. "Algorithms, Data Structures, Complexity, And Computability, Modeling Complex Systems"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Basic computational techniques"@en . . "6" . "Specific Competition\nCE8 - Know how to program, at least, in a relevant language for scientific calculation in Astrophysics\nCE11 - Know how to use current astrophysical instrumentation (both in terrestrial and space observatories) especially that which uses the most innovative technology and know the fundamentals of the technology used\nGeneral Competencies\nCG1 - Know the advanced mathematical and numerical techniques that allow the application of Physics and Astrophysics to the solution of complex problems using simple models\nCG4 - Evaluate the orders of magnitude and develop a clear perception of physically different situations that show analogies allowing the use, to new problems, of synergies and known solutions\nBasic skills\nCB6 - Possess and understand knowledge that provides a basis or opportunity to be original in the development and/or application of ideas, often in a research context\nCB7 - That students know how to apply the knowledge acquired and their ability to solve problems in new or little-known environments within broader contexts\nCB8 - That students are able to integrate knowledge and face the complexity of formulating judgments based on information that, being incomplete or limited, includes reflections on the social and ethical responsibilities linked to the application of their knowledge and judgments\nCB10 - That students possess the learning skills that allow them to continue studying in a way that will be largely self-directed or autonomous\n6. Subject contents\nTheoretical and practical contents of the subject\nThe theoretical and practical contents of the subject are divided into the following topics:\n\nTopic 1. Introduction to programming with Python\n 1.1 Introduction to programming languages\n ​​1.2 Installation and startup\n 1.3 Data types\n 1.4 Operators\n 1.5 Modules\n 1.6 Operations and data structure\n 1.7 Control flow statements\n 1.8 Reading and writing files\n 1.9 User-defined functions\n 1.10 Running codes with exceptions\n 1.11 Passing arguments on the command line\n 1.12 Classes\n 1.13 Graphs\n\nTopic 2. Statistical analysis of data\n 2.1 Introduction\n 2.2 Libraries\n 2.3 Material\n 2.4 Previous concepts: measurement; precision and accuracy; random and systematic errors; observable; bias; estimator; noise; data model\n 2.5 Characterization of measurements: mean value, median and mode; deviations; variance; significance; covariance matrix\n 2.6 Probability density distribution functions: continuous and discrete distributions; representation of distributions; obliquity/skewness and kurtosis; exercises\n 2.7 Probability functions: sampling of probability functions\n\nTopic 3. Linear and nonlinear adjustments\n 3.1 Method of least squares\n 3.2 Nonlinear functions\n\nTopic 4. Bayesian statistics\n 4.1 Information and entropy\n 4.2 Distance between probability functions\n 4.3 Bayesian Inference: axioms of probability theory; Bayes theorem; model comparison: evidence; steps in Bayesian inference; sampling of a lognormal-Poisson function\n\nTopic 5. Fourier analysis\n 5.1 Introduction\n 5.2 Fourier theorem\n 5.3 Properties: convolution; Fourier transform and differential operators; famous transformations; filters; discrete Fourier transform; algorithms; bookstores" . . "Presential"@en . "FALSE" . . "Master in Astrophysics"@en . . "https://www.ull.es/en/masters/astrophysics/" . "90"^^ . "Presential"@en . "The exceptional atmospheric conditions for top-quality astronomic observation to be found in the Canary Islands, together with its geographic proximity and excellent connections with Europe, justify the presence here of the European Northern Hemisphere Observatory (ENO). This fact, along with the consequent concentration of teachers and researchers around the Canary Island Institute of Astrophysics, the ULL Department of Astrophysics and the Observatories, generates the ideal atmosphere for a Master in Astrophysics in which direct contact with leading professionals represents exceptional value added. The Master has been designed based on an ample and rigorous choice of subjects, options and itineraries that that take the form of three specialities: “Theory and Computing Speciality”, “Observation and Instrumentation Speciality” and “Material Structure”\n\nGeneral skills\nKnow the advanced mathematical and numerical techniques that allow Physics and Astrophysics to be applied to solving complex problems using simple models\nUnderstand the technologies associated with observation in Astrophysics and the design of instrumentation\nAnalyse a problem, study the possible solutions published and propose new solutions or lines of attack\nAssess orders of magnitude and develop a clear perception of physically different situations that show analogies allowing the use of synergies and known solutions for new problems\nSpecific skills\nUnderstand the basic conceptual schemes of Astrophysics\nUnderstand the structure and evolution of the stars\nUnderstand the mechanisms of nucleosynthesis\nUnderstand the structure and evolution of galaxies\nUnderstand the models of the origin and evolution of the Universe\nUnderstand the structure of matter to be able to solve problems related to the interaction between matter and radiation in different energy ranges\nKnow how to find solutions to specific astrophysical problems on your own, using specific bibliography with minimum supervision\nKnow how to work independently on new research projects\nKnow how to programme, at least in one important language for scientific calculation in Astrophysics\nUnderstand the instrumentation used to observe the universe in the different frequency ranges\nUse current scientific instrumentation (both Earth-based and Space-based) and have a command of their innovative technologies\nKnow how to use current astrophysical instrumentation (both in terrestrial and space observatories), especially the instrumentation that uses the most innovative technology and know the foundations of the technology used\nApply the knowledge acquired to undertake an original research work in Astrophysics"@en . . . "1.5"@en . "FALSE" . . . "Master"@en . "Thesis" . "Not informative" . "no data"@en . "Not informative" . "None" . "no data"@en . "no data" . "FALSE" . "Upstream"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .