Monte Carlo Methods
Spring 2026
About the course
Computer simulation and related Monte Carlo methods are widely used in engineering and scientific work. Simulation provides a powerful tool for the analysis of real-world systems when they are not amenable to traditional analytical approaches. This course introduces upper-level undergraduates and graduate students to fundamental tools for designing, conducting and interpreting Monte Carlo studies.
This is a rigorous mathematics course. The focus is on the mathematical analysis of algorithms: their theoretical foundations, convergence properties and error analysis. Programming assignments, submitted as Jupyter notebooks, are an essential component, but this is not a programming course.
Prerequisites: linear algebra, and probability and some statistics at the advanced undergraduate level; some programming experience in Python.
Recommended textbooks
- R. Y. Rubinstein and D. P. Kroese, Simulation and the Monte Carlo Method, 3rd edition, Wiley, 2017.
- R. P. Dobrow, Introduction to Stochastic Processes With R, Wiley.
Course outline
The course has four units. Each week has a homework assignment and a short quiz.
- Monte Carlo estimation
- Sampling techniques
- Markov chain Monte Carlo
- Applications
The semester ends with a group final project in place of a final exam.