51ÖØ¿ÚÁÔÆæ

The course gives an overview of simulation based methods of statistical analysis. Markov chain methods for complex problems, e.g. Gibbs sampling and the Metropolis-Hastings algorithm. Bayesian modelling and inference. The re-sampling…

The course is given during the autumn semester at Lunds university and at the Technical University of Denmark in Lyngby. The graduate course in Advanced Time Series Analysis has its target audience amongst students with technical or…

Extreme value theory concerns mathematical modelling of extreme events. Recent developments have introduced very flexible and theoretically well motivated semi-parametric models for extreme values which now are at the stage where they can…

Time series analysis concerns the mathematical modelling of time varying phenomena, e.g., ocean waves, water levels in lakes and rivers, demand for electrical power, radar signals, muscular reactions, ECG-signals, or option prices at the…

The course deals with model building and estimation in non-linear dynamic stochastic models for financial systems. The models can have continuous or discrete time and the model building concerns determining the model structure as well as…

Least squares and maximum-likelihood-method; odds ratios; Multiple and linear regression; Matrix formulation; Methods for model validation, residuals, outliers, influential observations, multi co-linearity, change of variables; Choice of…

Bayesian methods for stochastic modelling, classification and reconstruction. Random fields, Gaussian random fields, Kriging, Markov fields, Gaussian Markov random fields, non-Gaussian observations. Covariance functions, multivariate…

Basic definitions. Continued study of AR (auto regressive), MA (moving average) and ARMA-processes. Line spectrum and parametric estimating methods. Sub space based techniques. Non-parametric spectral estimators, data-adaptive techniques…

The course consists of two related parts. In the first part we will look at option theory in discrete time. The purpose is to quickly introduce fundamental concepts of financial markets such as free of arbitrage and completeness as well as…

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…

A central part of the course is existence- and uniqueness theorems about measures defined on sigma-algebras, integration theory, conditional expectation and weak convergence in metric spaces.

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 the geometry of curves and surfaces, especially in three dimensions. In particular, we study the concepts of curvature and torsion. The course covers: The geometry of curves in Euclidean space, their curvature and…

The course treats: Finitely generated groups: free groups, Nielsen-Schreier Theorem, group presentations, finitely presented groups. Free products: free products with amalgamation, HNN extensions. Solvable groups: polycyclic groups,…

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: Groups: Permutation groups. Burnside's lemma with application to Pólya arithmetic. Sylow's theorems. Symmetric and alternating groups. The structure of finitely generated Abelian groups. Rings: Noetherian and…

The course treats fundamental properties of Banach and Hilbert spaces and the bounded linear operators defined on them: Banach spaces, the Hahn-Banach Theorem, weak convergence and  weak precompactness of the unit ball. Hilbert…

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…

The course treats applications of the Hahn-Banach theorem, weak convergence and compactness, the Riesz representation theorem, the use of orthonormal bases, boundedness, compactness and spectra of integral operators, the…

The course addresses political approaches to and perspectives on sustainability issues and place these in relation to the actual ability to address sustainability challenges. It tackles both central political factors as well the creation…

The course provides interdisciplinary perspectives from the field of environmental geography aimed at studying the dynamics of social and environmental change in particular places. It covers perspectives from a variety of research fields,…

The course briefly reviews economic theories and economic growth and analyses their environmental and social consequences, for instance, environmental degradation, social welfare and equity. Students will develop competencies in critically…

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…

The themes are covered significantly through a variety of scientific readings and reflection that exemplify different approaches and perspectives for analysing and interpreting present and future water resource availability, the political…

The main aim of the course is to provide conceptual frameworks for studying and evaluating the impact that social movements for sustainability can have on the public agenda and decision-making. The course is a seminar course,…

In the course we will discuss the broad field of gender studies and the central issues, key concepts and analytical tools in the current debates regarding inequalities, diversities and social change relevant for sustainability. The course…

The course also provides an understanding of and an ability to analyse and understand political questions and decision making in relation to climate mitigation and climate adaptation. Based on this, the course aims to provide a deepened…

By highlighting four key emerging and persistent global health challenges: The unavoidable health impacts of climate change (heat-stress, extreme cold, flooding, rising incidence of vector borne-diseases) The prevailing sanitation…

As a result, the notion of inner transformation (or inner transition) has emerged as a new area of exploration. The course explores this new area and creates space and opportunities for learning and knowledge development on this topic…

The course focuses on the ‘political’ character of sustainability issues, that is, the necessarily power-laden nature of both sustainability problems themselves, and the solutions that are proposed to address them. The course provides an…

This increase of sustainability discourses in the daily practices of society might contribute to shifting the current unsustainable trajectory. For this course, popular culture is defined as the entirety of attitudes, ideas…

The course constitutes a 3rd term elective (non-compulsory) course at LUMES, 51ÖØ¿ÚÁÔÆæ Master's Programme in Environmental Studies and Sustainability Science.

The course turns to active musicians and music teachers and students at a Music Academy or the equivalent. The course contains advanced development and practise methods regarding tone formation, articulation, timbres and fingering…

The course includes advanced development and practice of tone formation, articulation, timbre, finger technique, special grips, and Sons filés. The students will be introduced to the solo piccolo repertoire ranging from Vivaldi to…

Students will learn advanced development and practice of tone formation, articulation, timbre, finger technique, special grips, and solo repertoire for the contrabassoon. The teaching consists of a mix between group lessons and individual…

Students will learn advanced development and practice of tone formation, articulation, timbre, finger technique, special grips, and solo repertoire for the bass clarinet. The teaching consists of a mix between group lessons and individual…

‘Just practise enough and everything will be fine!’ Is it really that simple? Why does it feel so difficult and discouraging at times? This course is designed for students at music academies, but also for active musicians and music…

The course presents modern microeconomic theory and a set of applications. The applications considered include: The theory of economic decision making under risk and uncertainty, including the important notions of risk aversion and…

The first part of this course will discuss how rational people should make simple decisions and form empirical judgments. This part also discusses the systematic ways in which real human beings deviate from these models in practice. A…

This course gives the basis that is needed to enable students to empirically analyse economic data without making unrealistic assumptions. Modern econometric techniques are treated, and at the same time considerable emphasis is placed on…