Department of Mathematics
West Chester University
Office: Room 101
25 University Avenue
West Chester, PA 19383
Phone (610) 436-2440
Fax (610) 738-0578
Email: Department Chair
Colloquium talks will normally be on a Wednesday (usually in UNA 158 from 3:15-4:15), but check the information below.
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 firstname.lastname@example.org, if you would like to be on the e-mail list to receive advance notice of upcoming talks.
Previous Semesters: Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, 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.
Note: Talks will be added to the schedule throughout the semester. Check back for updates.
West Chester University
“Polynomials in Z[x] Which Are Irreducible Over Z But Are Reducible mod p, For Every Prime p”
It is well known that the polynomial x4 + 1 in Z[x] is irreducible over Z but is reducible mod p for every prime p. We shall discuss this phenomenon and also give a method to create such polynomials and give several examples.
For further information e-mail email@example.com
“Congruence by Superposition – Euclid Made Whole”
In The Elements, Euclid defined triangle “congruence” using the notion of superposition, but the idea was never formally postulated. In the 1899, in his book, Foundations of Geometry, David Hilbert set forth a modern treatment of triangle congruence by postulating by Side-Angle-Side axiom. In 2010, CCSSM Standards, returning to the notion of superposition, redefined congruence using rigid motions. In this talk we will discuss the questions: (1) Are these notions of triangle congruence equivalent, and (2) what constitutes a “proof” under the CCSSM Standards.
Dr. West is a life-long mathematics educator with degrees from SUNY Oswego, Rutgers University and the University of Texas at Austin. After teaching mathematics in high school for ten years, he moved to SUNY Geneseo where he held a faculty position in the Mathematics Department. During his thirty years at Geneseo he coordinated their highly successful secondary mathematics certification program, served as Chair of Mathematics and was promoted to the rank of Distinguished Teaching Professor of Mathematics.
Throughout his career, Dr. West has contributed to the improvement of mathematics teaching with his professional service. He has been a member of the Association of Mathematics Teachers of NYS for over 40 years, serving as its 38th president and as the editor of the NYS Mathematics Teachers’ Journal. He has served the Mathematical Association of America as the New York State Regional Coordinator of the American High School Mathematics Examination as a member of the Committee on Technology in Math Education and as a Visiting Lecturer. In addition, he has served the National Council of Teachers of Mathematics as both member and chair of the Regional Services Committee.
Dr. West’s teaching and leadership has been recognized with the SUNY Chancellor’s Award for Excellence in Teaching and the MAA Distinguished Teaching Award. In his retirement, Dr. West is a T3 National Instructor and continues to do mathematics, work on his old cars, read avidly and most importantly, watch his ten grandchildren grow!
Fitness is environment-specific, and many organisms have evolved the ability to alter resource allocation based on perceived environmental cues (e.g., food/mate availability, predation risk). We are developing an optimization model that examines relative resource allocation into growth, reproduction, and defensive morphology under varying conditions. Specifically, we are investigating how reproductive investment in terms of rate and amount changes as a function of predation risk. The survival function utilizes a modified Gompertz-Makeham law for mortality. The fecundity function is the product of the reproductive schedule and output. The reproductive schedule utilizes a gamma distribution and the output is modeled exponentially. Optimizing the fitness model yields the optimal resource allocation and resulting reproductive schedule. This allows us to understand the effects of phenotypic plasticity in life-history traits on the evolution of a post-reproductive period. As predation risk increases, more resources are allocated towards defenses. However, once predation risk is sufficiently high, it becomes more beneficial for the individuals to allocate all their resource towards reproduction.
A model is being developed that simulates the dorsal closure process, a stage of drosophila embryogenesis. The apical side of the amnioserosa (a cell monolayer- wound like region on the surface of the embryo) is being represented through polygonal two dimensional representations of cells, with forces acting on their edges and nodes. Those forces are being regulated by the action of actin and myosin. The model is granular enough so various subregions can be studied to the level of the individual cell. Various equations are being tested, describing the evolution of forces generated by the action of the actomyosin network, which itself might be biochemically driven. Eventually, the model may be used to understand mechanisms of dorsal closure that are not easily analyzed in the lab or produce simulation results that might drive new experiments.
Microbes form a large and central part of the global ecosystem. As a consequence of their short reproductive time and their proficiency at exchange of genetic material, it seems plausible that microbes in communities operate at high efficiency (in terms of free energy and nutrient usage) in many contexts. One obvious issue of interest would be the description of species within a microbial community and its dependence on the local environment. Description of niche structure of organisms and how that structure impacts competitiveness has long been a topic of interest among ecologists. Here, in the context of Yellowstone National Park microbial mat, we discuss influence of temporal environment on microbial community species structure. The possibilities of competitive exclusion and clocking behavior are discussed.
Professor Isaac Klapper is an expert in fluid dynamics and the mathematical modeling of the various aspects of biofilm formation, evolution and its interactions with its environment. He is the author of numerous publications and the receiver of several grant awards. He received his A.B. in Mathematics from Harvard University in 1986 and his PhD in Applied Mathematics from the Courant Institute, New York University (NYU) in 1991. He was an NSF postdoctoral fellow at the University of Arizona and a visiting assistant professor at UCLA in the Departments of Applied Mathematics. He served as a tenure-track and tenured faculty and rose to the rank of Full Professor at Montana State University where he was also affiliated with the Center of Biofilm Engineering (CBE) at Montana State. In 2012 he moved to Temple University with the appointment of Full Professor, Department of Mathematics with secondary appointment in the Department of Biology.
