Is there a better identity for pi than pi=4arctan(1)? Are the degree angle measures ever rational in a triangle whose side lengths form a Pythagorean triple? Which regular polygons may be built on a geoboard? The answers to these questions are intimately related to arctangent identities for pi, which we will explore using the number theory of the Gaussian integers. We will present some of the historical context as well as some directions for further research.

If you are interested in perhaps pursuing a mathematics major, you are invited to this meeting. Refreshments will be served and any questions you have about the majors will be answered.

Intuitively, the variation of a function f on [a,b] is a measure of how much the y-values of the function “vary” over the interval [a,b].  In effect, we are isolating the vertical component of arc length of the graph of f.  After providing a precise definition of the total variation of f on [a, b], we will consider those functions whose total variations finite on [a,b] and call this class of functions BV.  We will look at several examples of such functions, explore the properties of the class BV, and discuss some extensions of this concept.

Have you ever been so irritated with an integration problem that you wanted to hit it with a hammer? Come to the Mathematics Department's Pizza Lunch and learn how to do it right, how to crush unfriendly integrals using the trapezoid rule, and other numerical devices, as sledge-hammers.

The theory of bounded linear operators may be viewed as a generalization of linear algebra (matrices and linear transformations) to the setting of infinite-dimensional vector spaces (in particular Hilbert spaces).   Shifts and backward shifts serve as crucial examples of bounded linear operators defined on Hilbert spaces.  In this talk fundamental properties shared by such operators will be presented.  We will see that, just as a matrix has a spectrum of eigenvalues, a shift operator also has a spectrum, albeit of a slightly different flavor.

In 1807, Joseph Fourier discovered that he could superpose sines and
cosines to represent periodic functions. Since then, there has been an
explosion of interest in alternatives to this traditional signal
representations. Instead of just representing signals as superpositions
of sinusoids, we now have available alternate
systems - collection of parametrized waveforms - of which the wavelet
system is the best known. In this talk, we will discuss basic
properties of wavelets and a new approach overcoming the drawbacks of wavelets will be presented.

A tour of the mathematics that you might have accomplished in grade school, if only you had been many times brighter. We will add numbers, sets of numbers, and shapes. This talk is unofficially sponsored by Milk and Cookies.

May 7 -- Honors Lecture
“TBA”
Andrew Pike
4:30 in King 243