Tom Banchoff
Brown University

‘FLATLAND: THE MOVIE’ AND BEYOND

Now that "Flatland: the Movie" is reintroducing new generations of students to the dimensional analogy, how can we as teachers follow up the viewing experience to frame and direct geometric challenges for all levels?

Deanna Haunsperger
Carleton College

LIGHTS ON THE HORIZON

What do a square-wheeled bicycle, a 17th-century French painting, and the Indiana legislature all have in common? They appear among the many bright stars on the horizon of mathematics, or perhaps, more correctly, in Math Horizons. Math Horizons, the undergraduate magazine started by the MAA in 1994, publishes articles to introduce students to the world of mathematics outside the classroom. Some of mathematics' best expositors have written for MH over the years; here are some of the highlights from the first ten years of Horizons.

Patrick McDonald
New College of Florida

RANDOM WALKS AND NETWORK TOMOGRAPHY

A network is a graph with added structure associated to its vertices and/or edges. Networks occur as models for a remarkable spectrum of phenomena, with well known applications in the natural sciences and engineering. In this talk I will discuss a collection of interesting inverse problems for networks which may be roughly described as follows: Consider a network as a “black box” and suppose that we are permitted to perform a number of experiments designed to probe the internal structure of the box. Under what conditions do the experiments determine the network? Given the inverse problem has a unique solution, how can we recover the network? Three such inverse problems will be discussed in detail, each of which involves networks whose added structure includes the rules for a random walk on the vertices of the underlying graph. There will be a number of suggestions for future projects, many of which are appropriate for students. The talk will be self-contained and intended for a general scientific audience.