Brief lecture notes

These are the notes for the first half of Monte Carlo Methods and Applications in Fall 2024. These notes only list statements of important results covered in lectures. Motivation, intuition, and proofs will be done on the blackboard, and will not be on these notes.

1. Monte Carlo Methods, and why they are useful.
2. Basic Sampling Algorithms
3. Monte Carlo Integration
4. Introduction to Numerical Python
5. Markov Chain Monte Carlo (MCMC)
6. Using Metropolis Hastings on the Ising Model
7. Markov Chains
8. Ergodicity and Mixing
9. Metropolis Hastings Revisited
10. Simulated Annealing and Tempering