. "Applied Mathematics"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Numerical methods in scientific computing"@en . . "10" . "LEARNING OUTCOMES\nYou will learn to know the most common numerical methods and algorithms\nYou will understand the strenghts and weaknesses of these algorithms\nYou will be able to apply these algorithms using\nself-made programs\nnumerical libraries\nnumerical programs.\nCONTENT\nTools, computing environment in Kumpula, visualization\nBasics of numerics: floating point numbers, error sources\nLinear algebra: equations, decompositions, eigenvalue problems\nNonlinear equations: bisection, secant, Newton\nInterpolation: polynomes, splines, Bezier curves\nNumerical integration: trapeziodal, Romberg, Gauss\nFunction minimization: Newton, conjugate gradient, stochastic methods\nGeneration of random numbers: linear congruential, shift register, non-uniform random numbers\nStatistical description of data: probability distributions, comparison of data sets\nModeling of data: linear and nonlinear fitting\nFourier and wavelet transformations: fast Fourier transform, discreet wavelet transform, applications\nDifferential equations: ordinary and partial differential equations" . . "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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .