folks to explore on their own.

***Each participant should bring a laptop with GeoGebra already installed.  See http://www.geogebra.org.*** 
Optionally, you are encouraged to try the tutorial at http://webspace.ship.edu/msrenault before the conference.





Kevin S. Robinson (Millersville University Faculty)
20 minutes Research Talk
A Missed Opportunity: Sample Size for Estimating the Standard Deviation

Statistical education has focused on the sample size needed for estimation of means or proportions. The present work makes the case that sample size consideration for the standard deviation is of importance as well and can be incorporated into the Statistics curriculum by the use of technology. Illustrations are presented of sample size determination based on various criteria implemented using the free software, R. In general, the work illustrates how the advances in classroom technology and computing can lead to a missed opportunity in the traditional Statistics curriculum.




Carolyn D. Sealfon (West Chester University Faculty)
20 minutes Research Talk
The Cutting Edge: Selecting a Galaxy Cluster Mass Function via the Bayesian Razor

We apply a model-selection razor, based on Bayesian evidence, to the galaxy cluster mass function. The cluster mass function is sensitive to the initial conditions, composition, and evolution history of the Universe, and is thus a powerful tool to constrain cosmological theories. Various parameterizations of the mass function may be fit to current and upcoming observations. We show how the razor can estimate the minimum size cluster catalog that is required for different parameterizations of the mass function to lead to statistically significant conclusions.




Zhoude Shao (Millersville University Faculty)
20 minutes Research Talk
Existence and continuity of strong solutions of partly dissipative reaction diffusion systems

We consider partly dissipative reaction diffusion systems of the FitzHugh-Nagumo type and established the existence of strong solutions of such systems by a Galerkin type of argument. We aslo proved the continuity of strong solutions with respect to initial data in the space V×H¹(Ω), where V is a subspace of H¹(Ω) defined based on the boundary condition imposed for the u-component. The continuity result, the proof of which is based on an interpolation inequality of Nirenburg-Gagliardo type, is independent of the spatial dimension n.




Rosemary Sullivan (West Chester University Faculty)
20 minutes Research Talk
A Modification of Sylvester's Four Point Problem

In 1865, Sylvester posed the problem of finding the probability that four points randomly chosen with a uniform distribution over a compact convex region K in the plane form the vertices of a convex quadrilateral.  This led to substantial research on the ratio of the expected area of a random triangle formed by three independent and uniformly distributed points to the area of the convex region K , for different K.  In this talk we consider the problem of studying the behavior of the ratio of the expected area of a random triangle formed by three independent points, each with distribution P, to the expected square distance between two independent points each with distribution P.  We call this the Modified Sylvester Four Point Problem.
Lin Tan (West Chester University Faculty)
20 minute Research Talk
From Binomial Coefficients to Gaussian Polynomials

We will start with the binomial coefficients, viewed as the numbers of ways to choose k objects from n kinds of objects allowing repetition. A refinement leads naturally to the concept of the Gaussian polynomial.
The talk will be accessible to undergraduate students.


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