What really happens when we shuffle a deck of cards — and what mathematics lies behind this seemingly simple act?

Persi Diaconis explores the mathematics of three ways that real people shuffle real cards.

Remarkably, these three methods call for threes quite different kinds of mathematics.

Riffle shuffling leads to elementary combinatorics; overhand shuffling involves sophisticated coupling methods; and smooshing leads all the way to stochastic partial differential equations.

Behind these familiar ways of mixing cards lie challenging questions in analysis and probability.

Yet the problems themselves are easy to understand, making them an engaging gateway to surprisingly deep mathematics.

Along the way, the course will reveal connections to card tricks, gambling, probability, and other areas of mathematics.