Preface

These notes summarize two of the three classes held for undergrad-

uates at the 1996 Park City/IAS Institute in Probability. There

were twenty undergraduates participating, who were divided into an

advanced group and a beginning group. Both groups participated

in a class on computer simulations in probability. The beginner's

class, taught by Emily Puckette, discussed Markov chains and ran-

dom walks, covering material in the first few chapters of [L3]. This

book gives notes from the advanced class and the computer class.

The first ten lectures are those given to the advanced class by Greg

Lawler, and the last three summarize the material in the computer

class led by Lester Coyle. The material was coordinated so that some

of the major simulations done in the computer class related to topics

discussed in the advanced class. For this reason we have decided to

combine these notes into one book.

The title of the advanced lecture series (and of these notes) is

taken from a recent book [S], Topics in Contemporary Probability

and its Applications, edited by J. Laurie Snell, which contains a num-

ber of survey articles that are accessible to advanced undergraduates

and beginning graduate students. The lectures were based loosely on

three of the papers in that book: "Random Walks: Simple and Self-

Avoiding" by Greg Lawler, "How Many Times Should You Shuffle a

Deck of Cards?" by Brad Mann, and "Uniform Spanning Trees" by