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 120 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 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006, Summer 2006, Spring 2006.

Combinatorial Games Seminar

The Combinatorial Games Seminar will continue to meet each Thursday in Spring 2013.

E-mail Professor Mike Fisher for more details.

West Chester University

Presents

Dr. Matthew Beauregard (Job Candidate)

Department of Mathematics

Center of Atmospheric, Space and Engineering Research, Baylor University

Wednesday, February 6th, 2013 from 3:15 to 4:05PM

UNA 119

"Adaptive Splitting Methods in Application to a Quenching-Combustion Model"

Abstract:

The development of numerical methods continues to have a tremendous impact on scientific research,
in particular, to the study of partial differential equations. Compact methods serve as a fruitful way of
increasing the accuracy of a numerical method without increasing the computational cost. As a result,
a tremendous amount of focus in the literature has been placed on the study of compact methods and
their applications. Still, their application is often done blindly, without proper numerical analysis of the
numerical method. Here, the numerical solution of a nonlinear, degenerate reaction-diffusion equation of
the quenching type is investigated. An adaptive compact scheme is employed to obtain solutions for the
discretized system. The temporal step is determined adaptively through a suitable arc-length monitor
function. It is shown that the numerical solution acquired preserves the positivity and monotonicity of
the analytical solution. Strong stability is proven in a Von-Neumann sense via the ℓ2-norm. In light
of these achievements, subtle restrictions are imposed as a result of implementing the compact scheme,
providing a cautionary tale that employing numerical methods without proper analysis is a recipe for
divergence, inaccuracy, and inconsistent results.

Students are strongly encouraged to attend as the talk siphons directly from knowledge of calculus, linear
algebra, and systems of differential equations.

*Matthew Beauregard is a Postdoctoral Associate Professor at Baylor University, Department of Mathematics,
Waco, Texas. He obtained his Applied Mathematics, Aerospace and Mechanical Engineering Minor,
at the University of Arizona, Tucson, AZ in 2008; his thesis title was "Nonlinear Dynamics of Elastic Filaments
Conveying a Fluid and Numerical Applications to the Static Kirchhoff Equations" and his thesis
advisors were Dr. Michael Tabor, University of Arizona, and Dr. Alain Goriely, Oxford University. His
research develops and analyzes fully adaptive algorithms that attempt to approximate quenching-combustion
models, especially near the onset of blow-up, quenching, or the formation of a singularity. The algorithms
stem from expertise in the method of lines, operator splitting, Pade approximations, matrix and difference
equation theory, and partial differential equation theory.*

West Chester University

Presents

Dr. Mark A. McKibben (Job Candidate)

Goucher College

Thursday, February 7th, 2013 from 3:15 to 4:05PM

UNA 161

**Holey Rocks, Indecisive Fluids, Vanishing Beaches & Fiery Neurons:**

*The Unifying Nature of Implicit Stochastic Evolution Equations*

Abstract:

Hidden connections often lurk beneath the surface that, once discovered, enable mathematical models of seemingly disparate phenomena to be studied within a single, unified abstract framework. When the models consist of partial differential equations, the form of this structure is an *abstract evolution equation*.In this talk, we shall begin by illustrating, in a sequence of steps, how an abstract evolution equation can be derived to unify the study of the models alluded to in the title. Then, we will incorporate environmental noise into the models and develop an even more encompassing stochastic theory governing the evolution of these processes. The talk will end with brief commentary on current and future directions of research in this area, including how one accounts for sharp blows to the system, time delays, and “not-so-nice” noise (e.g., fractional Brownian motion).

