. "Applied Mathematics"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Mathematical methods of physics b"@en . . "5" . "LEARNING OUTCOMES\nAfter the course, the student will be familiar with basic concepts of calculus on differentiable manifolds and Riemannian geometry, which are mathematical tools used in physics e.g. in the contexts of general relativity and gauge field theories. The student will also be familiar with basics of Lie algebra representation theory, which is used e.g. in particle physics and condensed matter theory. The student can work with differential forms, express metrics in different coordinates and compute metric tensors of general relativity. He also understands basic representations of Lie algebras used e.g. in the theory of strong interactions.\n\nCONTENT\nDifferentiable manifolds and calculus on manifolds: differentiable manifolds, manifolds with boundary, differentiable maps, vector fields, 1-form fields, tensor fields, differentiable map and pullback, flow generated by a vector field, Lie derivative, differential forms, Stokes' theorem\n\nRiemannian geometry: metric tensor, induced metric, connections, parallel transport, geodesics, curvature and torsion, covariant derivative, isometries, Killing vector fields\n\nSemisimple Lie algebras and representation theory: SU(2), roots and weights, SU(3), introduction to their most common unitary irreducible representations" . . "Presential"@en . "FALSE" . . "Master's programme in Particle Physics and Astrophysical Sciences"@en . . "https://www.helsinki.fi/en/degree-programmes/particle-physics-and-astrophysical-sciences-masters-programme" . "120"^^ . "Presential"@en . "What are the laws of nature governing the universe from elementary particles to the development of the solar system, stars, and galaxies? In the Master’s Programme in Particle Physics and Astrophysical Sciences, you will focus on gaining a quantitative understanding of these phenomena.\n\nWith the expertise in basic research that you will gain in the programme, you might pursue a career in research. You will also acquire proficiency in the use of mathematical methods, IT tools and/or experimental equipment, as well as strong problem-solving and logical deduction skills. These will qualify you for a wide range of positions in the private sector.\n\nAfter completing the programme, you will:\n\n-Have wide-ranging knowledge of particle physical and/or astrophysical phenomena.\n-Have good analytical and computational skills and the ability to make sophisticated deductions.\n-Be able to apply theoretical, computational and/or experimental methods to the analysis and understanding of various phenomena.\n-Be able to apply your knowledge of particle physical and astrophysical phenomena as well as identify their interconnections.\n-Be able to formulate hypotheses and test them based your knowledge"@en . . . . "2"@en . "FALSE" . . . "Master"@en . "Thesis" . "no tuition, other costs may apply" . "Euro"@en . "15000.00" . "None" . "A Master’s degree in elementary particle physics or astrophysical sciences provides you with excellent qualifications for postgraduate education in research or for a career in diverse positions both in Finland and abroad. As a Master’s graduate you could begin a career in research and development in industry as well as in universities and other research institutes that enable you to conduct independent research on a topic that interests you."@en . "2"^^ . "TRUE" . "Upstream"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .