Master’s program in mathematics Eötvös Loránd University Budapest

About Eötvös Loránd University Established in It is the oldest university in Hungary. Number of students: (2015) It is the largest university in Hungary.

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 used to prove the equivalence of the inertial mass and the gravitational mass which was then later used by Albert Einstein as an experimental support for his general theory of relativity.

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

Faculty buildings

University Library (1561) Botanical Garden (1771)

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

Mathematical tradition Frigyes Riesz ( ) functional analysis Lipót Fejér ( ) Fourier-analysis John von Neumann ( ) mathematical foundations of quantum mechanics Pál Turán ( ) number theory and many others… Pál Erdős ( ) number theory, combinatorics…

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

Mathematical tradition 3 IMO hall of fame (among the top 100) Studied at Eötvös Univ.Teaches at Eötvös Univ. József Pelikán yesyes László Lovász yesyes Tamás Terpai yesyes Béla András Rácz yes Imre Ruzsa yes Gyula Lakos yesyes Géza Kós yesyes István Tomon yes Zoltán Gyenes yes Béla Bollobás yes

Mathematical tradition 4 Participation at the International Mathematics Competition for University Students YearRanking Number of participating universities

Mathematical tradition 5 Recent winners of major international prizes 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)

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

Research groups in applied mathematics EGRES – Egerváry Research Group on Combinatorial Optimization Geometric and Algebraic Combinatorics Research Group Numerical Analysis and Large Networks Research Group ELTECRYPT – Research Group in Cryptography LEMON – Library of Efficient Models and Optimization in Networks PIT – Protein Information Technology Group LNRG – Large Networks Research Group

Master’s program in mathematics (2 years) 100 credits (courses) + 20 credits (thesis) On request, all courses are offered (also) in English. Courses are offered in the form of lectures and problem sessions, sometimes as reading courses. Algebra Analysis Discrete mathematics Geometry Number theory Operations research Stochastics Courses in:

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)

Summer schools in mathematics

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

Péter Komjáth: Ultrafilters