*Mark McKibben is a professor of mathematics in the department of Mathematics and Computer Science at Goucher College in Baltimore, Maryland. He obtained his PhD at Ohio University, in 1999; his thesis title was “Existence Theorems for Nonlinear Functional Differential Equations” and his thesis advisor was Sergiu Aizicovici, Ohio University. His research interests, broadly speaking, is the field of applied functional analysis used to study theoretical issues (e.g., existence/uniqueness, controllability, convergence schemes of various kinds, stability) of abstract deterministic and stochastic evolution equations.*

West Chester University

Presents

Dr. Matthew Nick J. Moore (Job Candidate)

Courant Institute of Mathematical Sciences

Monday, February 11th, 2013 from 3:15 to 4:05PM

UNA 119

**Semi-analytical models for fluids interacting with structures**

Abstract:

Reduced models can lend unique insight into physical phenomena by stripping away all but the most essential principles. I will discuss the use of such models in the context of two fluid-structure problems. First, I will discuss motion in viscoelastic fluids. These fluids store and release elastic energy, leading to motion that is characteristically unsteady. A canonical example is the gravitational settling of body, in which terminal velocity is exceeded on a transient timescale. We have recently developed a "weak-coupling" method that gives semi-analytical solutions to this classical problem and other more complicated problems.

I will discuss a biologically-inspired extension in which the body is propelled by an oscillating force, intended to mimic a swimming stroke. Secondly, I will discuss the erosion of bodies by fluid flow. Inspired by natural examples such as the formation of landforms, our study focuses on the mutual interaction between changing shape and flow. Table-top experiments of soft-clay in flowing water reveal the formation of sharp corners and facets, contrary to the common notion that erosion tends to smooth bodies. We appeal to a semi-analytical flow-model that combines an outer flow with a boundary layer flow in order to rationalize these observations and make new predictions.

*Matthew "Nick" Moore is an Associate Research Scientist at the Courant Institute of Mathematical Sciences, New York University, New York. He obtained his PhD at University of North Carolina, in 2010; his thesis title was "Stratified flows with vertical layering of density" and his thesis advisors were Richard M. McLaughlin and Roberto Camassa, University of North Carolina. His research interests include Applied and computational mathematics, fluid mechanics especially fluid-structure interactions, complex fluids, evolution equations, nonlinearity, multi-scale problems, stability analysis.
*

West Chester University

Presents

Dr. Ivan Matic (Job Candidate)

Duke University

Wednesday, February 13th, 2013 from 3:15 to 4:05PM

UNA 119

**Decay and Growth of Randomness**

Abstract:

Formation of crystals, spread of infections, and flow of fluids through porous rocks are modeled mathematically as systems consisting of many particles that behave randomly. We will use fluctuations to quantify the randomness, and measure its decay as the number of particles increase.

Then we will study the opposite problem: growth of randomness. It turns out that situations exist where it is beneficial to increase chaos. As one example, we will study methods to anonymously distribute

*Ivan Matic is Assistant Research Professor at Duke University, Durham, North Carolina. He obtained his PhD at the University of California, Berkeley, in 2010; his thesis title was "Homogenizations and large deviations" and his thesis advisor was Fraydoun Rezakhanlou. His interests include probability, statistical mechanics, partial differential equations, combinatorics, and dynamical systems. His research focuses are large time behaviors of variational processes related to stochastic Hamilton-Jacobi and Hamilton-Jacobi-Bellman equations (HJ and HJB), random walks in random environments (RWRE), the stochastic Frenkel-Kontorova models (FK), Gibbs measures (GM), and first and last passage percolations (FPP, LPP).
*

West Chester University

Presents

Dr. Tadele Mengesha (Job Candidate)

Penn State University

Thursday, February 14th, 2013 from 3:15 to 4:05PM

UNA 161

**Mathematical analysis of the Linearized Peridynamic Model**

Abstract:

The talk presents a recent work on the mathematical analysis of certain nonlocal models. Our primary example is the peridynamic model of continuum mechanics: a derivative-free, integral-type continuum model that is found to be suitable for modeling materials that naturally form discontinuities such as cracks when deformed. The focus is on the linearized bond-based PD model for isotropic elastic materials. Our analysis is based on some nonlocal Poincare-type inequalities and compactness of the associated nonlocal operators. We also present the basic structural properties of the associated solution space such as compact embedding, separability, completeness and density along with regularity properties of solutions for different types of kernels. Using standard variational techniques we prove the well posedness of the system of equilibrium equations, given as "nonlocal" boundary value problems. Solutions to the nonlocal system are shown to converge to the Navier system of classical elasticity in the event of vanishing nonlocality. Some aspects of the time dependent equations of motion will also be discussed. (This is a joint work with Qiang Du.)

