. "Applied Mathematics"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Mathematical methods of physics a"@en . . "5" . "LEARNING OUTCOMES\nAfter the course, the student will be familiar with basic concepts of group theory, group representation theory, and topology. The student can identify different common groups, study if their representations are reducible, irreducible or not, and knows why the theory of groups and their unitary representations is important in quantum physics of systems with various symmetries. The student also understands distinctions between nonhomeomorphic topological spaces and understands the use of topological invariants (such as homotopy groups) in their classification.\n\nCONTENT\nGroup theory: finite groups, continous groups, conjugacy classes, cosets, quotient groups\n\nRepresentation theory of groups: complex vector spaces and representations, symmetry tranformations in quantum mechanics, reducible and irreducible representations, characters\n\nTopology: topological spaces, topological invariants, homotopy, homotopy groups" . . "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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .