Introduction to the course and fundamental concepts of probability.

The central limit theorem and stochastic sampling methods.

Direct sampling and Markov chains. The Metropolis method.

The binning technique to evaluate statistical errors. 

First-order Langevin dynamics and its approach to equilibrium.

The quantum variational method and the Jastrow and Jastrow-Slater wave functions.

a) The case of the Heisenberg model S=1/2 in one dimension (Jastrow function and Marshall sign).

b) The Gutzwiller wave function for the fermionic Hubbard model.

Optimization methods of variational wave functions.

Green's function method Monte Carlo for systems without the sign problem.