*Tadele Mengesha is a Research Associate at Pennsylvania State University. He obtained his PhD at Temple University in 2007; his thesis title was "Sufficient conditions for local minimizers in calculus of variations" and his thesis advisor was Dr. Yury Grabovsky, Temple University. His current research interests include Analysis of partial differential and integral equations, Calculus of Variations. Existence and uniqueness of nonlocal problems and application to peridynamics, regularity of solutions to PDEs with discontinuous coefficients, homogenization of differential and integral operators with oscillatory coefficients, stability of solutions to variational problems.
*

West Chester University

Presents

Dr. Meredith Hegg (Job Candidate)

Harvard University

Monday, February 18th, 2013 from 3:15 to 4:05PM

UNA 119

**Automatic Detection and Animation of Weather Fronts**

Abstract:

Accustomed as we all are to seeing weather maps depicting warm and cold fronts as well as other meteorological phenomena, it may surprise most people to learn that many of these features do not have universally accepted mathematical definitions. Several different models have been proposed to define warm and cold fronts, but nearly all involve differential operators of order two or higher. When applied to numerical simulation data, approximations of these operators can lead to problems related to noise amplification. As a result, the majority of weather front maps are currently generated manually using heuristic methods. Here we present a new model based on level curves of the norm of the temperature gradient. This model allows us to automatically detect and animate warm and cold fronts and also includes a method for tracing occluded fronts involving the eigenvectors of the Hessian matrix of the temperature function. We'll discuss the basis for this model and compare our results to hand-drawn maps produced by meteorologists.

*Meredith Hegg is a Preceptor in Mathematics at Harvard University. She obtained her PhD in Applied Mathematics at Temple University in 2012; her thesis title was "Exact Relations for Elasticity Tensors of Fiber-Reinforced Composites" and her thesis advisor was Dr. Yury Grabovsky, Temple University. Her thesis research was on exact relations in composite materials. Exact relations describe material properties that are maintained during the construction of composites. The theory of exact relations utilizes a non-linear transformation that sends exact relations to subspaces with algebraic properties. Ideas from representation theory are then used to find all exact relations. Her work focuses on elasticity in fiber-reinforced composites. She also has an additional project modeling weather fronts using numerical simulation data.
*

Spring 2013 Mathematics Colloquium presents

LILY KHADJAVI

Loyola Marymount University

"Social justice and mathematics: analyzing police

practice in Los Angeles"

Tuesday, February 19th, 2013 from 3:25 to 4:15PM

UNA 127

Although racial profiling is not legal, national polls indicate that most Americans believe it is a
regular police practice. Beginning in 2002, under the terms of a Consent Decree with the United
States Department of Justice, the Los Angeles Police Department collected and publicized general
tallies of all traffic stops, the outcomes of those stops, and the race/ethnicity of drivers.
Surprisingly, there have been few studies based on this data set.

Originally motivated by the desire to use real-world data and examine social justice issues in
introductory statistics courses, this project has resulted in interdisciplinary research in collaboration
with a law professor. Through the ACLU, we were able to gain access to disaggregated data from
the City of Los Angeles. As in many other parts of the country, we find significant racial and ethnic
disparities, for example in search rates. Perhaps most notably, there are significant disparities in
the police's use of searches based solely on driver consent, which are less likely to yield
discoveries. Since drivers almost universally agree to such searches, we are led to question
whether or not legal consent can be understood as an expression of free will. This talk tells the
story of this project, including an overview of the data, the social and legal issues raised, and the
statistical techniques used, and will be accessible to students and scholars from across disciplines.

