This course provides students with the fundamentals of the Monte Carlo method, or as it was originally known, the "method of statistical sampling." This course is meant to take mathematically and computationally mature students and given them a very comprehensive introduction including: Monte Carlo basics, random numbers, and many applications to problems in the physical and statistical sciences.

This course builds on the basics learned in Advanced Monte Carlo Methods I. We focus on Monte Carlo methods for the numerical solution on partial differential equations (PDEs), and their probabilistic foundations. In addition, the numerical solution of stochastic differential equations is studied. Student also must present results from their own investigations on a Monte Carlo problem.