Nov 09/04

Academic Seminar by Professor Rosenthal Thursday, November 18th, 2004 Sidney Smith 1072 at 3pm Approximating Continuous Functions by Polynomials with Prime Exponents A very well-known classical theorem of Weierstrass states that every continuous function on the unit interval [0,1] can be approximated uniformly on the interval by a sequence of polynomials. Suppose that we restrict the polynomials to those where all the exponents are prime numbers; what continuous functions can be uniformly approximated on [0,1] by such polynomials? The answer to this question can be obtained by putting together two fairly well-known theorems, one from elementary number theory and one from approximation theory. I'm not going to tell you the answer to the question or the theorems required to prove it unless you come to the lecture. In the lecture, however, I'll tell all. I'll give a very elementary proof of the number-theoretic result and will give an outline (assuming no background) of the proof of the approximation theorem. The lecture is meant to be entirely self-contained. Refreshments will be served after the talk.

Nov 24/04

General Meeting and Games Afternoon Thursday, November 25th, 2004 Sidney Smith 2129 from 1-4pm Refreshments will be served.