Lafayette College
Easton, PA
9:10 - 10:00
Math Bowl and Game Hour
Our Spring Conference opens with an activity that has become legendary in the Lafayette Mathematics department. We will have a contest, modeled on ``College Bowl” between various local teams of undergraduates. Gary Gordon and Liz McMahon will be the hosts and official (completely unbiased) judges.
At the end of the conference Lafayette College’s Math Club will host a game hour, where all interested undergraduates are invited to come and enjoy a variety of games (bridge, chess, …).
There are numerous contexts in which 'states' need to be reconfigured --- in robotics, manufacturing, protein folding, microfluidics, and group theory, among others. I'll demonstrate a geometric approach to reconfiguration which leads to very beautiful ideas in contemporary geometry and topology. Cube complexes and curvature will play a starring role in determining how to reconfigure a system optimally.
Biography: Robert Ghrist was born in Euclid, Ohio, presaging a disposition for geometry. Despite beginning professional life as a mechanical engineer (BSME, Univ. Toledo), the Fates prevailed and Ghrist became a mathematician (MS, Ph.D. in Applied Mathematics, Cornell Univ.). As an associate professor of Mathematics at the University of Illinois, Urbana-Champaign, Ghrist applies geometry and topology to problems in applied mathematics, engineering, and computer science. He lives in Urbana with his wife and three young children.
Conjugate Coupling: The romantic adventures of the quintessential quadratic
Here we will come to understand the "personality" of real numbers. Along the way we will encounter some beautiful ideas from number theory and develop an appreciation for diophantine approximation. Results of both the ancient and recent variety will be offered along with some surprising reality-TV style twists
Biography: Edward Burger is Chair and Professor of Mathematics at Williams College. His research interests are in number theory, and he is the author of over 30 research articles and three books - "The Heart of Mathematics: An invitation to effective thinking", "Exploring the Number Jungle: A journey into diophantine analysis", and "Making Transcendence Transparent: An intuitive approach to classical transcendental number theory." Burger was awarded the 2000 Northeastern Section of the MAA Award for Distinguished Teaching and 2001 MAA Deborah and Franklin Tepper Haimo National Award for Distinguished College or University Teaching of Mathematics. In 2002-2003 he was the Ulam Visiting Professor at the University of Colorado at Boulder, where he was awarded the 2003 Residence Life Teaching Award. Burger is an associate editor of the American Mathematical Monthly. The MAA named him the 2001-2003 Polya Lecturer. In 2004 he was awarded Mathematical Association of America's Chauvenet Prize.
Mathematicians have known the classification of surfaces for over a century, so what could possibly be left to say about them? In mathematics, as soon as we have an object of interest, we also need to understand the maps of that object to itself that preserve the essential properties of that object. The mapping class group of a surface is (essentially) the group of homeomorphisms of a surface to itself. The mapping class group arises in many fields of mathematics, including complex analysis, algebraic geometry, geometric group theory, low-dimensional topology, and even in the proof of Fermat's Last Theorem.
Despite its fundamental nature, the algebraic structure of mapping class groups is not yet fully understood. In this talk, we will discuss various known generating sets for mapping class groups which possess very different properties: some arise from the symmetry of surfaces, whereas others correspond to "twisting" a surface, much the way one twists a Rubik's cube. Counter to our intuition, symmetries can be expressed as a series of twists, and vice-versa.
Biography: Tara Brendle grew up in Mercersburg, Pennsylvania. She received her B.S. from Haverford College, and her M.A. and Ph.D. from Columbia University. She is in her 3rd year of a VIGRE postdoc at Cornell University in Ithaca, NY. Her research interests include geometric group theory and low-dimensional topology.
Tara has been involved in the EDGE Program (Enhancing Diversity in Graduate Education), a summer program for women at the beginning stages of a graduate program in mathematics, first as a graduate student mentor and later as a short course instructor and visiting speaker. She will also be teaching an undergraduate course in geometric group theory at this year's Program for Women in Mathematics at the Institute for Advanced Studies in Princeton.
The CUPM Curriculum Guide 2004
David Bressoud, Macalester College
The MAA Committee on the Undergraduate Program in Mathematics (CUPM) updates its recommendation for the undergraduate curriculum in mathematics roughly every ten years. The most recent and the most extensive set of recommendations ever produced by the CUPM was published in February, 2004. This is the first CUPM curriculum guide to look at all mathematics courses and the needs of all students taking mathematics rather than dealing solely with the preparation of majors in the mathematical sciences. This session will explain what can be found in this guide, suggest how it can be used, raise some issues about college calculus, and listen to your concerns about the undergraduate curriculum.
Biography: David Bressoud is DeWitt Wallace Professor of Mathematics
at Macalester College in St. Paul, Minnesota. He grew up in Bethlehem (graduating
from Liberty in 1968), went to Swarthmore, spent two years in the Peace
Corps (Antigua, West Indies), then went to Temple University where he studied
with Emil Grosswald. He taught at Penn State from 1977 until 1994 when
he emigrated to Minnesota. He has received the MAA Distinguished Teaching
Award and the MAA's Beckenbach Book Award for "Proofs and Confirmations:
The Story of the Alternating Sign Matrix Conjecture" and has been an MAA
Polya Lecturer. He is currently Chair of the College Board's AP Calculus
Development Committee, Chair of the MAA's CUPM, and Director of Macalester's
FIPSE- and NSF-sponsored program "Quantitative Methods for Public Policy."