# PROBABILITY METHODS IN PHYSICS

## Learning outcomes of the course unit

the student should master the basic concepts of Probability theory both from a theoretical viewpoint and in view of applications. An overlook of possible developments in mode advanced courses will be presented.

## Prerequisites

Courses of Calculus and Geometry at introductory level, Mathematical methods of Physics

## Course contents summary

Aim of the course is to provide the basis of the Theory of Probability; the student will acquire the fundamental concepts and the basic mathematical tools. Central to the course will be the physical applications which apply both analytical techniques and/or Monte Carlo simulations.

## Course contents

Historical considerations about the origin of the theory of probability. Probability space, elementary events. Statistical independence, Bayes’ formula. Combinatorial analysis, elementary distributions (Bernoulli, Poisson,etc). Random variables, expectation and variance. Probability distribution and generating function. Covariance. Continuous random variables. Uniform and normal distributions. The law of large numbers. Markov chains and Markov processes. Diffusion processes and stochastic differential equations. THe generation of quasi-random sequences. Hints about quantum probability

## Recommended readings

G.Boffetta, A. Vulpiani Probabilità in Fisica Springer, 2012.

E. Onofri, Metodi Probabilstici della Fisica: can be found on

http://www.fis.unipr.it/home/enrico.onofri

## Teaching methods

Both theoretical lectures and practical exercises will be interchangeable. Some home work will be reviewed together with the class.

## Assessment methods and criteria

There will be a final exam consisting in the presentation of a special subject by the student and subsequent discussion, open to the class