Kursen behandlar grundläggande egenskaper hos Banach- och Hilbertrum och begränsade lineära operatorer definierade på sådana rum: Banachrum, Hahn-Banachs sats, svag konvergens och svag prekompakthet av enhetsklotet. Hilbertrum. Exempel inklusive L2-rum. Ortogonalitet, ortogonalt komplement, slutna underrum, projektionssatsen. Riesz representationsteorem. Ortonormala mängder, Pythagoras satThe 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 spaces. Examples including L2 spaces. Orthogonality, orthogonal complement, closed subspaces, projection theorem. Riesz Representation Theorem. Orthonormal set

Kursen beskriver olika typer av acceleratorer (cyklotroner, mikrotroner, linac, linjär acceleratorer, lagringsringar, synkrotroner) i olika applikationer (synkrotronljus, högenergifysik, colliders, medicin, tumörterapi, industri). Vidare behandlas elektronstråleoptik och partikelstråleoptik och dynamik (magneter, dipoler, quadrupoler, fokusering, matrisformalism, betatronsvängningar, betatrontonerThis course describes different types of accelerators (cyclotrons, microtrons, linacs, linear accelerators, storage rings, synchrotrons) used in various applications (synchrotron radiation, high energy physics, colliders, medicine, tumor therapy, industry). The description of electron beam optics, particle beam optics and dynamics (magnets, dipoles, quadrupoles, focusing, matrix formulation, betat

Kursen behandlar synkrotronljuskällors egenskaper och deras användning inom modern forskning. Uppbyggnaden av strålrör med de speciella optiska komponenter som behövs för fokusering, avbildning eller diffraktion är en central del i kursen. En översikt av experimentella tekniker och metoder för spektroskopi, strukturbestämning, avbildning, mikroskopi, tomografi och så vidare ingår också. KurseThis course is about the properties and use of synchrotron radiation in modern science. The design and construction of the optical elements required for focusing, imaging and diffraction constitute a central part of this course. An overview of experimental techniques and methods used in spectroscopy, structure determination, imaging, microscopy, and tomography is also part of the curriculum. Furth

A particular focus is put on energy transitions, including both societal and environmental dimensions. In this context we will discuss for example energy justice dimensions and spatial aspects (land demand) in the context of the transition. Further the course will examine the present debate regarding energy demand, energy efficiency and energy end-use technology status and potential, as well as iA particular focus is put on energy transitions, including both societal and environmental dimensions. In this context we will discuss for example energy justice dimensions and spatial aspects (land demand) in the context of the transition. Further the course will examine the present debate regarding energy demand, energy efficiency and energy end-use technology status and potential, as well as i

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, although it starts with a few lectures on the history and different theoretical perspectives on social movements, introducing the students to the relevant literature. TThe 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, although it starts with a few lectures on the history and different theoretical perspectives on social movements, introducing the students to the relevant literature. T

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 crises (causing preventable deaths and disease outbreaks, contributing to the poverty trap, affecting economic output, polluting the environment) The global dietBy 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 crises (causing preventable deaths and disease outbreaks, contributing to the poverty trap, affecting economic output, polluting the environment) The global diet

Kursen behandlar distributionsteorins grunder, testfunktioner, distributionsbegreppet, distributioner med kompakt stöd, operationer på distributioner, faltning, homogena distributioner och Fouriertransformen.The course treats the foundations of distribution theory test functions, the concept of a distribution, distributions with compact support, operations on distributions, convolution, homogeneous distributions and the Fourier transform.

Kursen behandlar: Grupper: Konjugatklasser. Burnsides lemma med tillämpning på Polyaräkning.Sylows satser. Strukturen hos ändligt genererade abelska grupper. Ringar: Noetherska och Artinska ringar och moduler. Artin-Wedderburns sats. Ändligt genererade moduler över en huvudidealring med tillämpning på Jordans normalform. Lineär algebra: Multilineära avbildningar. Tensorproduct 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 Artinian rings and modules. Artin-Wedderburn's theorem. Finitely generated modules over a principal ideal domain with application to the Jordan's normal form of matri

Kursen behandlar grundläggande egenskaper hos mått med tecken och komplexamått: Hahn- och Jordanuppdelning, absolut kontinuitet och Radon-Nikodyms teorem, singularitet, Lebesgue-uppdelning av mått, deriverbarhet av ändliga Borel-mått på R^d, deriverbarhet av absolutkontinuerliga funktioner, Hardy-Littlewoods maximalfunktion och uppskattningar för densamma, Hardy-Littlewoods maximalfunkThe 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 measures on Rd, differentiability of absolutely continuous functions, the Hardy-Littlewood maximal function and the weak type estimate for it, the Hardy-Lit

