**[Cr:2, Lc:2, Tt:0, Lb:0]**

This course is expected to be credited by 4th or 5th year BS-MS students in Chemistry.
Given the general nature of the subject, students from Physics and Biology majors
may also be interested.

- A review of probability theory: random variables; probability density and cumulative distribution functions; mean, variance and moments; important distributions; multiple random variables and joint distribution function; covariance and statistical independence; sums of independent random variables; central limit theorem; conditional probability; Markov chains (4 lectures)
- Integraton by sampling: hit and miss integration method; one-dimensional integrals using uniform and non-uniform sampling; random numbers by inversion method; optimal and importance sampling; Monte Carlo method for multi-dimensional integrals and sums (4 lectures)
- Multi-dimensional distributions: simple methods for generating independent non-uniform random numbers; multi-dimensional gaussian distribution; rejection sampling; rejection sampling with repetition and its error analysis; Markov chain and detailed balance condition; Metropolis method and its simple applications; Statistical mechanics applications to interacting particles and Ising model (8 lectures)
- Stochastic processes: Brownian motion, diffusion equation and Langevin approach; random walk and Wiener processes; Stochastic differential equations ; white noise; Stochastic integrals; Ornsteinâ€“Uhlenbeck colored noise; Focker-Planck equation (4 lectures)
- Numerical methods for stochastic differential equations; Euler and Milstein methods; Some applications (4 lectures)

- R. Toral & P. Colet, Stochastic Numerical Methods, 1st edition, Wiley-VCH (2014)
- A. Papoulis & S. Pillai, Probability - Random Variables and Stochastic Processes, 4th edition McGraw Holl, 2017
- N.G. Van Kampen, Stochastic Processes in Physics and Chemistry, 3rd edition, Elsevier (2007)
- R. Y. Rubinstein & D. P. Kroese, Simulation and the Monte Carlo Method, 3rd Edition (2016)