2009-2010 Milliman Lectures
Department of Mathematics
University of Washington

NICK TREFETHEN
Professor of Numerical Analysis
Oxford University

April 13th, 14th, and 15th
4:00 - 5:00pm
(See below for locations.)

Lecture I:
Four Bugs on a Rectangle (and the Biggest Numbers You've Ever Seen)
(Tuesday, April 13th in Kane 220. Joint with MathAcrossCampus.)

Abstract: Suppose four bugs at the corners of a 2 x 1 rectangle start chasing each other at speed 1.  Bug 1 chases bug 2, bug 2 chases bug 3, and so on.  What happens next will amaze you -- or at least it amazed me!  As we follow the bugs to their eventual collision at the center, we will encounter the biggest numbers you've probably ever seen and confront some fundamental questions about what it means to try to understand our world through mathematics.
View video of the lecture here.

Lecture II:
Approximation Theory in One Hour
(Wednesday, April 14th in Savery 260)

Abstract: My first love was approximation theory, and during my current sabbatical I have returned to this subject to write a book called Approximation Theory and Approximation Practice.  This talk will be a fast tour of about twenty of the main theorems of this book (with a handout), each illustrated by chebfun computations on the computer. We will see vividly how approximation ideas are at the heart of all kinds of practical computational problems including quadrature, rootfinding, and solution of differential equations.
View video of the lecture here.
A handout from this lecture.

Lecture III:
You Can't Beat Gibbs and Runge
(Thursday, April 15th in Savery 260)

Abstract: Suppose you sample an analytic function f in n equispaced points in [-1,1].  Can you use this data to approximate f in a manner that converges exponentially as n → ∞? Many algorithms have been proposed that are effective for moderate values of n, but we prove that they must all fail in the limit n → ∞: exponential convergence implies exponential instability.  This is joint work with Rodrigo Platte and Arno Kuijlaars.
View video of the lecture here.

Speaker Bio: Nick Trefethen is Professor of Numerical Analysis and Head of the Numerical Analysis Group at Oxford University. He is the President of the Society for Industrial and Applied Mathematics. Nick is an Institute for Scientific Information Highly Cited Researcher whose contributions to scientific computing and numerical analysis also include four influential books. He is the "father" of pseudospectral theory. Among his many honors, he is the winner of the inaugural Leslie Fox Prize for Numerical Analysis, a Fellow of the British Royal Society, and a member of the US National Academy of Engineering. He has been invited to lecture both at the International Congress of Mathematicians and at the International Congress on Industrial and Applied Mathematics.