51ÖØ¿ÚÁÔÆæ

The course treats basic theory of analytic functions: Elementary properties of analytic functions in one variable. Complex differentiability and Cauchy-Riemann equations. Calculation rules. Elementary examples of analytic functions:…

The course treats: Existence and uniqueness of solutions to initial value problems for systems of ordinary differential equations. Approximation of solutions and continuous dependence on parameters. Linear systems with variable and…

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 course treats multiplicative number theoretic functions, Möbius inversion formula, properties of Euler's totient function, primitive roots and indices, quadratic residues, the Legendre symbol and its properties, the quadratic…

The course treats: quadratic forms and matrix factorisation, convexity, separating planes and Farkas’ Lemma, the theory of optimization with and without constraints, Lagrange functions, Karush-Kuhn-Tucker theory, duality, methods for…

The course comprises: Matrices and determinants. Linear spaces. Spectral theory.The Jordan normal form. Matrix factorizations. Matrix polynomials and matrix functions. Norms. Scalar products. Singular values. Normal matrices…

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…

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 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 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 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 learn about a gender perspective on Science and Technology. The course starts with a theoretical part, where we look at what we know from research and investigations. During this you will familiarise yourself with…

The course gives you  fundamental skills in data handling using Python. The focus is on exploratory data analysis, leveraging visualizations and data summaries to extract insights from datasets. Additionally, the course covers data…

The course covers broad programming aspects essential for scientists.  The following aspects are addressed: Use of UNIX-based operating systems, such as Linux Overview of the use of programming in various scientific fields …