Mathematics Talks
Spring 2008
April 9, Dr. Lynn Bodner, Monmouth University, Symmetries of Islamic Patterns, 3 p.m., Howard Hall 309
Abstract
People of every known human society have used tilings and patterns to cover the floors and walls of their homes from even the earliest of times. A main characteristic in Islamic decoration is the use of a finite number of tile shapes to create intricate, infinitely repeating geometric designs. And, although the variations among the designs seem to be unlimited, they all may be classified mathematically as belonging to only a finite number of possible classes based on the isometries (distance-preserving transformations) permitted by each pattern. There are only seven possible "strip" (or frieze) groups for one-dimensional patterns and 17 possible "wallpaper" groups (also known as plane crystallographic groups) for two-dimensional patterns. This talk will explain and then illustrate how strip patterns may be analyzed and categorized according to the set of symmetries that exist in the design as a whole, using beautiful examples of Islamic art found throughout the world.
February 14, Dr. Ileana Ionascu, Philadelphia University, Reflexivity Properties for Operators on Hilbert Spaces, 3 p.m., Howard Hall 205
Fall 2007
November 14, Kappa Mu Epsilon Undergraduate Colloquium, Michael Leibrock, Commerzbank, The Merging of Financial Mathematics and Wall Street; Trends and Opportunities All Math Students Should Know, 2:30 p.m., Howard Hall 309
Abstract
During the last decade, Investment Banks and Hedge Funds have fueled an explosion of new complex financial products and structured vehicles. While offering the potential of substantial profits for market participants, these new products also carry significant risks and complexities.
During this discussion, learn how financial mathematics is at the forefront of efforts to help firms adequately measure, monitor, and control such risks. You will see examples of financial tools employed in the market today by portfolio managers and risk managers and hear about actual career opportunities for math majors with top-tier Wall Street firms.
October 5, Dr. Betty Liu, Monmouth University, Computer Simulations of Blood Flow in Curved Atherosclerotic Arteries, 2:30 p.m., Howard Hall 309
Abstract
Heart attack is the chief cause of death in the United States. A heart attack occurs when the blood supply to an area of heart muscle is blocked. The most frequent cause of loss of blood supply to the heart is atherosclerosis, which preferentially occurs in the arteries with bends or branches. It involves complex interactions between the artery wall and blood flow. Both clinical observations and experimental results show that hemodynamics plays a significant role in the physical processes that lead to atherosclerosis. Therefore a detailed hemodynamic evaluation of disturbed flow in atherosclerotic arteries is important to understanding the progression of atherosclerosis and may have useful clinical value, such as early detection of a highly stenosed artery segment, prediction of future disease progression, and treatment planning. Dr. Liu will present work on the investigation of blood flow in atherosclerotic arteries by computer simulations. Through numerical solutions obtained under various values of physiological parameters, program attendees will observe the flow pattern in curved arteries with stenosis.
Spring 2007
February 12, Dr. Suneal Chaudhary, University of Utah, An American Option Pricing Method on Statistically Estimated Processes, 9 a.m., Howard Hall 316
Abstract
This talk presents a fast, flexible numerical technique to price American options and generate their value surface through time. The method runs faster and more accurately than the standard CRR binomial method in practical cases and calculates options on a considerably broader family of new, useful underlying asset processes. The technique relies on the Fast Fourier Transform (FFT) to convolve a transition function for the underlying asset process. The method allows the underlying asset process to be quite general; the classical standard geometric Brownian motion, the Variance Gamma process (Madan, 1998), and a novel, purely empirical transition function are compared by computing their respective American put value surface and the exercise boundaries.
