Donna Beers, Simmons College
Sonja Sandberg, Framingham State College

"Outside Academia: Sabbaticals in Government and Industry"

Donna Beers and Sonja Sandberg independently came to the same conclusion about how to spend a sabbatical: They both wanted a real-world experience.  Although on first glance their experiences appear quite different, upon closer examination their experiences were really quite similar.  Donna worked for MathSoft, Inc., in Cambridge, MA and her responsibilities involved helping to launch MathCad 2000.  Sonja worked at the United States Department of Agriculture where she had an opportunity to see how mathematics can play a role in U.S. policy decisions.  In this presentation, they will describe their expectations for the sabbatical, what possibilities they explored, how they actually (and eventually) found positions, how it feels to work at a sit-at-your-desk, nine-to-five, job, and what they learned about mathematics in the work place.

Sonja Sandberg is a Professor of Mathematics at Framingham State College where she has taught since 1985. She received her undergraduate degree in applied mathematics from MIT and her Ph.D. in Mathematical Sciences from Southwestern Medical Center. Her research interest involves using mathematical tools to answer questions in biology and medicine. She received a Bunting fellowship in 1991 to spend a sabbatical modeling the population dynamics of the Lyme disease tick. She is presently on sabbatical in Washington, DC where she is spending the year with the US Department of Agriculture learning about risk assessment as applied to food safety issues, and the economics of crop insurance; this work is supported by a fellowship from the American Association for the Advancement of Science (AAAS).

Donna Beers is Professor of Mathematics at Simmons College where she has taught since 1986. She earned her undergraduate and Ph.D. degrees in mathematics from the University of Connecticut. Her research specialty is commutative algebras and she has contributed to the solution of the group ring isomorphism problem and to the structure of valuated abelian groups. At Simmons she chaired the Mathematics and Computer Science Department from 1993-99, leading the Department in a program review that led to the creation of a Financial Mathematics major and new quantitative reasoning courses for non-majors. A particular focus for her teaching has been teacher preparation and effective use of technology. In Fall, 1999, she spent a sabbatical leave in the Research and Development division of MathSoft, Inc., where she helped to launch Mathcad 2000 and two on-line certificate courses. She has been an active member of the MAA, serving as Vice Chair of the Northeastern Section of the MAA from 1992-93 and as Chair from 1993-95. She is a member of the MAA editorial boards of The American Mathematical Monthly, the Dolciani Mathematical Expositions, and the FOCUS/MAA Online.

Brigitte Servatius, Worcester Polytechnic Institute

"Rigidity theory and some of its applications"

A framework is a mathematical model of a physical structure: Each vertex of the framework corresponds to a ball joint located in space, the edges correspond to rigid rods connecting the joints. A very general class of physical structures, from scaffolding or bridges to glasses, ceramics or molecules of proteins, may be described this way. The mathematical task is to develop a method for predicting rigidity without building a model. Geometry and combinatorics provide the fundamental tools. Although rigidity has been studied since the time of Maxwell(1864), it is only in the last 25 years that it has begun to find applications in the basic sciences. Concentrating on the combinatorial aspects of the theory, we will describe the major results of the last decade and their applications to CAD, statistical physics and biochemistry.

Tensegrities are structures built from rods, cables and struts. Cables have definite maximal lengths, while struts may be extended but have a well defined minimum length. Cables rods and struts are joined at their endpoints by vertices. Tensegrities have recently received much attention because of the interest in the underlying mathematics, the beauty of the so called super stable tensegrities (they hold their shape in a very strong sense, cables and struts may be replaced by rubber bands) and their applications. In the workshop we will experience through experimentation with sticks and rubber bands some of the exciting features of super stable tensegrities and develop some of the theory.

Brigitte Servatius received MS degrees in Mathematics and Physics from the University of Graz, Austria and a PhD in Mathematics from Syracuse University in 1987. Since then she has been teaching at WPI. Her main research interests are matroids, especially rigidity matroids, as well as graph and combinatorial group theory. She enjoys coaching the Putnam Team, directing graduate and undergraduate research and using models puzzles and games in the classroom. She is editor of the Student Research Projects for the College Math Journal and editor of the Pi Mu Epsilon Journal.

Joseph Gallian, University of Minnesota-Duluth

"The Mathematics of Identification Numbers"

Modern identification numbers have a built-in "check'' to partially ensure that the numbers have been correctly entered into a computer or have been correctly scanned by an optical device. In this lecture we examine some of the common coding schemes that you encounter everyday. Among them are codes found on retail items (UPC code), mail (ZIP code), credit cards, airline tickets, money orders, travelers checks, personal checks, pop cans, books and magazines.

Biographical Information:

Joseph Gallian, University of Minnesota-Duluth, received his Ph.D. from Notre Dame in 1971. Since then he has been the recipient of numerous teaching honors. These include: Trever Evans Award for Mathematical Exposition, 1996; MAA Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching 1993; U. Minnesota System Continuing Education and Extension Distinguished Teaching Award 1991; U. Minnesota, Duluth Blehart Distinguished Teaching Award 1984; Math. Assoc. of Amer. Allendoerfer Award for Mathematical Exposition 1977; U. Minnesota System Morse Award for Contributions to Undergraduate Education 1976. His numerous books, research articles, workshops and presentations are all indicative of his interest in a wide variety of mathematical topics. Professor Gallian has been extremely active in the MAA, having served as Associate Editor of Mathematics Magazine, the American Mathematical Monthly, and MAA Online. His skill as a speaker is attested to by the fact that he was chosen as the MAA Polya lecturer for 1999/2000 and 2000/2001.

