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The course treats: Convergence of sequences of analytic functions. Locally uniform convergence, normal families, Montel’s theorem. In-depth study of conformal mappings. Riemann sphere, stereographic projection, Möbius…

The course treats: topological spaces and metric spaces with examples, product topologies, continuity of functions, connectedness, completeness, and compactness, including the Arzela-Ascoli Theorem, examples of applications and topological…

The course treats: Fourier series, Fourier transform and finite Fourier transform, L^2 convergence of Fourier series, pointwise convergence, Cesàro means and Fejer’s theorem, Weyl’s criterion, the Fourier inversion theorem, Parseval’s and…

This course treats the general notion of a measure defined on a sigma-algebra, construction of measures with help of outer measures, in particular the Lebesgue measure in Rd. These concepts are then used to define the integral of a…

The course treats: Linear systems of ordinary differential equations in the complex plane. Power series solutions. Singular points. Frobenius method. Some classical differential equations and special functions. Boundary value…

The course covers: Differentiable manifolds, their tangent spaces and tangent bundles. Riemannian metrics and their unique Levi-Civita connection. Geodesics and the important Riemann curvature tensor and its influence on the local…

The course treats: • homotopy theory, the fundamental group, covering spaces • the Brouwer fixed point theorem, the Borsuk-Ulam theorem • deformation retracts, fundamental groups and homology of surfaces • surgery of manifolds, also called…

The course treats: Group representations: linear representations, equivalent representations, regular representation, induced and restricted representations, irreducible representations, Maschke’s Theorem, dual representations and…

The course treats: The method of characteristics and nonlinear equations of the first order. Laplace’s equation. The heat equation. The wave equation. The Cauchy–Kowalevski theorem. Sobolev spaces. Existence, uniqueness and…

The course treats basic properties of signed and complex measures: Hahn and Jordan decomposition, absolute continuity and the Radon-Nikodym theorem, singularity, Lebesgue decomposition of measures, differentiability of finite Borel…

This course provides opportunities for participants to enhance their knowledge and skills in sustainability science through a deeper comprehension of the strengths and weaknesses of participatory methods. The course is based on…

This course covers modern econometric tools and empirical strategies used by economists and demographers for the analysis of cross-sectional and panel micro-data. The course teaches the econometric theory behind these techniques but also…

The course gives an introduction to basic concepts within time series analysis. The univariate analysis of time series in this course is based upon ARMA/ARIMA and ARCH-/GARCH models. Multivariate time series analysis is based on VAR models…

The course covers and discusses recent advances in Labour Economics, with an emphasis on empirical applications. Each lecture focuses on a specific topic. The course starts by discussing theories of labour supply and demand, and proceeds…

The course deals with the mechanisms behind and the effects of international trade. The course uses an advanced treatment in terms of topics and methodology, qualifying the student to carry out advanced analyses and the study of issues…

The objective of this course is to give the students an understanding and hands-on knowledge of fundamental methods within financial risk management. The course deals with two main topics: measurement and management of market risk and…

The course primarily treats issues related to economic growth using advanced dynamic macroeconomic models with intertemporally optimising agents. Within the framework of growth theory, dynamic models in continuous and discrete time…

The aim of this course is to provide students with the theoretical understanding of how a geographic database is built-up and how it can be used. You will study key concepts for handling geographic databases with special focus on spatial…

The course contains a number of different basic components of spatial analysis, both in terms of theoretical background and analytical methods. Some of the concepts and techniques covered in the course are point pattern analysis,…

The degree project requires a literature review and special studies. In addition, it includes a number of compulsory elements, in the form of lessons and seminars, which deal with, among other things, scientific writing in English and…