. "Astronomy"@en . . "English"@en . . "Fields and particles"@en . . "2" . "Variaional principle of field theory, Symmetries and conservaion laws, Classiicaion of elementary paricles and interacions, Quantum electrodynamics and the photon, Weak interacion and the neutrinos, Strong interacion (quarks and hadrons), Symmetry breaking, Foundaions of the Standard Model" . . "Presential"@en . "TRUE" . . "Partial differential equations"@en . . "4" . "First order linear and quasilinear PDEs.\n\nSecond order linear PDEs, classiicaion.\n\nParabolic and hyperbolic iniial value problems.\n\nHilbert spaces, Fourier series, linear operators.\n\nEllipic boundary value problems.\n\nEigenvalue problems, separaion of variables. Fourier series expansion of the soluion.\n\nGreen’s funcion, spherical funcions.\n\nParabolic and hyperbolic iniial- boundary value problems.\n\nFourier transform, wavelets." . . "Presential"@en . "TRUE" . . "Relativity"@en . . "2" . "The principle of special relativity. Minkowski spaceime. Relaivisic kinemaics, velocity addiions, Lorentz transformaion, ime dilataion, Lorentz contracion. Astrophysical applications: superluminal moions, relaivisic beaming. Relaivisic dynamics. 4-vectors, mass increase. Principle of general relativity. Curved manifolds, curved spaceime, covariant and contravariant representaion. Einstein equaions. Robertson-Walker metrics, Schwarzschild and Kerr metrics. Astrophysical applicaions: perihelion moion, light delecion, dynamics around black holes." . . "Presential"@en . "TRUE" . . "Astronomical instrumentation 1-2"@en . . "4" . "Semester 1: Overview of astronomical databases. Observaional and pracical work, guided reading.\r\n\r\nTopics: Ideniicaion of objects in astronomy; Evoluion of notaion, naming and catalogizaion of stars and stellar like objects; Stellar catalogs, their contents and usage; Pariion of the sky, the role of the constellaions; Sky maps, sky atlases; SAO Atlas, Photographic surveys, Carte du Ciel, NGS-POSS, SDSS\r\n\r\nSemester 2: Introducion to observaional and data analysis techniques in astronomy. Basics of CCD technology and processing of the raw data from a CCD unit.\r\n\r\nTopics: Astronomical coordinate systems; Introducion to the Izsák telescope and CCD camera; Principles of CCD cameras, photo efect, charge coupling; Sources of noise in CCD images: dark current, pixel nonuniformity, shot noise," . . "Presential"@en . "TRUE" . . "Astronomical informaion technology"@en . . "2" . "Review of programming skills:\n\nalgorithms\nC / C++ programming language\nIntroducion to astronomical image processing:\n\ntechnical images (bias/dark/lat)\nastronomical image format (its)\nIntroducion to IDL (Interactive Data Language) programming language:\n\nIDL used for data input/output/analysis\nIDL used for its image format - IDL used for scieniic visualizaion\nusing the IDL Astronomy Users Library (http://idlastro.gsfc.nasa.gov)" . . "Presential"@en . "TRUE" . . "Astronomical spectroscopy 1-2"@en . . "4" . "Electromagneic radiation, astronomical sources in the visible and other spectral ranges\nHistory and basics of astronomical spectroscopy\nSpectroscopes, how they work and their applicaion in astrophysics\nInfrared and ultraviolet spectra of stars, interstellar medium, galaxies, AGN-s\nX-ray sources and their spectra\nSpectral analysis sotware tools: IDL, IRAF, and CLASS (GILDAS)\nReducion and analysis of HI 21cm, CO (J=1-0) 2,6mm and NH3 (1,1) 1,3cm spectra\nReducion and analysis of opical spectra of stars, spectral classiicaion\nReducion and analysis of opical spectra of galaxies, determinaion of redshit\nWriing spectroscopic observaion proposals for measurements with facility telescopes: one for the visible and one outside the visible range" . . "Presential"@en . "TRUE" . . "Celesial mechanics 1-4"@en . . "8" . "Semester 1: General perturbaion theory\nCanonical perturbaion theory: Hamilton-Jacobi method, acion-angle variables. The fundamental theorem of perturbaion theory, Delaunay's lunar theory and eliminaion method. Poincaré-Zeipel method. Theory of resonant perturbaions. Lie transform perturbaion theory. Superconvergent perturbaion theory. Ordered and chaoic moions: KAM theory.\nOrdered and chaoic orbits in the restricted three-body problem. Lyapunov indicators. Poincaré mappings. Hénon-Heiles problem. Symplecic mappings, symplecic integrators.