Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture David Bressoud, President of the MAA, Macalester College
Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture
What is the role of proof in mathematics? Most of the time, the search for proof is less about establishing truth than it is about exploring unknown territory. In finding a route from what is known to the result one believes is out there, the mathematician often encounters unexpected insights into seemingly unrelated problems. I will illustrate this point with an example of recent research into a generalization of the permutation matrix known as the "alternating sign matrix." This is a story that began with Charles Dodgson (aka Lewis Carroll), matured at the Institute for Defense Analysis, drew in researchers from combinatorics, analysis, and algebra, and ultimately was solved with insights from statistical mechanics. This talk is intended for a general audience and should be accessible to anyone interested in a window into the true nature of research in mathematics.
Chris Rodger, 2008-2009 Section Lecturer, Auburn University
How to Master Scheduling a Series of Dinner Parties
In this talk I will give descriptions, along with some solutions, of the problem of seating people at dinner tables so that each person gets to meet as many other people as possible. Techniques used involve both graph theory and combinatorial design theory, with plenty of pictures to make them all clear!
Ron Gould, 2008 Section Teaching Award Winner, Emory University
Never Give a Non-Mathematician an Even Break
In this talk we will consider several situations where being a mathematician definitely gives you the advantage. In each case, applying a little elementary mathematics sways the outcome of the event.
These situations will include a "mind reading" card trick, where knowing the mathematics is critical to the performance of the trick, a simple coin flipping game where we can greatly tip the odds of winning in our favor and a paint-ball shootout, where a simple strategic change helps improve our chance for victory.