Learning objectives
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 unit content
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.
Full programme
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
Bibliography
G.Boffetta, A. Vulpiani Probabilità in Fisica Springer, 2012.
E. Onofri, Metodi Probabilstici della Fisica: can be found on
http://www.eoinfnpr.it
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
Other information
In the aventuality that some student or the teacher himself should be obliged to stay at home, we shall activate a communication channel through internet. It is essential that each participant let the teacher know an active email address.