\nSemester 2: Dynamics of planetary systems\nResonances of irst and second order. Resonant encounters, capture into and passing through a resonance. Muliple resonances.Resonances in the Solar System.\nDynamics of the Solar System: Moion of giant planets. Stability of the Solar System. Rotaion of the planets and moons. Dynamics of resonant asteroids.\nExoplanetary systems: Dynamical classiicaion of muliple planetary systems. Resonant, interacing and hierarchical systems. Planet-disk interacions. Stability of exoplanetary systems.\nSemester 3: The three-body problem\nThe general three-body problem: Equaions of moion and irst integrals. The Lagrange-Jacobi equaion. Classiicaion of inal coniguraions. The Euler-Lagrange soluions.\nThe restricted three-body problem: Equaions of moion, the Jacobi-integral. Equilibrium soluions and their stability. Zero velocity curves. Regularizaion transformaions. Periodic and numerical soluions. The ellipic restricted three-body problem. The Hill-problem.\nSemester 4: Theory of ariicial satellites\nThe gravitaional potenial. Terrestrial gravitaional perturbaions.\nLunisolar perturbaions. Non-gravitaional perturbaions." . . "Presential"@en . "TRUE" . . "Observational astronomy 1-4"@en . . "8" . "Classicaion and characterisics of planetary bodies. Formaion of the Solar System. Formaion and evoluion of planets. Moon and Mercury. Venus. Earth as a planet. Mars. Gas giants. The Jovian system. Sytems of Saturn, Uranus, Neptune. Small solar system bodies. Interplanetary dust.\nSemester 2: The Sun\nHistorical introducion. Standard solar model, solar neutrinos. Helioseismology. Solar rotaion. Instrumentaion for solar observing. Polarisaion of light and its applicaions in solar physics. The quiet photosphere. Chromosphere and corona. Acivity phenomena: sunspots, faculae, prominences, lares, CMEs. Acive regions and the solar acivity cycle. Basics of solar dynamo theory. Solar wind and the heliosphere.\nSemester 3: Special stars and objects\nStars with anomalous spectra: Ae/Be stars, C and S spectral types, Wolf-Rayet stars. Variable stars. Pulsaing variables. Erupive variables. Rotaing and cataclysmic variables változócsillagok. Binary stars. Supercompact variables X-ray binaries. Miniquasars, black hole candidates. Quasars and acive galacic nuclei.\nSemester 4: Remarkable individual objects\nMapping of the Milky Way Galaxy. Spiral arms. The galacic center. Remarkable objects in the Sagitarius and Carina arms. Remarkable objects in the Perseus ar, Crab nebula. Our cosmic neighbourhood, the Orion spur. The Orion star forming region. The nearest stars. Remarkable star clusters. Magellanic clouds. Local group. >>Virgo Supercluster. Remarkable objects beyond our supercluster." . . "Presential"@en . "TRUE" . . "Seminar in modern astronomy 1-4"@en . . "8" . "Students gain experience in giving scieniic presentaions and in reading/processing scientific papers.\nAstronomical Seminar 1:\ngiving a 15-20 minutes long presentaion, based on a short scieniic paper Astronomical\nSeminar 2:\ngiving a 15-20 minutes long presentaion, based on a long (min. 10 pages) scieniic paper Astronomical\nSeminar 3:\ngiving a 20-40 minutes long presentaion, based on one or more scieniic papers of total lebgth exceeding 10 pages, in the form of a free review of the subject Astronomical\nSeminar 4:\ngiving a 20-40 minutes long presentaion, based on one or more scieniic papers of total lebgth exceeding 10 pages, in the form of a free review of the subject" . . "Presential"@en . "TRUE" . . "Structure of the universe 1-2"@en . . "4" . "Semester 1: Cosmology\nBrief history of cosmology - introducion to general relaivity - models of the expanding universe - the standard cosmological model – thermodynamics of the expanding universe – paricles in the early universe – cosmic microwave background – dark mater and dark energy – paradoxes of standard cosmology – the inlaionary model\n\nSemester 2: Large-scale structure\nBrief introducion to galaxies – extragalacic distance measures – acive galaxies and quasars – galaxy clusters – surveying the large-scale structure – visible and dark mater – surveying the invisible mater – staisical descripion of the