Probability

1) The course provides basic notions and methods of probability theory, based on measure theory. Students will be taught basic topics at the level required for their further study in mathematics.
2) The course aims at giving precise and systematic knowledge on real and vector random variables (laws, moments, independence, conditional laws etc.). This is required for an appropriate understanding of probabilistic models and for further study in probability, statistics, stochastic processes, stochastic calculus and their applications.
3) The most important limit theorems of the theory of probability will be carefully presented (laws of large numbers and central limit theorem). Basic applications will be given, in particular to statistics.

Students will acquire the basics of probability theory required to further pursue their study towards mathematics or its applications, either in mathematical statistics or in stochastic processes or in stochastic calculus and its applications.