Undergraduate Seminar (395-0-91)

Instructors

Ursula Porod

Meeting Info

Lunt Hall 104: Mon, Wed, Fri 3:00PM - 3:50PM

Overview of class

Math 395, Spring 2026
Instructor: Ursula Porod

TITLE: Markov Chains and Mixing Times

How many shuffles will mix a deck of cards? For commonly used riffle shuffling, the answer is 8. This is an amazing result, considering that the number of possible orderings of a deck of 52 cards exceeds 1067. Moreover, the Markov chain that models card shuffling exhibits a "cut-off phenomenon": Transition from the initially ordered to a completely random state of the deck does not happen gradually in time but rather suddenly, akin to a phase transition.

This seminar is about the mathematics underlying the study of mixing times—the length of time a Markov chain has to run to be sufficiently close to stationarity—as well as related phenomena. We will cover some well-known results from the literature.

Prerequisites: Probability and Markov chain theory (such as Math 311-1,2 or Math 310-1,2), basic Linear Algebra.

Class Materials (Required)

No required materials.

Class Materials (Suggested)

No materials suggested.

Class Attributes

Advanced Expression

Enrollment Requirements

Enrollment Requirements: Preregistration in this course is reserved for students who are majoring in Mathematics. Registration in this course is reserved for students who are majoring or minoring in Mathematics.