distribuion of mater – origin and evoluion of large-scale structure – the cosmic microwave background and its connecion to the large-scale structure" . . "Presential"@en . "TRUE" . . "Theoretical astrophysics 1-4"@en . . "10" . "Semester 1: Physical foundaions\nThermodynamics: ideal gas, parial ionisaion, Saha equaion. Degeneraion of mater. Nuclear reacions. Basics of luid mechanics and magnetohydrodynamics. Linear perturbaions, waves in homogeneous media, perturbaions in straiied media. Turbulence and convecion. Radiaive transfer equaion\n\nSemester 2: Stellar structure and evoluion\nApplicaion of luid mechanics to stars. Thermodynamics of stellar plasma. Radiaive and convecive transfer of energy. Simpliied models, polytropic spheres. Numerical methods in the modelling of steallr structure and evoluion. Stability of stars: theory of linear pulsaion. Basics of numerical modelling of nonlinear pulsaions. Introducion to asteroseismology. Stellar evoluion: energy producion and nucleosynthesis. Phases of stellar evoluion.\n\nSemester 3: Radiaive transfer\nSaha equaion, Fowler-Milne theory of stellar spectra. Radiaive equilibrium in stellar atmospheres. Transfer equaion. Limb darkening. Theory of Fraunhofer lines. Mechanisms of absorpion, damping, Doppler broadining. Theory of the growth curve, determinaion of stellar composiion. Nontehrmal radiaion processes: synchrotron radiaion, nonthermal bremsstrahlung, comptonisaion.\n\nSemester 4: Difuse matter\nRadiative transfer and raditaive processes in difuse media. Interstellar molecules. The luid dynamics of difuse mater, shock waves. Interstellar dust and gas. Interstellar magneic ields. Interstellar medium in the Milky Way Galaxy. Star formaion. Planetary nebulae and supernove remnants." . . "Presential"@en . "TRUE" . . "Galactic astronomy 1-4"@en . . "8" . "1st semester:\r\nHistory of radio astronomy, atmospheric radio window\r\nBasic deiniions and terms, radio emission mechanisms\r\nInstrumentaion: single-dish radio telescopes and interferometers\r\nVery Long Baseline Interferometry networks, data processing, image reconstrucion; applicaions in astrophysics, astrometry and geodesy\r\nNext-generaion radio astronomy instruments\r\n2nd semester:\r\nClassiicaion of celesial radio sources\r\nRadio astronomy in the Solar System\r\nGalacic radio astronomy, the Galacic Centre\r\nExtragalacic radio sources, acive galacic nuclei\r\n Cosmological applicaions\r\nCosmic microwave background radiaion" . . "Presential"@en . "TRUE" . . "Radio astronomy 1-2"@en . . "4" . "N.A." . . "Presential"@en . "FALSE" . . "Infrared astronomy 1-2"@en . . "4" . "N.A." . . "Presential"@en . "FALSE" . . "Astrostatistics 1-2"@en . . "4" . "Fundamental principles and results of broad ields of staisics applicable to astronomical research. The material is roughly at a level of advanced undergraduate courses in staisics.\r\n\r\nSemester 1: Probability; Staisical inference; Probability distribuion funcions; Nonparametric staisics; Data Smoothing;\r\n\r\nSemester 2: Regression; Mulivariate analysis; Clustering, classiicaion; Censored and truncated data; Time series analysis; Spaial point processes;" . . "Presential"@en . "FALSE" . . "Dynamics of stellar systems 1-2"@en . . "4" . "A comprehensive descripion of the dynamical structure and evoluion of galaxies and other stellar systems\r\n\r\nSemester 1: Introducion; Potenial Theory; Orbits of stars; Equilibria of Collisionless Systems\r\n\r\nSemester 2: Stability of Collisionless Systems; Disk dynamics and spiral structure; Kineic theory; Collisions and encounters; Galaxy formaion" . . "Presential"@en . "FALSE" . . "Advanced astronomical informaion technology 1-2"@en . . "4" . "Semester 1: Review of programming skills: algorithms, C or C++ programming languages. Overview of the basic numerical methods; implemening Euler's method; implemening Runge-Kuta methods; elements of parallel programming; CUDA / OpenMP / MPI\r\n\r\nSemester 2: overview of astronomical image processing; IDL (Interacive Data Language) programming language; data analysis using IDL; image processing using IDL; IDL Astronomy Users Library (http://idlastro.gsfc.nasa.gov)" . . "Presential"@en . "FALSE" . . "Astronomy from space 1-2"@en . . "4" . "Motivaion for space research, scieniic and social