Abstracts for 2009/10

Abstract: We will describe David Gale’s game of Chomp, which is a mathematical game whose moves require eating a chocolate bar. The game is a topic of ongoing research, including a recent summer project by first-year undergraduates. We will discuss an interesting generalization of the game and some of the questions and techniques of combinatorial game theory.

Bio: Alex Meadows received his PhD from Stanford University and is now Assistant Professor of Mathematics at St. Mary's College of Maryland. His research spans partial differential equations, geometric analysis, and combinatorial game theory. He is faculty advisor to the math club and the improv club, and he is an amazingly good basketball player.

Ms. Brittany Fuller, Ms. Calie Giangi, Mr. Bobby Markey, and Ms. Amanda Rebovich (MATH 395)

Title: Speaking the Universal Language: Mathematics Study Abroad Trip in Greece

Abstract: All across the world, communicating with one another can be difficult due to the various languages spoken. However, there is one language that is accepted and understood across all cultures: mathematics. In this presentation, we 5 Longwood students will share our experiences from a study abroad trip to Greece in the summer of 2009. We will discuss how mathematics is depicted through Greek history and how our mathematical studies are a direct relation to the findings of ancient mathematicians, such as the Greek Pythagoreans. We will also discuss how mathematics influences other disciplines of studies through various forms of thinking. Finally, we will discuss future opportunities for current Longwood students to have the same life-changing experiences through the speaking the international language of mathematics abroad.

Brittany Fuller is a Junior, Mathematics Secondary Education major. She has been actively involved in the Cormier Honors College for two years. She is a Longwood Ambassador. She has also become very involved in Kappa Delta Pi, the International Honors Society for Educators. Brittany is currently in her second year of begin a Resident Assistant. She hopes to graduate in Spring 2011.

Calie Giangi is a mathematics major with a biology minor, and is planning on getting a masters in biostatistics after graduating.

Bobby Markey is a senior mathematics student at Longwood University getting his teaching licensure to teach grades 6-12. He was the former president of the Longwood Math Club, Treasurer of the Longwood chapter of Pi Mu Epsilon, and a 2009 recipient of the Longwood Citizen Leader award. He recently placed 7th at the National Problem Solving Championships in Portland, Oregon and presented research on coordinated tutoring in the calculus classroom with Dr. Sharon Emerson-Stonnell at the 2009 Joint Mathematics Meeting in Washington, D.C.

Amanda Rebovich is a third year math secondary education major. She is a member of the Society of Physics Students and is planning on attending the programming competition in November. After graduation she plans on getting a masters in mathematics.

Catherine Swandby is a senior majoring in chemistry with minors in both biology and mathematics. After graduating from Longwood her future plans are to attend graduate school in chemistry with a concentration in medicinal chemistry and/or biochemistry.

Abstract: The primary objective of phase 1 clinical trials is to identify a safe and effective drug administration in humans. In these trials, various doses of a potential drug or drug combination are monitored to establish the optimal dose to be recommended for the treatment of patients with a certain medical condition. The optimal dose is that which obtains a certain response yet possesses an acceptable toxicity rate. It is reasonable to assume that response due to a agent being tested increases with dose, hence we aspire to give patients as much of that agent as possible. However, it is also often true that toxicity increases with dose. Therefore, phase 1 studies seek to find the dose, referred to as the maximum tolerated dose (MTD,) that is closest to some pre-specified toxicity rate. Many model based designs have been proposed during last two decades. Among these designs is the widely used continual reassessment method (CRM), proposed by O’Quigely, Pepe and Fisher (1990). CRM has been shown to out-perform the standard designs in cancer studies in addressing concerns raised by the conduct of such trials, such as (1) ineffectiveness of the treatment at low doses, (2) severe toxicity expected at high doses, (3) insufficient information regarding the dose-toxicity relationship at the beginning of the trial, (4) possible treatment benefit for the patients, (5) need for efficient design with a small number of patients.

Bio: Nolan Wages is a Ph.D. candidate in the Department of Statistics at the University of Virginia and Assistant Professor of Mathematics and Computer Science at Hampden-Sydney College. His research investigates the statistical methodology underlying the design of phase 1 clinical trials for chronic disease. Specifically, his research has lead to the development of a model-based design for multi-drug trials that generalizes the widely-accepted continual reassessment method (CRM).

Title: The Traveling Salesman, Graph-theoretic Independence, Fullerenes, and Automated Conjecture-making

Abstract: Given a number of cities and the distances between them and a salesman who must visit them all, what is the best route for him to take? Is there an efficient way to answer this question. Given a network of nodes and edges, what is the maximum number of nodes that have no edges between them. Is there an efficient way to answer this question? Recent work on automating mathematical conjecture-making will be described, as well as connections between this work and the previous questions, and even to the question of determining which chemical isomers are stable.

