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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…

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 treats: The real numbers: axioms, examples of proofs of basic arithmetical rules. The elementary functions, polynomials, rational functions, the exponential function and the natural logarithm, the trigonometric functions…

The course treats: Elementary logic and set theory Basic properties of the natural numbers and the integers: induction, divisibility, Euclid’s algorithm Basic properties of polynomials: divisibility, Euclid’s algorithm Complex…

The course treats: Functions of several variables, basic topology in R^n. Continuity, theorems about continuous functions. Differentiable functions, gradients and directional derivatives. Taylor's formula. Extreme values…

Variable substitution, inverse and implicit functions, curve and surface integrals, Green's formula, Gauss Divergence Theorem, Stokes Theorem are treated.

The course treats Matrices: matrix operations, matrix inverse, matrix rank Determinants: definition and properties Linear spaces: subspace, span, linear dependence/independence, basis, dimension Euclidean spaces: scalar product,…

The course treats: Properties of the real numbers R: completeness axiom, Cauchy sequences, cardinality of rational and irrational numbers. Topology in Rn: open and closed sets, p-norms, convergence, compactness and the Bolzano…

The course treats: Basic properties of Fourier series of functions in one variable. Exponential form and trigonometric form. Riemann-Lebesgue lemma. Elementary conditions for pointwise and uniform convergence. Gibbs phenomenon. Basic…

The course treats variational problems with and without constraints, Euler equations with and without constraints, Legendre, Jacobi and Weierstrass necessary condition for local minimum, Hilbert invariant integral and Weierstrass…

The course treats: Number theory: the fundamental theorem of arithmetic, modular artithmetic. Groups: definition, basic examples of groups, subgroups, normal subgroups, factor groups, isomorphisms and homomorphisms, Lagrange's theorem,…

The degree project requires a literature survey and specialised studies. Furthermore, a number of compulsory activities are included, in the form of teaching sessions and seminars that treat e.g. scientific writing in English and Swedish,…

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…

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…

The thesis should be a synthesis and further development of the knowledge and competences gained during the three terms of course work in LUMES on top of undergraduate studies. The thesis work should develop…

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 course covers specific methods, techniques and debates around measures designed to mitigate climate change. It familiarises the student with technical, social and governance processes to implement, among others, large-scale renewable…

The aim of the course is to provide students with an in-depth understanding of climate change adaptation, centered around the concepts of risks, vulnerability and justice. The course presents and discusses various solutions for climate…

The course deals with societal transformation as a concept and as action in relation to climate change. It links to previous programme courses on mitigation and adaptation and introduces processes and potential for more fundamental changes…

The course explores a range of methods and tools for understanding and taking action on societal challenges posed by climate change and aims to analyse the implications, challenges and opportunities in applying them in practice. Building…

The study of media, communication and culture has a rich tradition in various methodological positions in the social sciences and humanities. This course critically evaluates established methodological perspectives on research methods in…

This course is intended to cover fundamental questions on the very substance of science and the scientific method; on what distinguishes good and proper science from pseudoscience, from charlatanry and plain cheating; the relation between…

In this course we will try to address these and similar questions, by looking at and discussing the wealth of gender science applied to physics. The course will consist of two parts: This part is an introduction to gender science and how…

You can perform a Master's Degree project of 30, 45 or 60 credits in either General Molecular Biology, or one of the specialisations Medical Biology, Microbiology or Molecular Genetics and Biotechnology. The prerequisites for a Master´s…

The course contains elements of research ethics with a focus on principles of good scientific practice and regulations for ethics review and procedures on issues of misconduct. The course also provides knowledge and training in…

During the course, the student studies a research area related to current research. Possible themes include human rights in governmental and non-governmental organizations, human rights and political values, migration and refugees,…

During the course, the student studies a research area related to current research. Possible themes include human rights in governmental and non-governmental organizations, human rights and political values, migration and refugees,…

The course is for you who want to integrate self reflection and techniques to meet tentions in your work and studies as a musician. Methods and reflecting perspectives are combined to understand the complexity in professional musicianship…

The course deals primarily with economic decision making concerning consumption and production. The course starts with a treatment of the underlying principles that guide an individual's optimal consumption decisions under both certainty…

This course starts with an introduction to descriptive statistics, probability theory and inference. Thereafter, the course treats problems connected with establishing and quantifying the relationship between different economics variables…

The course provides a deepened overview of macroeconomic theory. It deepens the content of the introductory course by adopting a more thorough analysis and problematizing the streangths and weaknesses of different theories and models, both…

The course begins with development gaps, and the relationships between per capita income and other measures of development. Thereafter it reviews the theories of economic growth and the development process. It focuses on the role of…

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…