Paul Blanchard, Boston University

"The Ordinary Differential Equations Course at Boston University"

At Boston University we have revised our standard sophomore-level course in ordinary differential equations so that it now includes a greater emphasis on numeric and qualitative techniques. In this presentation, we shall discuss the natural relationship between numerical results and qualitative theory, and we will demonstrate a number of exercises and projects that are typical of our approach. We will also illustrate our use of animation in the course.

Biographical Information:

Paul Blanchard grew up in Sutton, MA, spent his undergraduate years at Brown University, and received his Ph.D. from Yale University. He has taught college mathematics for twenty-five years, most at Boston University. He has coauthored or contributed chapters to four different textbooks. His main area of mathematical research is complex analytic dynamical systems and the related point sets---Julia sets and the Mandelbrot set. Most recently his efforts have focused on reforming the traditional differential equations course. He currently heads the Boston University Differential Equations Project and leads workshops in this innovative approach to teaching differential equations. When he becomes exhausted fixing the errors made by his two coauthors, he usually heads for the golf course with his caddy, Glen Hall.

Dan J. Kleitman, Massachusetts Institute of Technology

"Mathematics and Good Will Hunting"

Recently, a review of Good Will Hunting appeared in the Notices of the AMS. In an accompanying note, Dan J. Kleitman wrote, "One day this spring I got a phone call from someone asking if I would talk to two young men who were writing a screenplay for a movie." The resulting award-winning movie is well known, especially in the Boston area. This talk will be a collection of anecdotes both on the mathematical conversations leading up to Good Will Hunting, as well as some experiences in the life of an extra.

Biographical Information:

Daniel J. Kleitman is a Professor of Mathematics at the Massachusetts Institute of Technology. His interest in the theory of computing and combinatorics has led to a wide variety of articles on topics ranging from binary search procedures to covering polygons with rectangles. Since 1969 he has mentored numerous graduate students, many of whom returned to M.I.T. last summer to attend the special conference "Kleitman and Combinatorics: A Celebration."   While he has always been well known in his chosen field, Professor Kleitman now enjoys the added recognition of being the mathematics advisor (and an extra) for the movie Good Will Hunting.

Christophe Gole, Smith College

"A Dynamical System for Plant Pattern Formation"

Plants display with astonishing frequency spiral patterns with number of spirals given by the Fibonacci sequence. Although this well-known phenomenon has received a lot of attention from scientists and mathematicians throughout the centuries, no clear elucidation of the formation mechanisms has emerged yet. In this talk we propose a simple dynamical system model, based on assumptions made by botanists and physicists, in which the Fibonacci spiral patterns occur as attracting fixed points. We mention other possible, non-spiral patterns in plants predicted by this model.

Biographical Information:

Christophe Gole has received his Ph.D. at Boston University in 1989. He has held postdoctoral positions at the IMA, ETH, IHES, Stanford University, SUNY Stony Brook and UC Santa Cruz. He received an NSF Postdoctoral Fellowship in 1991. He has been at Smith since 1997. Apart from plant pattern formation, his research interests are in conservative dynamical systems.

John Goulet, Worcester Polytechnic Institute

"Teaching Calculus with an Outcomes Based Approach"

After years of teaching calculus in a traditional manner with grades determined by exams and labs, in 1999 I began teaching in a goals or outcomes oriented manner instead. Initially, this began with identification of 15 desired goals or outcomes for the course, with the passing of the course being interpreted as successful demonstration of capability in each one. Only then would a grade be assigned. This talk concerns the motivation, implementation, lessons learned, reactions and future considerations of three such endeavors which allowed me to personally reinvent my teaching, and my students to substantially reconsider their approach to learning.

John Goulet has a B.S. in Mathematics from WPI, and a PhD from RPI. He has been teaching mathematics at the undergraduate level since 1976, as well as computer information systems from 1986-1993.  He has been teaching at WPI since 1993 and
is also coordinator for the college's Masters for Mathematics Educators program there.  He received the Ralph Huston Award at RPI as outstanding graduate instructor of mathematics and the EMSEP award in 1999 at WPI as Faculty Member of the Year.

Pressure Regulation in the Brain: Compartmental Models
Zsuzsanna M. Kadas, St. Michael's College

We give an overview of a family of models being used to study the regulation of pressure and fluid flow in the brain. The goal is to understand the onset of various pressure-related conditions such as Normal Pressure Hydrocephalus and Space Adaptation Syndrome, and to propose countermeasures.  The basic structure of the models, a system of between 4 and 16 ordinary differential equations, could be presented in a first course in O.D.E.'s. We describe how respiratory and cardiac oscillations must be incorporated as forcing functions, and touch upon the complications that arise in determining parameter values when direct clinical data cannot be easily obtained.

Various Notions of Distance
Mike Cullinane, Keene State College

Distance functions play an important role in several branches of mathematics, including analysis and topology.  Examples will be used to motivate the properties many mathematicians believe any "reasonable" notion of distance should possess.  It shall then be demonstrated, via the consideration of computer science oriented examples, that none of these properties is absolutely essential for the construction of "reasonable" distances.

Wanted:  Synonyms for "Not Quite"
Bill Hillery, Keene State College

A weak distance function d defined on a set X requires only that d maps elements of XxX into the non-negative reals.  Metrics, with their numerous applications, are clearly members of this diverse family.  Other members, while less well known, exhibit numerous interesting properties. This talk will discuss various members of this family and highlight some settings in which metrics would not be the preferred functions.

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