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Master’s program in mathematics Eötvös Loránd University Budapest

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About Eötvös Loránd University Established in 1635. It is the oldest university in Hungary. Number of students: 28 661 (15. Oct. 2013) It is the largest university in Hungary.

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Who was Eötvös Loránd? Loránd Eötvös (1848 — 1919): Hungarian physicist. He is remembered largely for his work on gravitation and surface tension, and the invention of the torsion pendulum. The Eötvös pendulum was essential to prove the equivalence of the inertial mass and the gravitational mass. This result was then later used by Albert Einstein as an experimental support for his general theory of relativity.

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Structure of the university 8 faculties: Faculty of Education and Psychology Faculty of Humanities Faculty of Informatics Faculty of Law and Political Sciences Faculty of Primary and Pre-school Education Faculty of Science (2 nd largest faculty) Faculty of Social Sciences Faculty of Special Education

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Faculty buildings

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University Library founded in 1561

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Botanical Garden established in 1771

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Nobel Prize laureates Fülöp Lénárd 1905 Physics György Békésy 1961 Medicine Albert Szentgyörgyi 1937 Medicine János Harsányi 1994 Economics György Hevesy 1943 Chemistry

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Mathematical tradition Frigyes Riesz (1880-1956) functional analysis Lipót Fejér (1880-1959) Fourier-analysis John von Neumann (1903-1957) mathematical foundations of quantum mechanics Pál Turán (1910-1976) number theory and many others… Pál Erdős (1913-1996) number theory, combinatorics…

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Mathematical tradition 2 László Lovász combinatorics Wolf prize, Kyoto prize Endre Szemerédi combinatorics Abel prize and many others… László Babai combinatorics Gödel prize Miklós Laczkovich analysis Ostrowski prize

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Mathematical tradition 3 IMO hall of fame (among the top 100) Studied at Eötvös Univ.Teaches at Eötvös Univ. József Pelikányesyes László Lovászyesyes Tamás Terpaiyesyes Béla András Ráczyes Imre Ruzsayes Gyula Lakosyesyes Géza Kósyesyes István Tomonyes Zoltán Gyenesyes Béla Bollobásyes

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Mathematical tradition 4 Participation at the International Mathematics Competition for University Students YearRanking Number of participating universities 2005271 2006443 2007160 2008143 2009465 2010790 2011377 2012768 2013572 2014273

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Mathematical tradition 5 Winners of major international prizes in 2012: Éva Tardos- Gödel prize (for outstanding papers in theoretical computer science) László Lovász, Balázs Szegedy- Fulkerson prize (for outstanding papers in discrete mathematics ) András Máthé- Banach prize (for a doctoral dissertation in mathematics) Endre Szemerédi-Abel prize (for outstanding scientific work in mathematics) Katalin Marton- Shannon award (for consistent and profound contributions to information theory)

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Departments, research areas Department of Algebra and Number Theory Department of Analysis Department of Applied Analysis and Computational Mathematics Department of Computer Science Department of Geometry Department of Operations Research Department of Probability Theory and Statistics Mathematics Teaching and Education Centre

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Master’s program in mathematics Usually 2 years 100 credits (courses) + 20 credits (thesis) Courses in: Algebra Analysis Discrete mathematics Geometry Number theory Operations research Stochastics On request, all courses are offered (also) in English.

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Structure of the program 1.Basic courses (20 credits) 2.Core courses (30 credits in 4 subject areas) 3.Special courses (44 credits in 3 subject areas) 4.Free courses (6 credits) 5.Thesis (20 credits) Courses are offered in the form of lectures and problem sessions, sometimes as reading courses.

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Titles of some recent MSc diploma works 1.Ranks on the Baire class α functions (real analysis) 2.Galois representations (algebra) 3.Symmetric submodular functions and their applications (combinatorial optimization) 4.Integral Geometric Formulae (geometry) 5.Classification of High-Dimensional Simply-Connected Manifolds (differential topology) 6.Elliptic curves (algebraic number theory) 7.Model Theoretic Spectrum Functions and Algebraic Logic (algebraic logic) 8.Integer Carathéodory property for the bases of a matroid (combinatorics) 9.Fractional order Sobolev spaces (functional analysis) 10.Routing Problems (operations research)

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Summer school in discrete mathematics June 2014 Participants from: Brasil, Germany, Hungary, Japan, Korea, Netherlands, Poland, Spain, Switzerland, Turkey, UK, USA

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Application deadline: October 31 to begin in February May 31 to begin in September

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Next: The grid with applications Key ingredients: Gábor Szegő (1895 – 1985) Regularly planted forest Miklós Laczkovich György Pólya (1887 – 1985)

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