Mathematics & Computer Science
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- Problem of the Month
Date: 9/15/2005 (Thursday)
Title: Outwitting the Lying Oracle
Abstract: Imagine that you are placing bets on the outcomes of coin tosses and you are playing against an oracle who knows what the outcomes will be. He is willing to tell you how the coin will land, but he may lie. How much should you bet on each coin toss in order to maximize your winnings? We will look first at the situation where the oracle may lie up to k times out of n tosses and the player always agrees with the oracle. Then the player will try to outwit the oracle by placing a large bet, hoping to induce him to lie, and then disagreeing with his prediction. Finally, we will generalize our results to cover any possible set of "lie patterns" by the oracle, e.g., lying at least once, but no more than 3 times, and never twice in a row, out of 10 tosses.
Bio: Dr. Robb Koether grew up in Glen Burnie, MD just a mile or so from Dr. Bill Abrams. Dr. Koether earned his B.S. degree in mathematics at the University of Richmond in 1973, and his M.A. and Ph.D. degrees in mathematics from the University of Oklahoma in 1974 and 1978, respectively. After leaving OU, he taught math at Campbell University in NC for four years. In 1981 he came to Hampden-Sydney College where he has been teaching mathematics and computer science ever since. His wife Cindy also teaches at HSC. They have three children, all grown and recently married. Dr. Koether enjoys bicycling, camping, and hiking.
Date: 10/13/2005 (Thursday)
Title: What do Universities and Pornography have in Common?
Abstract: Academics often makes claims on the line of "...with the ever increasing need for instant information, users often ______." They do not, however, often explain this claim in any way. What does it mean to have an "ever-increasing need" for information? Why does it have to be instant? What does this mean for those of us who have to support the creation, storage, and retrieval of that information? Most importantly, why should we trust this information or make business and policy decisions based on it?
Information retrieval (search) has become a hot issue in both academia and the networked world at large. We see this in Google's stock value, as well as in research dollars committed to search projects (both from academic programs like NSF and from the military). As search interests grow, trust in search results seems to grow with it. Our lab has recently begun evaluation and creation of search engines, extending our existing academic search engine projects to cover broader topics like popular culture. This talk will broadly address search needs as they are currently understood, and dive into more specific discussions of complex indexing (academic citations) and the successes and failures of interest research done by analysis of search logs (what universities and pornography have in common).
Bio: Matthew Peters is a PhD candidate in Information Sciences & Technology at the Pennsylvania State University. His research covers issues of universal access, information management, and human-computer interaction, with a specific emphasis on computer supported cooperative learning tools for informal science education. He is a part of the Computer Supported Collaboration and Learning lab and the Center for Human-Computer Interaction at Penn State.
Date: 11/8/2005 (Tuesday)
Speaker: Dr. Keith E. Mellinger
Assistant Professor of Mathematics
Department of Mathematics
University of Mary Washington
Title: Can you hear me now? The Mathematics of Error-Correcting Codes for Digital Communication
Abstract: The theory of error-correcting codes has a rich, but short history beginning in the late 1940s and growing steadily since. Although the applications have changed immensely, the basic principles behind the correction of digitally transmitted messages has remained unchanged and the mathematical theory has progressed constantly. In this talk, I will start by looking at some of the major historical moments in the development of error-correcting codes. From there, I will discuss some of the techniques for using geometry to construct error-correcting codes. I'll outline some of the contributions made by my undergraduate students as well as some of the open problems that I still struggle with myself. The talk should be accessible to a general mathematical audience.
Bio: Keith E. Mellinger earned a Ph.D. (2001) and M.S. (1997) in mathematics from the University of Delaware, after receiving a B.S. (1995) in mathematics from Millersville University (Pennsylvania). He was a VIGRE post-doc at the University of Illinois at Chicago prior to joining the University of Mary Washington in the fall of 2003. Dr. Mellinger is a 04-05 Project NExT fellow through the Mathematical Association of America, and he and colleague Debra Hydorn received a grant in 2004 to host the Central Virginia Regional Conference for Undergraduate Research in the Mathematical Sciences. He has delivered professional presentations throughout the country and in Greece, Italy and Canada, and has been published in several research journals. His research interests are in discrete mathematics, in particular, finite geometry and coding theory, and he just received a $25,000 grant from the National Security Agency to continue his work on geometric constructions of graphs and codes. On the side, Dr. Mellinger serves as a brief/script reviewer and mathematical content consultant for CyperChase, an educational television show for children ages 8 through 11. He enjoys spending time with his wife and 2 dogs, and playing guitar and mandolin in a local Fredericksburg bluegrass band.
Date: 11/29/2005 (Tuesday)
Title: A Brief Excursion into Matrix Population Modeling
Abstract: Linear stage-classified matrix models have been used with success in many ecological and demographic modeling processes, in part because of the certainty imparted by linearity. Computers and techniques from dynamical systems have opened the door to a wider use and better understanding of non-linear models, but their behaviors in many ways resists the easy rigor which can be applied to linear models. In this talk, I will first present some basic information about stage-classified matrix models, focusing in particular on the classical linear Leslie model. Then, I will try to demonstrate and explain some of the interesting behaviors exhibited by a class of non- linear models similar to the Leslie models.
