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
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