This page contains the abstracts for the invited talks at the NES/MAA Fall 2005 Meeting at the University of New Hampshire.  As abstracts are received, they will be posted here.

Dave Abrahamson, Rhode Island College
 "Take Me Out To The Simplex"

Abstract:  Over the last few decades, a growing number of questions in the world of baseball have drawn the attention of mathematical modelers.  We will survey some of the results, including the "Pythagorean prediction" of a team's record, the relative importance of various offensive statistics, and a recent use of linear programming to study the outcomes of the annual Cy Young Award voting.

Biography:  Dave Abrahamson received his B.S. in Mathematics from Harvey Mudd College and his Sc.M. and Ph.D. in Applied Mathematics from Brown University.  Carlton Fisk's Game 6 homer made him late with a real analysis assignment, and he later had to proofread his dissertation during Fernandomania. He is celebrating his twentieth year at Rhode Island College, during which time the Red Sox have won the World Series once.

Carl Cowen, Indiana University - Purdue University at Indianapolis (IUPUI)
"Connections Between Mathematics and Biology"

Abstract:  Dr. Rita Colwell, a research microbiologist and former Director of the National Science Foundation, regards the mathematical sciences as the backbone for US Scientific and Engineering research. Many scholars see the next few decades as a time of intensive progress in the biological sciences.  Dr. Colwell sees mathematics as being an integral part of the progress in biology, not a traditional view, but a forward looking one.

In this talk, Dr. Cowen will outline some of the research areas in the emerging collaborations between mathematical and biological scientists.  In addition, Dr. Cowen, who began his study of the mathematics of neuroscience in 2002-03 at the Mathematical Biosciences Institute at Ohio State University and who worked in 2003-04 as a junior post-doc in the lab of Prof. Christie Sahley in the Purdue University Biology Department, will illustrate the connection between mathematics and neuroscience with a discussion of the Pulfrich phenomenon, an experiment that helps illuminate how the brain
processes visual images. There are few mathematical or biological prerequisites for this discussion.

Biography:  Carl Cowen was born and raised mostly in Indiana.  He was educated at Hanover College, Indiana University, and the University of Warwick (England), and received his PhD in pure mathematics from the University of California, Berkeley.  He was at Purdue University from 1978 to 2004, but before that he had a post-doc position at the University of Illinois and had teaching experience in junior high school and small colleges.  He was Director of Purdue's Actuarial Science Program from 1992 to 1997 and was Head of Purdue's Mathematics Department from 1997 to 2002.
Since August 2004, he has been Dean of the School of Science at IUPUI (Indiana University - Purdue University at Indianapolis) where he has had the chance to promote research and education at this rapidly developing young institution.  In addition to his academic work, he has been involved in the governance of each of the three major mathematical organizations, and he is currently serving as President of the Mathematical Association of America.

For many years, his primary research interests have been in operator theory and complex analysis, specifically, studying operators on a space of analytic functions given by composition with fixed functions.  His primary pedagogical interests have been in teaching linear algebra, both to math majors and to engineering students.  He has directed about 25 undergraduate students in research mostly on topics in linear algebra, and he has supervised several PhD students.

In 2002-03, he spent a sabbatical year at the Mathematical Biosciences Institute at The Ohio State University where he began changing his research attention to the mathematics of neuroscience.  In 2003-04, he worked with biologists at Purdue to develop a mathematical model of parts of the sensory system of the medicinal leech and also to develop and teach a course on computational neuroscience for senior math and biology majors.
 

Karen J. Graham, University of New Hampshire
"The Mathematical Preparation of Teachers: History, Issues, and Challenges"

Abstract: The mathematical preparation of teachers continues to be an integral part of undergraduate programs at a majority of mathematics departments in US colleges and universities. The broader mathematics community has a long history of support for strong mathematics content preparation for prospective teachers. However, issues remain about what mathematics teachers at various levels should know and how they should come to know it. This talk will present a brief history of the preparation of mathematics teachers in the US, an overview of current issues and research in the area of mathematics teacher preparation, and challenges that we face.

Biography: Dr. Karen J. Graham is Professor of Mathematics in the Department of Mathematics and Statistics and Director of the Joan and James Leitzel Center for Mathematics, Science, and Engineering Education at the University of New Hampshire (UNH). She received her Ph.D. in Mathematics Education from UNH in 1986. She taught mathematics in Pine Plains NY prior to beginning work on her doctorate and taught at Western Michigan University, Kalamazoo, MI prior to joining the faculty at UNH in 1987. Dr. Graham also directs the UNH Master of Science for Teacher (MST) in mathematics program. Her professional and scholarly interests include the teaching and learning of calculus, mathematics education reform based research, and mathematics teacher development. Dr. Graham has served as the project director of many state and federally funded projects. She has presented numerous workshops at local, state, regional, and national conferences. She has served as on several national and regional committees/professional boards and as president of the NH Association of Teachers of Mathematics and the Association of Teachers of Mathematics in New England. In addition she has served as a documentation consultant on several national research projects designed to explore mathematics education reform efforts, the QUASAR (Quantitative Understanding: Amplifying Student Achievement and Reasoning) Project, the R3M (Recognizing and Recording Reform in Mathematics Education) Project, and the CCH Evaluation and Documentation Project. In 1999, Dr. Graham received the Richard H. Balomenos Mathematics Education Service Award from the NH Association of Teachers of Mathematics.
 

