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
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