*Lily Khadjavi received her bachelor's degree from Harvard University and her PhD in Mathematics from the
University of California, Berkeley. She is an Associate Professor of Mathematics at Loyola Marymount
University in Los Angeles, and this academic year is a Visiting Scholar at the Research and Evaluation Center
at John Jay College of Criminal Justice in New York. Her research interests range from algebraic number
*

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

West Chester University

Presents

Ms. Kathleen "Taffy" McAneny (Job Candidate)

Ph.D. Candidate, University of Delaware

Monday, March 4th, 2013 from 3:15 to 4:15PM

UNA 162

**Teachers' Voices: Experiencing Work Outside of Professional Development**

Abstract:

The purpose of this study was to better comprehend the experience teachers have when they are asked to implement practices learned in professional development. Data sources consisted of semi-structured interviews with twelve of the thirteen participants of professional development that requested such implementations. The analysis of the interviews resulted in the development of five major themes to capture the essence and to illuminate the teachers' experience. The themes are concerns, choices, awareness, reflection, and change. These findings can inform researchers in professional development of the importance of listening to the voices of teachers when studying the programs.

*Light Refreshments Following the Colloquium
*

West Chester University

Presents

Dr. Kathleen "Katie" Acker (Job Candidate)

American University

Wednesday, March 6th, 2013 from 3:15 to 4:15PM

UNA 162

**Mathhappy: My Research and Me**

Abstract:

Mathematics Education as a specialty has allowed me the luxury of choosing a wide variety of topics to research. My published research and my conference presentations reflect this diversity, focusing on themes of education equity, alternative education, history of mathematics and teaching with technology.

While I will review my earlier work, I primarily intend to discuss my experiences using

technology. I also want to think aloud about how to answer the question:

How can emerging technologies be effectively used to enhance all aspects of learning in the mathematics classroom?

Clearly there are previous studies that report upon curricular changes and efficacy of instruction made possible with the inclusion of graphing calculators, spreadsheet programs, and online sources into the mathematics classroom. In my opinion, there are three questions and their implications open to both development and research. They are:

How does the adoption of tablet computers by schools and smart phones by students change instruction delivery and assessment?

What does an ideal e-text for mathematics resemble?

How best could a mathematics classroom be effectively "flipped‟?

*Light Refreshments Following the Colloquium
*

West Chester University

Presents

Dr. Rachael Brown (Job Candidate)

Wednesday, March 27th, 2013

UNA 162

**Community Development in Mathematics Professional Development**

Abstract:

This session will share a study considering how a group of middle grades mathematics teachers developed into a community during a 14-week PD experience. The concept of creating a community of practice is a relatively recent idea in education. There is little written, however, about the possibility of a community of practice developing in a short period of time – though the time frame of this PD is consistent with many PD experiences in the United States. In this study, the design of the PD included focus on mathematics content knowledge and active engagement in high cognitive demand tasks with rational number concepts. Both are common recommendations for effective PD. This study found that a community of practice could be developed in this setting. Although no data were collected on the path of the community after the PD, this study provides an example of success of community of practice development within a PD setting with a facilitator intent on not only improving teachers' understanding of rational numbers but attempting to cultivate a community.

*Light Refreshments Following the Colloquium
*

Spring 2013 Mathematics Colloquium presents

PETER SCHUMER

Middlebury College

"Patterns in Pascal's Triangle"

Wednesday, March 27, 2013 from 3:15 to 4:15PM

UNA 155

In 1653, Blaise Pascal published his "Treatise on the Arithmetical Triangle" which included a description of his eponymous triangle together with some applications to algebra, combinatorics, and probability. Since that time, a
great deal more of its structure has been discovered and analyzed. In this
talk we will investigate some of the fascinating patterns contained within this
arithmetic triangle.