Bio: Matt Sosa graduated from Iowa State University in 1997 with a B.S. in Mathematics and a B.S. in Physics. After three years in the Eberly College of Science at Penn State University, his graduate career was interrupted by military service in 2001, and he was awarded an M.A. in Mathematics for his work up to that time. He has since returned and is working to complete a Ph. D in Mathematics under his advisor Dr. Howard Weiss.
Date: 2/2/2006 (Thursday)
Speaker: Randall Helmstutler
Assistant Professor of Mathematics
Department of Mathematics
University of Mary Washington
Title: Vector Calculus as Algebraic Topology
Abstract: The techniques of algebraic topology need not be as lofty and abstract as chain complexes or long exact homotopy sequences. One of the oldest areas of algebraic topology--de Rham cohomology--can be understood from the point of view of basic vector calculus (indeed, this is its origin). We will describe how the theory of line integrals of vector fields leads to algebraic invariants of geometric objects in Euclidean spaces. This "simplified" version of algebraic topology is sufficient to produce most of the first results commonly encountered in introductory algebraic topology, including the Brouwer no-retraction theorem.
Bio: Randall Helmstutler earned his Ph.D. from the University of Virginia in 2004, specializing in an area of topology known as axiomatic homotopy theory. A native Virginian, he is currently on the mathematics faculty at the University of Mary Washington.
Date: 3/2/2006 (Thursday)
Title: Iterative Methods Using Classical Means
Abstract: An iterative method for calculating a solution to an equation is one in which successive approximations are made. An important question in numerical analysis is how quickly the iterates, or approximations, converge to a solution. Newton's method is perhaps the most commonly used iterative method for solving f(x)=0 (if f(x) is differentiable) and this is due in part to its convergence rate. In this talk we'll present two iterative methods for calculating square roots of numbers that rely on arithmetic, geometric, and harmonic means. We'll discuss the convergence rates of these methods and display some surprising connections to Newton's method.
Bio: Dr. Trapp received her Ph.D. from Carnegie Mellon University in numerical analysis. She has spent time at both Los Alamos and Sandia National Laboratories working on numerical solutions for partial differential equations. Currently she is an Assistant Professor at the University of Richmond with a research focus on mimetic methods for solving Maxwell's equations.
Date: 3/28/2006 (Tuesday)
Title: Deformation of Biological Membranes
Abstract: Using the mathematical approach of elasticity theory, we can describe how a biological membrane is deformed by an applied force. In this talk we will focus on applying elasticity theory to Magnaporthe grisea, a fungus that destroys from 10% to 30% of the rice harvest each year. The fungus attaches to a rice leaf and forms a dome-shaped structure, the appressorium, in which enormous pressures are generated that are used to blast a penetration peg through the rice cell walls and infect the plant. In fact, the pressure in one 5 micron diameter appressorium is equivalent to approximately forty times the pressure in your car tire. We developed a model of the appressorial design in terms of a bioelastic shell that can explain the shape of the appressorium and its ability to maintain that shape under the enormous increases in turgor pressure that occur before and during penetration.
Bio: Anthony Tongen earned his Ph.D. in Applied Mathematics from Northwestern University in 2002 focusing on Computational Materials Science. His current research is in Mathematical Biology. Anthony Tongen is currently an Assistant Professor at James Madison University.
Date: 4/20/2006 (Thursday)
Title: Developing a 2020 Vision for Mathematics Education
Abstract: The undergraduate mathematics curriculum in the year 2020 should look very different from what we see today, particularly the curriculum in the first two years. There are many pressures being exerted to make significant changes. This presentation will highlight the issues and outcomes in the first two years of college mathematics. There will also be a presentation of a new B.S. in Applied Mathematics at Virginia Military Institute.
Bio: Lee S. Dewald graduated from The Citadel with a BS in Mathematics in 1969. He served in the U.S. Army for 23 years including assignments in Vietnam, Fort Hood, Fort Sill, Fort Knox, Fort Lee, and West Point. He commanded three artillery batteries, was an associate professor of mathematics at the United States Military Academy, and was the Program Director of the Operations Research Systems Analysis Military Applications Course I at Fort Lee, VA. He has a Masters Degree in Operations Research from the Naval Postgraduate School and an MBA from Long Island University. His Ph.D. is in Operations Research with a minor in mathematics from the Naval Postgraduate School. He started teaching for Florida Tech as an adjunct professor in 1991; became an associate professor of management at the Fort Lee Graduate Center in 1992; and had been the Director of Graduate Studies at Fort Lee since December 1994 until August 2002. In August 2002 he joined the Department of Mathematics and Computer Science of the Virginia Military Institute in Lexington, VA. He has been the Head of the Department of Mathematics and Computer Science since August of 2004. He is married to Margaret (nee Kieser) with two children and three grandsons. His hobbies include stamp collecting, bridge, hunting, fishing, and sports (softball, basketball, and racquetball).
Bio:Danny Cline was born in West Virginia and received two B.S. degrees from West Virginia University, one in Mathematics and one in Chemical Engineering. He went on to study mathematics at the graduate level at Virginia Tech, earning his M.S. in Mathematics and, in 2004, his Doctorate in Number Theory. Since the fall of 2005, he has been an Assistant Professor of Mathematics at Lynchburg College. His mathematical interests are primarily in number theory and the philosophy of mathematics.