Askey to give Academic Excellence Visiting Scholar Lectures

The second Academic Excellence Visiting Scholar is Professor Richard Askey from the University of Wisconsin. The visit will extend from February 24th to the 29th, 2008.

All of the talks can be understood by students who have had advanced calculus, and the second talk by students who have had a good high school geometry course or who are math students.

Binomial theorem, gamma and beta functions and extensions

Tuesday, February 26, 2008
Howe/Russell Hall E130

The binomial theorem goes back centuries, yet there are still interesting things one can do with it and extensions which were found not that long ago which are very important. The gamma and beta functions are not as old, a bit under 300 years. There are important extension of them which have been found much more recently, both in one and in several variables. Some of these results will be described, proven, and/or used.

What is Ptolemy's theorem and why it is useful to know a few different ways to prove it?

Wednesday, February 27, 2008
Howe/Russell Hall 130

Ptolemy was best known for his astronomy work, but his book on this contains an important theorem in geometry which is still of interest. The theorem deals with quadrilaterals inscribed in a circle, and was important to Ptolemy as a tool to construct what we would call tables of values of trigonometric functions. We know better ways to do that now, but Ptolemy's theorem is still important, both as a way of learning important ways of attacking some geometry problems, and because of other uses of it. A number of proofs will be given, including Ptolemy's geometric proof, Euler's proof using the law of cosines, a combination of these two proofs to extend Ptolemy's theorem to general quadrilaterals, and ways to reduce this problem to a simple problem on a line.

Orthogonal polynomials — what are they and some of the things one can do with them

Friday, February 29, 2008
Howe/Russell Hall 130

Most of you know the names of some of the important classical orthogonal polynomials, Hermite polynomials, Legendre polynomials, and Chebyshev polynomials, and may even know some places where these polynomials arise. There are a number of other classical type orthogonal polynomials which will be discussed. The problems they arise in range from stable distribution of charges on an interval, which is connected eventually with Selberg's multidimensional beta integral, to the Rogers-Ramanujan identities, which themselves show up in statistical mechanics and other unlikely places in addition to their interpretation as partition identities for special classes of integers.