*Peter Schumer is the Baldwin Professor of Mathematics and Natural Philosophy at Middlebury College. He
earned his B.S. and M.S. from Rensselaer Polytechnic Institute and earned his Ph.D. from University of
Maryland, College Park. His areas of interest are elementary and analytic number theory, history of
mathematics, and combinatorics. He has written two books, Introduction to Number Theory (PWS) and
Mathematical Journeys (Wiley) and many articles in the areas listed above. He is the recipient of The Trevor
Evans Award of the MAA for the article, "The Magician of Budapest" that appeared in Math Horizons. His
other academic interest is playing and promoting the game of go (have played in 17 U.S. Opens and
countless smaller tournaments). He has had sabbaticals at UCSD, Stanford, San Jose State U., Doshisha
Univ. in Kyoto, and Keio Univ. in Tokyo. He has taught courses on mathematics and on the game of go in
Kyoto, Japan and Shanghai, China.*

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

Spring 2013 Mathematics Colloquium

presents

MARC CHAMBERLAND

Grinnell College

Wednesday, April 10, 2013 from 3:15 to 4:15PM

UNA 155

The use of computer packages has brought us to a point where the computer
can be used for many tasks: discover new mathematical patterns and
relationships, create impressive graphics to expose mathematical structure,
falsify conjectures, confirm analytically derived results, and perhaps most
impressively for the purist, suggest approaches for formal proofs. This is the
thrust of experimental mathematics. This talk will give some examples to
discover or prove results concerning geometry, integrals, binomial sums,
dynamics and infinite series.

*Marc Chamberland obtained his PhD from the University of Waterloo in 1995. He joined Grinnell College in
1997 where he is now the Myra Steele Professor of Natural Sciences and Mathematics. He has published
over 40 articles in the areas of differential equations, dynamical systems, and number theory and has spoken
about his research in several countries. He is a strong advocate of using computers in mathematical
research and has developed an NSF-supported, upper-level, undergraduate course in Experimental
Mathematics. Outside of mathematics, he enjoys time with his family (with three children), biking, and
meditation.*

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

3:20 to 4:15PM UNA 120

Irina Svyshch (West Chester University Masters Student)

**"Thesis Talk"**

Abstract:

In this thesis we will discuss some basic similarities and differences between real and complex differentiation and line integration. We will show several isomorphic approaches to complex numbers, in particular, the relationship between matrix and complex multiplication. Then, we will discuss significant differences between real and complex differentiation. We will show a non-traditional proof of the theorem on Cauchy-Riemann equations using only the complex linearity of the complex derivative. It turns out that line integration in real and complex cases has many similarities. These similarities will be explored during our discussion. We will finish by showing how the complex variable Cauchy-Goursat Theorem can be proved using the real Green’s Theorem.

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

West Chester University

Presents

Dr. Howard Cohl (Job Candidate)

National Institute of Standards and Technology

Gaithersburg, Maryland

Tuesday, April 23rd, 2013 from 3:15 to 4:15PM

UNA 161

**Fourier and Gegenbauer expansions for a fundamental solution of Laplace's equation on Riemannian spaces of constant curvature**

Abstract:

A fundamental solution of Laplace's equation is derived on Riemannian spaces of constant curvature, namely in hyperspherical geometry and in the hyperboloid model of hyperbolic geometry. These fundamental solutions are given in terms of finite-summation expressions, Gauss hypergeometric function, definite integrals and associated Legendre functions with argument given in terms of the geodesic distance on these manifolds. Fourier and Gegenbauer expansions of these fundamental solutions are derived and discussed.

*Light Refreshments Following the Colloquium
*

West Chester University

Spring 2013 Mathematics Colloquium

presents

**CARL POMERANCE**

Dartmouth College

Wednesday, April 24, 2013 from 3:15 to 4:15PM

UNA 155

*A number theorist, Pomerance specializes in analytic, combinatorial, and computational number theory, with applications*
*in the field of cryptology. He considers the late Paul Erdös as his greatest influence.*

*Pomerance was an invited speaker at the 1994 International Congress of Mathematicians, the Mathematical Association*
*of America (MAA) Pólya Lecturer for 1993--95, and the MAA Hedrick Lecturer in 1999. More recently he was the*
*Rademacher Lecturer at the University of Pennsylvania in 2010. He has won the Chauvenet Prize (1985), the Haimo*
*Award for Distinguished Teaching (1997), and the Conant Prize (2001).*

