FS23 – MTH 496 section 1 - Harmonic analysis on hyper cube and learning
Instructor: Alexander Volberg
Hypercube (also called Hamming cube) is the collection of long strings of +1 and −1. The functions on hypercube are called Boolean functions if they also assume only values ±1. In “big data” one can think that each string is the collection of positive and negative attributes of your “clients”, and the value of your function means whether the client “drops” the service or joins it. Knowing part of your function you wish to predict what will happen with the next client, if you are given client’s attributes. Can you recognize a function if you know it only on a part of its domain of definition? Of course not, but you have more chances if you know something about its spectral concentration. This is what we will try to study for functions on Hamming cube. We describe the basics of analysis of Boolean functions, we also describe some rudiments of the mathematics of learning theory and another theory called social choice, a topic studied by economists, political scientists, mathematicians, and computer scientists. Harmonic analysis on Hamming cube has many unusual and interesting features, and, recently started to play a role as one of mathematical foundation of big data.
Recommended Background – STT 351 or STT 441
FS23 – MTH 496 section 2 - Nonlinear Dynamics and Chaos
Instructor: Keith Promislow
This course introduces the exciting field of dynamical systems with an emphasis on bifurcation and chaos in applied models. Nonlinear differential equations and iterative maps model a beating heart, tumor growth, animal conflict, ecological systems, as well as mechanical, electrical, and economic oscillations. Through linear and nonlinear techniques we will analyze the behavior of models with emphasis on prediction of the onset of qualitative change.
Required Background: MTH 320 & (MTH 235 or MTH 340)