The course is an introduction to the modern theory of asset pricing. We will have 10 lectures of three hours each. The first two hours will have a standard lecture approach. The last hour will sometimes be devoted to applications and problem solving. The course is theoretical. The empirics of asset pricing is covered in other courses.

Overview:

This module is an advanced course in ship dynamics covering the analysis methods available for ship stability and trim, the response of ships and...

This module aims to offer an overview of the basic notions that appear in the classical theory of modular forms. These are analytic objects encoding a lot of...

This module aims to offer an overview of the basic notions that appear in the classical theory of modular forms. These are analytic objects encoding a lot of arithmetic information which makes them a central point of study in number theory and arithmetic geometry. Modular forms also arise naturally in a variety of other research fields like transcendence proofs, differential equations and mirror symmetry.

The main objects of interest are functions on the complex upper half plane that transform in a special way under the action of SL_2(Z). Two concrete constructions of such functions will be covered: Eisenstein series and theta series. We will also show that the space of modular forms for a specific weight is finite dimensional, which makes all these functions algorithmically computable. Furthermore, we will introduce Hecke operators and show that the L-functions associated to eigenfunctions are of arithmetic nature. Throughout the module, several applications to congruences and positive definite quadratic forms will be highlighted.

This course is an introduction to elementary number theory. The main focus is on solving equations and congruences in integers, although various other rings...

This course is an introduction to elementary number theory. The main focus is on solving equations and congruences in integers, although various other rings will appear in the proofs of theorems.