environment, poliical and legal issues\nPhases of space missions, criical points and examples\nChronology and milestones of lunar and planetary exploraion\nHigh energy and infrared astronomy and space applicaions\nSpace observatories and observaions\nOrbits, trajectories and maneuvers\nRocket engines and fuels and their use\nLaunch vehicles, and spaceports\nOn-board systems\nHungarian space research, achievements and science teams\nMajor space research and technology insituions and organizaions (ESA, NASA, JAXA)" . . "Presential"@en . "FALSE" . . "The history of astronomy 1-2"@en . . "4" . "N.A." . . "Presential"@en . "FALSE" . . "Introduction to astronomy 1-4"@en . . "8" . "N.A." . . "Presential"@en . "FALSE" . . "Astrometry 1-2"@en . . "4" . "Semester 1 focuses on the basics of astrometry (coordinate systems, ime, efects perturbing the observaions) and the methods of transformaions and reducions. Paricular atenion is paid on the acquirement of skills in conversion calculaions.\n\nTopics: Spherical astronomy; Astronomical coordinate systems; Transformaion between coordinate systems; Rising and seing of celesial bodies; Time and calendar; Efects perturbing the observaions; Precession and nutaion\n\nSemester 2 gives on introducion to the subject of celesial mechanics.\n\nTopics: Two-body problem; Ellipical moion; Orbital elements and their connecions to the constants of integraion; Kepler's laws; Orbit determinaion from three observaions; Restricted three-body problem; Jacobi-integral and zero-velocity curves; Stability of the equiblirium points; Perturbaion theory; Dynamics of the Solar System" . . "Presential"@en . "FALSE" . . "Astrophysics 1-2"@en . . "4" . "Semester 1: Elements of potenial theory,: shell theorems, virial theorem, Poisson equaion. Basics of cosmology. Elements of radiaive transfer. Thermal radiaion. Random walk, difusive approximaion, transport coeicients, Rosseland opacity. Equaions of stellar structure. Overview of stellar evoluion.\n\nSemester 2: Eddington's criical luminosity. Stellar winds and driving mechanisms. Parker's solar wind model. Spherical (Bondi) accreion. Scatering in 1/r potenial. Applicaion to plasmas: transport coeicients. Applicaion to stellar systems: stellar encounters, collisional relaxaion. Basics of stellar dynamics. Elements of gravitaional lensing. Free-free transiions, bremsstrahlung. Thermal bremsstrahlung. Elements of the theory of accreion, thin accreion disks, Shakura-Sunyaev model." . . "Presential"@en . "FALSE" . . "Information technology in astronomy 1-3"@en . . "6" . "no data" . . "Presential"@en . "FALSE" . . "Master in Astronomy"@en . . "https://www.elte.hu/en/astronomy-msc" . "120"^^ . "Presential"@en . "The objective of the Astronomy Master's Degree Program is to provide a comprehensive knowledge of astronomy including related interdisciplinary areas. Students will also acquire competencies in the wider field of scientific research, in the use of technical language, in team work and in the communication of scientific results, they will also develop an ability to resolve novel or unusual problems arising in a multidisciplinary context.\n\nThe objective of the Astronomy MSc programme is the formation of fully trained astronomers and astrophysicists capable of supervised observational and theoretical research in astronomy and related fields."@en . . "2"@en . "FALSE" . . "Master"@en . "Thesis" . "8380.00" . "Euro"@en . "8380.00" . "Mandatory" . "Career opportunities\r\nAfter completing the requirements listed above, students are awarded an MSc degree. The MSc degree qualifies its holder to take up positions in the relevant fields and to enlist to a postgraduate (PhD) study programme.\r\n\r\nJob examples\r\nPostgraduate (PhD) studentships at a Hungarian, European or international university research assistant's positions at a Hungarian, European or international research institute industry positions where a strong training in IT, signal processing, physics and electromagnetic wave analysis are an advantage, including telecommunications, computer technology, software companies, air control, satellite communications, etc."@en . "1"^^ . "FALSE" . "Upstream"@en . . . . . . . . . . . . . . . . . . . . . . . . . "Faculty of Science/ Department of Astronomy"@en . .