Bio: Craig Larson received his Ph.D. from the University of Houston, and is now an Assistant Professor of Mathematics at Virginia Commonwealth University (VCU). His research spans graph theory, the investigation of the structure of maximum independent sets in graphs, the theory of various graph invariants, as well as applications to chemistry.

Abstract: Did you know that discrete mathematics can increase the number of kidneys available for patients who need a transplant? In a kidney paired donation, one patient and his incompatible donor is matched with another patient and donor in the same situation for an organ exchange. Patient-donor pairs can be represented as the vertices of a graph, with an edge between two vertices if a paired donation is possible. Then, a maximum matching on that graph is an arrangement in which the largest number of people can receive a transplant. Our simulations demonstrating paired donation's impact on the kidney shortage even motivated Congress to pass a law allowing the United Network for Organ Sharing to use our algorithm in a nationwide program. At the intersection of math and medicine, this work is both a source of exciting puzzles and an example of how mathematics can meaningfully impact people’s lives.

Bio: Sommer Gentry is Assistant Professor of Mathematics at the U.S. Naval Academy and is also affiliated with the Johns Hopkins University School of Medicine. She studied operations research at Stanford University and M.I.T. She was a Department of Energy Computational Science Graduate Fellow, and a winner of the CSGF contest for excellence in technical writing that conveys computational science to a lay audience. She designed optimization methods used for nationwide kidney paired donation registries in both the United States and Canada. Her work has attracted the attention of major media outlets including Time Magazine, Reader’s Digest, Science, the Discovery Channel, and the Diane Rehm show. She is a recipient of the Mathematical Association of America's Alder Award for distinguished teaching by a beginning college or university mathematics faculty member.

Abstract: The Mathematical Sciences Digital Library MathDL) was begun by the Mathematical Association of America (MAA) in January 2001 as a collection within the National Science Foundation's National Science Digital Library (NSDL). In 2008 MathDL was combined with MAA's NSDL pathway project, The Math Gateway. This new digital library continues to carry the MathDL name. This talk will review the development of MathDL, sample some of the resources available through the Library, and discuss possible future development.

Bio: Lawrence (Lang) Moore is an associate professor emeritus at Duke University. He is executive editor of MathDL and PI on the supporting NSF grant. Professor Moore has a long-time interest in the use of technology in undergraduate mathematics education. Together with his colleague David Smith, he worked on Project CALC, an NSF-supported calculus renewal project that led to the publication of the first edition of Calculus: Modeling and Application in 1996. This was followed by the Connected Curriculum Project (CCP) and the development of the CCP digital library, now a MathDL partner. The second edition of Calculus: Modeling and Application, a strictly online text, was developed with NSF support and is currently being published by the MAA.

Abstract: The formula used to compute quarterback passer ratings in the National Football League is not well known and is generally assumed to be quite complicated. In this talk, however, we will see how to use some simple tools from Linear Algebra to determine the formula. Topics will include systems of equations, projections, least-squares solutions, numerical sensitivity, and the condition number of a matrix.

Bio: Owen Byer is a Professor of Mathematics at Eastern Mennonite University. His undergraduate degree was from Messiah College and he earned a PhD in mathematics from the University of Delaware (Extremal Graph Theory). He is currently in his 12th year at EMU. His hobbies include NFL football, bridge, and playing basketball.

Abstract: In order to make complex problems tractable, academics have a natural tendency to pare down complexity and to avoid hard-to-define problems. Unfortunately this creates a gulf between the kinds of problems that industry faces and those that academia attempts to solve. One can see this gulf in tools and techniques that academics create that cannot be applied to more than a few thousand lines of code, and in graduates who have never seen more than a few hundred lines of code that they did not write themselves.

In this talk we focus on one key attribute of industrial problems that is ignored by much academic work: scale. Using examples from NVIDIA's Software Infrastructure and Operations team, we explore issues of scale along many dimensions: architecture, code, process, teams, and time.

As we discuss the examples, we also consider the implications for academic teaching and research, and discuss strategies for achieving scalability. The problems that arise are perhaps not as sexy or novel as those in academia, but they are just as challenging, almost always dominating the more "academic"

Bio: David Coppit manages the development team for NVIDIA's driver verification system (DVS), a distributed build and test system for display drivers. Before joining NVIDIA in 2008, he was an assistant professor of Computer Science at the College of William and Mary and a research scientist at Incogen, a bioinformatics company. He received his graduate degrees from the University of Virginia, and his undergraduate degrees from the University of Mississippi.