Course: Numerical methods and Montecarlo by Sebastiano Pilati

Main topics

Introduction to elementary numerical algorithms (with examples):

• Root solvers
• Integration
• Solving differential equation

  Introduction to Monte Carlo methods:

• Monte Carlo integration
• random numbers generators
• Sampling non-uniform probability distribution functions
• Markov chains
• Correlations and statistical analysis of Monte Carlo simulations

  Simple models in statistical physics:

• Ising Model
• Phase transitions (critical slowing down)
• Smart sampling algorithm
• Finite-size scaling

  Introduction to quantum Monte Carlo:

• Diffusion Monte Carlo (bosons)
• Fermions and the sign promblem
• Path Integral Monte Carlo

  Introduction to Molecular dynamics