1. Monte Carlo Methods in Scientific Computing
3-7 November 2003
Beijing International Center for Computational Physics
This set of powerpoint slides MC-0 to MC-15 is copyright J.-S. Wang. I thank Dr Yu Xijun for his kind invitation to organize this workshop. I also thank the other lectures Profs Bo Zheng, Junni Zhang and Pei Lucheng for their contributions to this workshop. A soft copy of the slides is available at
The background Monte Carlo carpet is from

2. Outline (Monday) What is Monte Carlo Introduction to probability
Random number generator
Numerical integration
Quasi-Monte Carlo method
Markov chain

3. Outline (Tuesday) Metropolis and other algorithms
Selected applications
Convergence and Monte Carlo error
Quantum Monte Carlo methods
Variational, diffusion Monte Carlo
Trotter-Suzuki formula

4. Outline (Wednesday) Cluster algorithms Re-weighting methods
Extended ensemble methods (Multi-canonical, simulated tempering, replica MC, replica exchange)
Transition matrix MC, flat-histogram and Wang-Landau

5. Thursday
Morning: Non-equilibrium dynamics in statistical mechanics and other applications (by Bo Zheng)
Afternoon: Markov chain Monte Carlo in statistics (by Junni Zhang)

6. Friday
Whole day: Monte Carlo method and its characteristics (by Pei Lucheng)

7. Reference Books
M H Kalos and P A Whitlock, “Monte Carlo Methods”, John Wiley & Sons, 2nd ed, 2008.
D P Landau and K Binder, “A Guide to Monte Carlo Simulations in Statistical Physics”, 4th ed, Cambridge, 2015.
J S Liu, “Monte Carlo Strategies in Scientific Computing”, Springer,2002.
Other books and references will be introduced at the bottom notes with the slides later.