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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: Number theory: divisibility, prime numbers, the Euclidean algorithm, Chinese remainder theorem, modular arithmetic Sets, functions and relations, equivalence relations Combinatorics: the four cases of counting with…

The aim of the course is to give necessary knowledge of digital image analysis for further research within the area and to be able to use digital image analysis within other research areas such as computer graphics, image coding, video…

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 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 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: 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 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 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,…