February 16, Iliana Ignatova, University of South Carolina, The Minimum Sum Method for Medicare Fraud Investigations, 10:30 a.m., Howard Hall 316
February 20, Rachael Welder, University of Montana, Preservice Elementary Teachers’ Mathematical Content Knowledge of Prerequisite Algebraic Concepts, 9 a.m., Howard Hall 316
February 21, Joseph Rusinko, University of Georgia, Tropical Mathematics, Howard Hall 316
February 26, Dr. Micah Chrisman, University of Hawaii, Mapping Class Groups: Presentations and Thurston Type, 9 a.m., Howard Hall 316
Abstract
In this talk, Dr. Chrisman will define the mapping class groups of closed orientable surfaces and discuss some of the theorems developed during the 20th century to deal with them. In particular, he will discuss the Dehn-Lickorish Theorem, the presentations for the genus 1 and 2 case, and the Nielsen-Bers-Thurston Classification Theorem. The major focus will be on the difficulty of recognizing the Nielsen-Thurston type of a mapping class from its decomposition into Dehn twists (the most popular way of expressing mapping classes).
Secondly, Dr. Chrisman will discuss a short exact sequence involving the mapping class group and the integral symplectic group. This allows us to reduce some of the difficulties down to matrix algebra. However, the surjection fails to recognize Nielsen-Thurston type. Dr. Chrisman will discuss his algorithm for determining the complex conjugacy class of finite cyclic subgroups of the integral symplectic group, which correspond to finite order mapping classes.
This talk is designed to be audience friendly and includes many examples and pictures. No knowledge of low-dimensional topology is assumed.
April 13, Dr. Bob Smith, Monmouth University School of Business Administration, Dr. Susan Marshall, Monmouth University, Feedback, Control, and Prime Number Distribution, Howard Hall 307
Abstract
Feedback and control systems model complicated phenomena and help explain, for example, why a driven car stays on the road. Mathematically, these systems are modeled by differential equations whose solutions result in either explosive or damped behavior combined with either oscillatory or non-oscillatory behavior. We explain the intuitive feedback inherent in prime number distribution (that "too many" primes "knock out" additional potential future primes), and model this feedback as a differential equation. The solution to this differential equation intuitively explains why the density of primes "stays on the road" [a density of 1/ln(x)], and why the total number of primes crosses its approximation infinitely many times. The solution also motivates some surprising conjectures. This talk combines previous results of others with new results and interpretations. This is joint work with Dr. Susan Marshall, of Monmouth University.
Fall 2006
September 22, Dr. Bonnie Gold, Monmouth University, Introduction to the Philosophy of Mathematics
October 20, Dr. Joseph Coyle, Monmouth University, An Introduction to Inverse Problems
Abstract
Inverse problems were considered by Plato in his Republic. They played a role in the discovery of the planet Neptune, and were used in the creation of medical imaging techniques such as CAT scans and MRIs. Inverse problems are often best understood in the context of the more familiar, but closely related, so-called direct problem. The aim of the talk will be to give some insight into the relationship between direct and inverse problems from both a mathematical and layman's point of view.
November 8, Kappa Mu Epsilon Undergraduate Colloquium, Dr. Michael Jones, Montclair State University, A Voting Theory Approach to Golf Scoring
Abstract
The Professional Golfer's Association (PGA) is the only professional sports league in which the rules describing how an event is scored change according to the event. Even without including match play or team play, PGA tournaments can be scored under stroke play or the modified Stableford scoring system; these two methods of scoring are equivalent to using voting vectors to tally an election. This equivalence is discussed and data from the 2004 Masters and International Tournaments are used to examine the effect of changing the scoring method on a tournament's results.
With as few as three candidates, elementary linear algebra and convexity can be used to show that changing how votes are tallied by a voting vector can result in up to seven different election outcomes (ranking all three candidates and including ties) even if all of the voters do not change the way they vote! Sometimes, regardless of the voting vector, the same outcome would have occurred, as in the 1992 U.S. presidential election. Dr. Jones relates this to the question, "Can we design a scoring vector to defeat Tiger Woods?," and answers it, retrospectively, for his record-breaking 1997 Masters performance.
