INQUIRY BASED LEARNING – THE NEXT GENERATION

Edward B. Burger, Williams College

Thursday, August 10, 1:00 pm – 3:00 pm

Speakers in the session will include Michael Starbird. University of Texas at Austin, "Teaching Independent Thinking"; Dick Canary, University of Michigan, "Inquiry Based Learning at the University of Michigan"; Maria Terrell, Cornell University, "Good Questions for Mathematics Eduction"; and Edward Burger, Williams College, "A Crash Course on How Not to Teach".

ISOPERIMETRIC PROBLEMS

Frank Morgan, Williams College

Thursday, August 10, 2:15 pm – 5:15 pm

Members and alums of the Williams College NSF SMALL Undergraduate Research Geometry Group and perhaps others will report on work on isoperimetric problems and open questions in various settings, including Riemannian manifolds and manifolds with density, such as Gauss space.

COMPUTATIONAL CONVEXITY AND ITS APPLICATIONS

Jesus De Loera, University of California Davis

Tyrrell McAllister, University of California Davis

Thursday, August 10, 1:00 pm – 4:40 pm

Methods from computational convexity are finding more and more applications in such diverse fields as optimization, representation theory, algebraic geometry, number theory, and theoretical computer science.  In this session, researchers in these fields will report on the remarkable advances made in recent years using the tools of computational convexity. Speaker will include  Matthias Beck, San Francisco State University, “Enumerating Integer-Points in Polytopes: Applications to Number Theory”;  Tyrrell McAllister, UC Davis, “Convex Polyhedra and Representation Theory”;  Maurice Rojas, Texas A&M,  “Convexity, and Phase Transitions for Detecting Real Roots”;  James Lawrence, George Mason University, “Combinatorial Problems and Computational Convexity”; Paul Goodey, University of Oklahoma, "Projection Functions of Convex Bodies."

GEMS OF RECREATIONAL MATHEMATICS
Arthur T. Benjamin, Harvey Mudd College
Ezra A. Brown, Virginia Polytechnic Institute and State University
Friday, August 11, 1:00 pm – 3:00 pm
Our speakers are Joe Gallian, University of Minnesota at Duluth, “Weird Dice”; Richard Guy, University of Calgary, “Three Gems We All Know (Don't We?)”; Laura Taalman, James Madison University, “Sudoku Variations and Research”; and Daniel Velleman, Amherst College, “Fast Growing Sequences”.

CHAOTIC DYNAMICS AND FRACTAL GEOMETRY

Mario Martelli, Claremont McKenna College

Friday, August 11, 1:00 pm – 4:30 pm

Speakers include Jim Yorke, Kathleen Alligood, Elena Nusse, Celso Grebogi, Ethan Akin, Tim Sauer, Carlos Castillo-Chavez, and John Guckeneimer.

PHYSICAL KNOTS

Dorothy Buck, Imperial College London

Friday, August 11, 3:15 pm – 5:15 pm

Louis Kauffman, University of Illinois at Chicago
Ken Millett, University of California Santa Barbara
Eric Rawdon, Duquesne University
Thomas Banchoff, Brown University

POINTING THE WAY TO PROOF

Diane Herrmann, University of Chicago
Carol Schumacher, Kenyon College

Friday, August 11, 1:00 pm – 3:00 pm

Speakers will include: Michael Starbird, University of Texas - Austin; James Morrow, Mt. Holyoke College; Chris Stevens, St. Louis University; and Don Albers, MAA

STORIES FROM THE HISTORY OF MATHEMATICS AS A TOOL FOR TEACHING

David Bressoud, Macalester College

Saturday, August 12, 1:00 pm – 3:00 pm

Speakers will include John McCleary, Vassar College, "Euler's Easy Solutions to Difficult geometric problems";  Rob Tubbs, University of Colorado, Boulder, "From e^pi to 2^(sqrt2), Motivating the Solution to Hilbert's 7th problem";  Fred Rickey, U.S. Military Academy at West Point, "Some Tested Examples for Using History in Your Classroom"; and Ed Sandifer, Western Connecticut State University, "Theorem First, or Example First: Newton vs Leibniz Again."

GRAPH THEORY IDEAS FOR UNDERGRADUATE RESEARCH

Aparna Higgins, University of Dayton

Saturday, August 12, 3:15 pm – 5:15 pm

This session will highlight some topics in graph theory that are intriguing to undergraduate researchers. The speakers, all of whom have successfully guided undergraduate students in research, will present areas such as graph labeling, the Erdos-Ko-Rado theorem and Kneser’s conjecture, graph pebbling, and using Graffiti.pc for generating conjectures. The speakers have directed undergraduate research in intensive summer experiences and in undergraduate thesis activities. The session will provide insight into what makes a topic in graph theory suitable for investigations by undergraduates, and will provide additional avenues of research.  The speakers are Ermelinda Delavina of University of Houston - Downtown, Anant Godbole of East Tennessee State University, Glenn Hurlbert of Arizona State University and Cynthia Wyels of California State University Channel Islands.