*He is a Fellow of the American Association for the Advancement of Science (AAAS) and of the American Mathematical*
*Society. He is the president of the Number Theory Foundation, a past vice president of the MAA and past chair of the*
*Mathematics Section of the AAAS. He is the author of nearly 200 published papers and one book.*

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

3:20 to 4:15PM UNA 155

Hal Switkay(West Chester University )

**"Visualizing 24 Dimensions, Listening to Groups"**

Abstract:

We continue to discuss the sensible communication of abstract information. Examples will be drawn from among the following topics: the graphical and cartographic display of data; the geometry of the 24-dimensional Leech lattice; melodies associated with finite groups.

*Hal M. Switkay grew up in Philadelphia, PA. He earned his B.A. and M.A. in mathematics at the University of Pennsylvania with a minor in philosophy, and his Ph.D. in mathematics at Lehigh University in the study of set theory. After graduation, his interests shifted towards exceptional mathematics, symmetry, lattices, groups, higher-dimensional geometry, voting, statistics, and the sensible communication of abstract information. He has taught mathematics, from remedial to advanced, has done public speaking, is a musician and composer, and has earned certification as a teacher of Tai Chi Easy™ and as a practitioner of reiki and Thai massage. He has earned a certificate from West Chester University’s graduate program in applied statistics, and is currently enrolled in West Chester University’s graduate certificate program in business. His business card lists the following interests: mathematics; music; philosophy; health and wellness.*

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

West Chester University

Presents

Ms. Kim Johnson (Job Candidate)

Wedesday, May 5th, 2013 from 3:15 to 4:15PM

UNA 161

**The proportional reasoning of pre-service teachers at the beginning of their teacher preparation program**

Abstract:

The purpose of this study is to examine the proportional reasoning of pre-service teachers at the beginning of their teacher preparation program using a developmental shifts model described by Lobato and Ellis (2010). The analysis of the data suggests that the shifts model is hierarchical for those participants who have either made all four shifts in their proportional reasoning or who provide evidence of only completing the first shift. The remaining participants provide evidence that they are in the process of making shifts 2, 3, and 4. For these participants the model does not appear to remain hierarchical. This is based upon the inconsistent evidence they provide while completing proportional reasoning problems. The findings in this study provide teacher educators with knowledge about the nature of the development of pre-service teachers' proportional reasoning. In particular, this study highlights four misconceptions: reasoning quantitatively, recognizing ratios as measurement, misconceptions about ratios and fractions, and the obstacle of linearity. Transformative learning theory (Mezirow, 1991) explains how pre-service teachers can overcome these misconceptions. This theory requires a disorienting dilemma in order to help individuals engage in rational discourse and critical reflection about previous assumptions. This study on proportional reasoning illustrates how four problems were able to provide pre-service teachers with a disorienting dilemma causing them to engage in rational discourse with the researcher and critically reflect on their previous assumptions in order to transform their proportional reasoning. The knowledge gained from this research can be used to develop courses to transform the understanding that pre-service teachers have of ratio and proportion. This ultimately will enhance the proportional reasoning opportunities they provide their students in their future classrooms.

*Light Refreshments Following the Colloquium
*

3:20 to 4:15PM Room TBA

Professor Sergei Sergeev (University of Birmingham, UK)

**"Tropical convexity over max-min semirings."**

Abstract: We develop an analogue of convex geometry over the max-min semiring, starting with description of segments, hyperplanes and semispaces, and some separation and non-separation results. We derive the max-min analogues of Caratheodory, Radon and Helly theorems, and give some colorful extensions.

Dimension of max-min convex sets will be also introduced and discussed.

This talk is based on joint work with Prof. Viorel Nitica.

**For further information e-mail **vnitica@wcupa.edu.

Note: Talks will be added to the schedule throughout the semester. Check back for updates.