The purpose of the computer class was to introduce students to

the idea of Monte Carlo simulations and to give them a chance to do

some nontrivial projects. The previous computer experience of the

students varied widely, some having significant programming back-

grounds and some having never computed. We first used Maple and

then C as the languages for simulations. While these sections are

labeled as "lectures" they actually represent a summary of many lec-

tures, and the topics were not really presented in the order that they

appear here. Lecture 11 discusses simulations for random walks and

includes some basic material on curve fitting to estimate exponents.

It ends with a discussion of the most serious project done in this

area, the estimate of the intersection exponent. Lecture 12 discusses

simulation topics other than random walk that were discussed in the

class, including sampling from continuous distributions, random per-

mutations, and finally a more difficult project — using Markov Chain

Monte Carlo as discussed in Lecture 8 to estimate the number of ma-

trices with certain conditions. The last lecture discusses a different

area, simulations of stochastic differential equations for applications

in finance.

We conclude the book with a number of problems that were pre-

sented to the students. The difficulty of these problems varies greatly;

some are routine, but many were given more to stimulate thought

than with the expectation that the students would completely solve

them. They are numbered to indicate which lecture they refer to. Of

particular note are the problems from Lectures 11 and 12. These are

representative of the simpler projects that we gave to the students as

they were learning how to do simulations, and are typical of simula-

tion problems that we give to students when we teach undergraduate

probability.

We would like to thank a number of people who helped with the

program for undergraduates, including: Emily Puckette, the third

member of our team; Chad Fargason, who helped write some of the

software used in the labs; David Levin, who helped in the preparation

of these notes; Brad Mann and Robin Pemantle, for providing copies