Introduction to the differential and integral calculus in one real variable: fundaments of mathematical thinking, numbers, sequences, basic point set topology, continuity, differentiable functions, ordinary differential equations, Riemann integration.

Introduction to differential and integral calculus in several real variables, vector calculus: differential, partial derivative, implicit functions, inverse function theorem, minima with constraints; Riemann integral, vector fields, differential forms, path integrals, surface integrals, divergence theorem, Stokes' theorem.

Complex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, special functions, conformal mappings, Riemann mapping theorem.

The course aims at providing an introduction to mathematical finance. Starting from a review of probability theory and a summary of martingale theory, an introduction to stochastic integration including its application to mathematical finance will be given. Topics addressed include Ito's formula, Girsanov's Theorem, put-call parity and option pricing in the Black-Scholes Model.

Introduction to probability and statistics

Basic concepts from probability and statistics:- introduction to probability theory- short introduction to basic concepts and methods from statistics

The goal of this seminar is to present various stochastic methods for claims reserving.These methods enable to set adequate reserves for open claims and todetermine prediction errors of these estimators.

This lecture covers the mathematical modelling of interest-rate and credit risks and the application of quantitative models to the pricing of interest-rate and credit derivatives.