Monte Carlo Methods - Course Notes

Probability background

My summary of the probability background.
My notes from the undergraduate probability course (Math 464).

Here are some standard undergrad probability textbooks:

G. Grimmett, D. Welsh, Probability: An Introduction
R. Durrett, The Essentials of Probability Theory
D. Stirzaker, Elementary Probability
Hole, Port and Stone, Introduction to Probability Theory

Course Notes

These notes can either be downloaded as one big pdf (first link), or by individual chapters. There will evolve with time and early versions of a chapter will be full of mistakes and large gaps. The big file with all the sections has the date it was created so you can check to see when things were last updated.

All the chapters
Chapter 1 - Introduction
Chapter 2 - Basics of direct Monte Carlo
Chapter 3 - Pseudo-random number generators
Chapter 4 - Generating Non-uniform random variables
Chapter 5 - Variance reduction
Chapter 6 - Importance sampling
Chapter 7 - Markov chain background
Chapter 8 - Markov chain Monte Carlo
Chapter 9 - Convergence and error bars for MCMC
Chapter 10 - Optimization
Chapter 11 - Further topics