Kursen ger en introduktion till användningen av synkrotronljus och till användningen av högbriljant vakuumultraviolett- och röntgenstrålning. Kursen ger en beskrivning av uppbyggnaden av strålrör och en orientering om hur olika experiment utnyttjar en facilitet. En kort genomgång av synkrotronljusets betydelse för forskning inom fysik, kemi och biologi ges. Några exempel på metodik som fotonelektrThis course gives an introduction to the use of synchrotron radiation with different wavelengths. The design of beam lines and an introduction to different experiments at a synchrotron radiation facility is part of the course. The importance of synchrotron radiation for research in the fields of physics, chemistry and biology is discussed and examples are given of various experimental techniques (

Kursen ger deltagarna möjlighet att förbättra sina kunskaper och färdigheter inom hållbarhetsvetenskap genom en djupare förståelse av styrkorna och svagheterna med deltagande metoder. Kursen bygger på transformativt studentlärande där studenterna utvecklar kunskaper och färdigheter i problemlösningsprocesser för hållbarhet genom iterativa aktiviteter som idéskapande, reflektion, teoribildning, intThis 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 transformative student learning whereby students develop knowledge and skills in sustainability problem solving processes through iterative activities such as idea generati

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 ecology of water resource challenges, water-related vulnerability and adaptation measures, and uncertainties in climate modelling coupled to freshwater resourcesThe 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 ecology of water resource challenges, water-related vulnerability and adaptation measures, and uncertainties in climate modelling coupled to freshwater resources

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. Inner transformation, as used here, describes changes in the sphere of human interiority related to people’s (expanded) consciousness, mindsets, values, and beAs 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. Inner transformation, as used here, describes changes in the sphere of human interiority related to people’s (expanded) consciousness, mindsets, values, and be

The course deals with how theories about the resilience concept have developed within sustainability science. The course starts with a historical overview of the resilience concept within development- and sustainability science. The course then goes on to critically examine resilience as a concept and as an approach. Resilience has come to mean many things. There is for example, a resistance amonThe course deals with how theories about the resilience concept have developed within sustainability science. The course starts with a historical overview of the resilience concept within development- and sustainability science. The course then goes on to critically examine resilience as a concept and as an approach. Resilience has come to mean many things. There is for example, a resistance amon

About the course Climate Change and Society The course provides an interdisciplinary and state-of-the-art perspective on climate change with a particular emphasis on its social, economic, political and cultural dimensions. As a students you will receive a close understanding of the intertwined social and biophysical dynamics of both drivers and impacts of climate change, and of the different soluAbout the course Climate Change and Society The course provides an interdisciplinary and state-of-the-art perspective on climate change with a particular emphasis on its social, economic, political and cultural dimensions. As a students you will receive a close understanding of the intertwined social and biophysical dynamics of both drivers and impacts of climate change, and of the different solu

Kursens mål är att studenter efter avslutad kurs skall ha förvärvat följande kunskaper och färdigheter: Kunna beskriva och förklara olika acceleratortyper och deras funktionssätt Kunna beskriva hur fotoner och neutroner produceras med hjälp av acceleratorer och leds till experiment Känna till och kunna beskriva andra foton-/neutronkällor och tillhörande kärnreaktioner Kunna diskutera ochIn this course, you will learn about different types of accelerators for the production of photons and neutrons for research. methods of producing photons with highly relativistic electron beams in combination with special magnets called undulators and the method of producing neutrons by letting a relativistic proton beam hit a target. the experimental stations, the experimenta

The 2030 Agenda for Sustainable Development, with the 17 Sustainable Development Goals (SDGs), was adopted by all the United Nations Member states in 2015 as a call to action to end poverty, protect the planet and ensure peace and prosperity for all people. This course provides an interdisciplinary and state-of the-art perspective on Agenda 2030 and the Sustainable Development GoalThe 2030 Agenda for Sustainable Development, with the 17 Sustainable Development Goals (SDGs), was adopted by all the United Nations Member states in 2015 as a call to action to end poverty, protect the planet and ensure peace and prosperity for all people. This course provides an interdisciplinary and state-of the-art perspective on Agenda 2030 and the Sustainable Development Goal

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 student’s potential for professional sustainability work and/or for further research. The process puts great demands on the capacity to wThe 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 student’s potential for professional sustainability work and/or for further research. The process puts great demands on the capacity to w

Kursen ger en översikt över ekonomiska teorier och ekonomisk tillväxt och analyserar deras miljömässiga och sociala konsekvenser, så som degradering av miljön eller inverkan på social välfärd och jämlikhet. Studenter utvecklar förmågan att kritiskt utvärdera implikationer från olika ekonomiska paradigm för transformativ förändring samt att kunna avväga deras respektive för- och nackdelar. Under kuThe 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 assessing the implications of different economic paradigms for transformative change and weighing the trade-offs for each. During the course, students will: C

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 draws on global, regional and local empirical examples to illustrate issues of how gender and sustainability interact. We will analyse similarities, differencesIn 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 draws on global, regional and local empirical examples to illustrate issues of how gender and sustainability interact. We will analyse similarities, differences