The aim of the course is to practice and deepen the mathematical techniques taught in the general introductory mathematics courses in view of routine and practically efficient applications in the applied courses (emphasis on stochastics in finance and insurance mathematics) and for corresponding diploma and other theses.

The course is intended (not only, but especially) for students that have little practice and practical experience with those techniques.

The subject should be flexible. Important fixed elements are the following:
Concrete work with unconditional and conditional expectations and probabilities, concrete parametric families of probability distributions (Gaussian, multivariate Gaussian, Gamma, Poisson, Beta,...), Meeting some special functions, Cholesky decomposition and simulation, moments, mixed moments, Laplace- and Fourier transformations and inversion formulae, use of simple differential equations and recursions,...