Ron Graham, University of California, San Diego (UCSD)
"Packing Discs in the Plane"

Abstract: A classical problem in geometry deals with finding the densest packings of equal discs in the Euclidean plane. While the solution to this problem has been known for more than a hundred years (hexagonal is best), there are many variations of this problem which are completely unsolved. In this talk, I will describe some of what is currently known and what is still unknown.

Biography:  Ron Graham is one of the world's best-known mathematicians and computer theorists.  He pioneered worst-case analysis in scheduling theory, online algorithms, quasi-randomness, and Ramsey Theory.  He holds the Irwin and Joan Jacobs Endowed Chair in Computer and Information Science at the University of California at San Diego (UCSD), and is Chief Scientist of the California Institute for Telecommunications and Information Technology.  He joined the UCSD faculty in 1999, after a 37-year career with AT&T.  He received his Ph.D. in mathematics from the University of California at Berkeley in 1962. From 1962-1995, he was director of information sciences at AT&T Bell Labs, and from 1996-99 Chief Scientist of AT&T Labs.  In 2003, Graham won the American Mathematical Society's annual Steele Prize for Lifetime Achievement.  The citation noted that he "has been one of the principal architects of the rapid development worldwide of discrete mathematics in recent years. ... [and] his talks and his writings have done much to shape the positive public image of mathematical research in the USA, as well as to inspire young people to enter the subject."

Dr. Graham is in the Guinness Book of World Records for using (in 1977) the largest number ever in a mathematical proof, now known as "Graham's number."  He is the Treasurer of the National Academy of Sciences, a Fellow of the American Academy of Arts and Sciences, a fellow of the American Association for the Advancement of Science, a past President of the AMS, and Past President of the MAA.  He is a highly skilled juggler and trampolinist, and is a past president of the International Jugglers Association.  In addition to the Steele Prize, he has won numerous awards in the field of mathematics, including the Polya Prize in Combinatorics from SIAM, the Euler Medal from the Institute of Combinatorics and Its Applications, the Lester R. Ford Award from the MAA, and the Carl Allendoerfer Award from the MAA.

 Dusa McDuff, SUNY at Stony Brook
"Symplectic Topology Today"

Abstract:  The past twenty five years has seen striking advances in our understanding of symplectic topology. This subject studies the topological and geometric structures underlying Hamilton's formulation of classical mechanics.  The structures in question are global, and it took many years to find tools with which to see them.  In the 1980s several different strands of inquiry came together, crystallizing in foundational theorems about the nature of symplectic space and the canonical transformations that preserve its structure. The tools initially came from variational calculus and differential geometry but, fed by ideas from physics, have now been extensively developed, leading to new insights about global Hamiltonian systems as well as the structure of 3 and 4 dimensional manifolds.  This talk will describe some of the main results and techniques, and aims to give a idea of where the subject stands now.

Biography:  Dusa McDuff grew up in Scotland. She obtained her Ph. D. from the University of Cambridge, U.K., in 1971. After lectureships at the universities of York and Warwick, she came to Stony Brook in 1978, where she is now a
Distinguished Professor. She is a Fellow of the Royal Society (London) and a member of the National Academy of Sciences. For the past twenty years she has worked in the area of symplectic topology.

Carl Pomerance, Dartmouth College
"Primal Screens"

Abstract:  Prime numbers, the very building blocks of the integers, remain an enigma. Yet we make progress, sometimes with the energetic aid of undergrads. This non-stressful talk will highlight recent progress and some of the many unsolved problems still on our plates.

Biography:  Carl Pomerance received his B.A. from Brown University in 1966 and his Ph.D. from Harvard University in 1972 under the direction of John Tate. Currently he is a mathematics professor at Dartmouth College, after previous positions at the University of Georgia and Bell Labs. A number theorist, Pomerance specializes in analytic, combinatorial, and computational number theory, with applications in the field of cryptology.  He considers the late Paul Erdos as his greatest influence.

Peter Winkler, Dartmouth College
"Submodular Percolation"

Abstract:  Suppose you need to upgrade a computer system, one component at a time. Is it possible that you may have to downgrade a component at some point, in order to keep things running smoothly? More generally, when can a process be designed so as to avoid making backward steps?  We examine the case where the process can be modeled as a path through a (modular) lattice, and the object is to avoid large values of some submodular function. In this case it turns out that there is always a chain, i.e. a path with no backward moves, which is as good as any path. Moreover, this chain beats any path in a novel order on real sequences which we call the ``worm order''.  Joint work (from last spring at MSRI) with Graham Brightwell (LSE), now continuing with Lizz Moseman (Dartmouth).

Biography:  Peter Winkler is Professor of Mathematics and Computer Science, and Albert Bradley Third Century Professor in the Sciences, at Dartmouth.  His research lies primarily in combinatorics, probability and the theory of computing; he also collects puzzles, both mathematical and mechanical, and is the author of "Mathematical Puzzles: A Connoisseur's Collection" (AK Peters, 2004). In some circles, Prof. Winkler is best known as the inventor of cryptologic techniques for the game of bridge, which have now been declared illegal for tournament play in most of the Western world.

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