“The World of Graph Theory: Coloring, Scheduling, and Solving Mysteries”
Graph Theory is a field of mathematics that encompasses tools and techniques for modeling and solving real world problems. In this talk, we explore graph coloring and some of its applications and show how graph theory can be useful in problem solving. In one of our problems, six professors are suspects in a library theft. We'll use their testimony together with some graph theory to identify the guilty party. We will also discuss related current research, some of which involves undergraduates. This talk is designed for a general audience.
Ann Trenk is a Professor of Mathematics at Wellesley College where she has taught since 1992. She has published over 30 research articles focused primarily on structured families of graphs and partially ordered sets. Her book, Tolerance Graphs, coauthored with Martin Golumbic, was published by Cambridge University Press in 2004.
In addition to teaching at Wellesley College, Professor Trenk has taught high school students both as a full-time teacher and in summer programs, and more recently has organized math enrichment activities for elementary school children. Professor Trenk was awarded the Wellesley College Pinanski Prize for Excellence in Teaching in 1995.
In ecological studies, identifying the number of species present in an ecosystem, also known as identifying the species richness, is key to measuring biodiversity and ecological stability. In order to analyze the species richness of a system, we performed a process known as rarefaction. Through rarefaction, we attempted to identify the number of samples needed to accurately represent a system.
We examined different methods of performing rarefaction, including the combinatorics method and the bootstrap method, and compared them. Both of these methods allowed us to construct a rarefaction curve that plots the number of species as a function of the number of samples taken. Using these rarefaction curves, we then extended the model by examining initial costs and coverages of the samples. These examinations served to identify the number of samples needed to represent the ecosystem. Once we identified the number of samples needed, we compared the results of different months and locations.
As a possible cause of any present differences between months and locations, we examined the number of degree days that occurred over each month. Degree days did not appear to cause any differences between locations.
We are studying which abiotic parameters best explain the presence or absence of brown trout in White Clay Creek and will subsequently use those parameters to develop a Habitat Suitability Index (HSI). The goal of finding an HSI for different habitats is to help researchers improve decision making and increase understanding of species-habitat relationships. Using the dataset provided by Stroud Water Research Center, we are analyzing the correlation or lack thereof between environmental factors and the quantity of brown trout present in that environment. Using fuzzy logic, we are developing a model to determine an HSI, which is a numerical index that represents the capacity of a given habitat to support a selected species.
“Financial Derivatives: Engines of the Economy or Weapons of Mass Destructio”
Financial Derivatives is the name for a wide variety of products traded in today’s financial markets. Used mostly for risk management, they can also be used for speculation and gambling. They can be both dangerous and beneficial. From a mathematical perspective, the key challenge is to properly evaluate the price and the risk inherent in a derivative contract. In this talk I will give an overview of the three main methods to price derivatives:
Klaus Volpert is associate professor of mathematics at Villanova University. He won the University’s Lindback Award for Excellence in Teaching in 2009 and the EPaDel’s Crawford Award in 2011. Early studies in his native Germany and the 1989 PhD from the University of Oregon were in pure mathematics (algebraic topology), but he has more recently been interested in problems in applied mathematics, specifically at the intersection with finance and economics. Outside of mathematics, he enjoys making music with his family and friends.
The sperm whale is the largest toothed whale. It is currently on the list of vulnerable species by the International Union for the Conservation of Nature and Natural Resources (IUCN). Even though a lot of research has been dedicated to sperm whales, very little is known about their population dynamics. In this talk I will first go over the brief results of our study to investigate the demographic characteristics of the endangered sperm whale population. Our results indicate that these survivorship rates are very delicate, and a slight decrease could result in a declining population, leading to extinction.
The Deepwater Horizon (DWH) oil rig exploded in April of 2010. This environmental disaster has encouraged substantial research efforts to better understand how such disasters affect the resilience of the Gulf of Mexico (GoM) ecosystem. In this talk I will demonstrate how mathematical models can be applied to understand the impacts of such disasters on the dynamics and persistence of marine mammal populations in the Northern GoM under certain assumptions. Matrix population models are developed to study the lethal and sub-lethal impacts. We investigate how reductions in the survival probabilities and in fecundity affect the sperm whale population. We then investigate the long term effect of such an environmental disaster on the population of sperm whales in the GoM. We also inspect the effects of demographic stochasticity on the recovery probabilities and the recovery time of the population.
Partial Differential Equation Models based on Cahn-Hilliard type equations will be discussed. Those Models have applications in various fields from material science to biology. Discontinuous Galerkin Finite Element Methods for the solution of Cahn-Hilliard type equations will be presented. For the underline schemes: solvability, energy stability, convergence and error estimates will be established. Simulation results will be provided. Current and future directions will be discussed.
Note: Talks will be added to the schedule throughout the semester. Check back for updates.