Aleksey Polunchenko, SUNY Binghamton
Suspect something fishy? How statistics can help detect it, quickly!
Suppose you are gambling at a casino in a game where you and a dealer take turns rolling a die. Suppose next that the die is initially fair, that is, each of its six faces has the same probability of showing up. However, at some point during the course of the game the evil dealer – without you seeing – replaces the die with an unbalanced one, and so from that point on the die’s faces are no longer equally probable. Yet as the new die looks exactly the same as the old fair one, you continue to gamble without suspecting anything. The natural question is: as the game progresses, can you somehow “detect” that the die has been tampered with?
Statistics is a branch of mathematics concerned with rational decision-making among uncertainty. We will see how such a question-- a gamble on its own—is approached with statistical techniques. Specifically, the talk will focus on the so-called quickest change-point detection problem, stats on the go!
Thursday, October 15, 4:00-4:50pm
Elizabeth Wilcox, SUNY Oswego
The Group Menagerie
Mathematicians are known for recycling language -- using familiar words to mean wild ideas seemingly with no resemblance to the original words! The word "group" is one such word ... What IS a mathematical group? Allow me to introduce you to some of the exotic and wild members of the Group Menagerie. No background in Abstract Algebra is assumed, and the audience may feel free to poke, prod, pet, and even bring home the creatures discussed.