| January
23, 2020 4:00 PM - 5:00 PM OW 141 |
Dr. Jesse Kinder, Dept. of Natural Sciences, OIT | Hypercubes
and Hyperspheres: Geometry in More Than Three Dimensions What is the volume of a 5-dimensional hypersphere? In this talk, I will demonstrate some interesting geometric properties of spheres and cubes in higher dimensions. Next, I will describe practical applications of these properties in applied mathematics: avoiding the "curse of dimensionality" in machine learning and error-correcting codes in communication and computation. I will conclude with a survey of experimental tests to determine whether our own physical universe might have more than three spatial dimensions. |
| February 13, 2020 4:00 PM - 5:00 PM OW 141 |
Dr.
Gregg Waterman |
Vectors to Function
Spaces The mathematical heart of signal processing is function spaces. In this talk we will develop the concept of a function space starting with vectors in two-dimensional Euclidean space. Along the way we will answer some questions: What is a basis and why do we care about having one? What is so great about an orthogonal basis? How can we have infinite dimensions? How can two functions be perpendicular to each other? |
| February 20, 2020 4:00 PM - 5:00 PM OW 141 |
Dr.
Gregg Waterman |
A Basic Introduction to
Wavelets Wavelets are a tool for signal analysis that was developed beginning in the mid 1980s, as an alternative to Fourier analysis. We will introduce wavelets using the very basic Haar wavelets. We will then contrast Fourier and wavelet analyses of some simple signals (functions). Our discussion will lean on the concepts developed in the previous talk on function spaces. |
March 12, 2020 4:00 PM - 5:00 PM OW 141 |
Dr. Peter Overholser, Dept. of Mathematics, OIT | Information
on information and why you can never come out ahead, no
matter how hard you try. “…nobody knows what entropy really is, so in a debate you will always have the advantage.” - John von Neumann The same formula emerged independently in the study of information and thermodynamics, and the quantity expressed came to be called “entropy” in both contexts. I’ll discuss the significance of entropy and show how the two notions interact in a famous example. |