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Budapest–ELTE–Mathematics

2018

Budapest, the city of

spas and thermal baths

Széchenyi Thermal Bath

Palatinus Bath

Gellért Thermal Bath

theatres and concert halls

National Theatre and Palace of Arts

Opera House Liszt Academy

bridges

Erzsébet bridge Liberty bridge

Chain bridge

sports events

2017 World Aquatics Championship

Budapest Marathon

Fencing Grand Prix

Eötvös Loránd

University

Semmelweis University

Budapest University of

Technology and

Economics

Corvinus University

and universities

Universities in Budapest22 institutions in higher education

Approx. 150.000 students

• 14 state institutions

• 4 maintained by churches

• 4 privately funded

Eötvös Loránd University

Established: 1635

Number of students: approx. 28.000

Profile: research university

Semmelweis University

Established: 1769


Profile: medical university

Budapest University of Technology

and Economics

Established: 1782


Profile: instutute of technology

Corvinus University

Established: 1920


Profile: business school

About Eötvös Loránd University

(ELTE)

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 (2nd largest faculty)

Faculty of Social Sciences

Faculty of Special Education

Established in 1635.


Number of academics: approx. 1600

It is the largest

university in Hungary.

It is the oldest university in Hungary.

Faculty

buildings

Faculty buildings

University Library (1561) Botanical Garden (1771)

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 generaltheory of relativity.

Between 1894 and 1895 he was the

minister of education in Hungary. During

the seven months he served as a minister

he initiated the establishment of more

than 400 new schools.

Nobel prize winners

Fülöp

Lénárd

1905

Physics

Albert

Szentgyörgyi

1937

Medicine

György Hevesy

1943

Chemistry

György

Békésy

1961

Medicine

János

Harsányi

1994

Economics

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,

graph theory

and many others…

Pál Erdős

(1913-1996)number theory, combinatorics…

Mathematics of the past 50 years

László Lovász

combinatoricsWolf prize, Kyoto prize, Neumann prize, Pólya prize, Fulkerson prize;

president of theHungarian Academy of

Sciences,former president of the

IMU

Endre Szemerédi

combinatoricsAbel prize, Pólya prize,

Steel prize, Shock prize;member of the

Hungarian Academy ofSciences

László Babai

combinatoricsGödel prize, Knuth

prize, Dijkstra prize,member of the

Hungarian Academyof Sciences

Miklós Laczkovich

analysisOstrowski prize, Széchenyi prize,member of the

Hungarian Academy ofSciences

and many others…

Programs in mathematics at ELTE

1) BSc program in mathematics (3 years) with subprograms in• pure mathematics• applied mathematics

170 credits for course work and

10 credits for thesis (total 180 credits)

Courses (with mandatory credit numbers for the pure mathematics program):

• algebra and number theory (31)

• analysis (43)

• combinatorics (12)

• classical and differential geometry (23)

• topology (11)

• set theory and mathematical logic (8)

• operations research (10)

• probability theory and statistics (15)

• ordinary and partial differential equations (10)

• computer science, programming (10)

Offered in Hungarian only.


2) MSc program in pure mathematics (2 years)

94 credits for course work,

6 credits for directed research and

20 credits for thesis (total 120 credits).

Courses in:

• algebra

• number theory

• analysis

• discrete mathematics

• geometry and topology

• operations research

• stochastics

Total number of offered courses is over 100.

The choice of courses is relatively free with some restrictions ensuring versatility.

Full program in Hungarian and in English.

Titles of some recent MSc diploma works

1. Galois representations (algebra)

2. Elliptic curves (algebraic number theory)

3. Model theoretic spectrum functions and algebraic logic (algebraiclogic)

4. Ranks on the Baire class α functions (real analysis)

5. Fractional order Sobolev spaces (functional analysis)

6. Integral geometric formulae (geometry)

7. Covering questions in discrete geometry (discrete geometry)

8. Hypersurface singularities and their invariants (differential topology, algebraic geometry)

9. Integer Carathéodory property for the bases of a matroid

(combinatorics)

10. Symmetric submodular functions and their applications

(combinatorial optimization)

11. Routing problems (operations research)

12. Departure processes of queueing systems (stochastics)


3) MSc program in applied mathematics (2 years)

Structure similar to the pure math program:

120 credits: courses + research projects + diploma work

5 specializations: general;

analysis;

computer science;

operations research;

stochatstics

4) BSc + MSc program in teaching of mathematics

(4.5 - 5.5 years)


Offered in Hungarian only.

Program for future teachers in elementary schools and highschools.

The first three years joint for the two types of programs.

Courses in mathematics and in didactics + practice teaching.


5) PhD program in:

• pure mathematics

• applied mathematics

• teaching of mathematics (4 years)

Mandatory course work but the program is research oriented: credits for

• courses

• directed studies

• research papers, conference talks

• teaching

Total number of credits: 240.

The program ends with writing and defending a thesis.

Mandatory comprehensive exam after 2 years.

Report about research progress every year.


Titles of some recent PhD works

1. Numerical solution of fractional partial differential equations(numerical analysis)

2. Posets and extremal set systems (combinatorics)

3. Rank functions and Polish groups in descriptive set theory (real analysis)

4. The chip-firing game (graph theory)

5. Dynamic models of epidemic spread on adaptive networks (differential equations)

6. Decomposition theory of forms(functional analysis)

7. Hilbert schemes of points on some classes of surface singularities(algebraic geometry)

8. Cayley graphs(group theory)

9. Multivariate threshold models with applications to wind speed data(stochastics)

10. On the intersection of geodesic balls (differential geometry)

11. Pseudorandom sequences and lattices(number theory)

Special programs for students

1) Competitions• The Miklós Schweitzer competition takes place each October:

it is a take home exam for 10 days with 10 to 12 research level

problems (the competition is considered by many to be one of

the most difficult mathematics competitions in the world)

2) Research projects• possibility to do research on selected topics with the guidance of faculty

members or external researchers; the resulting papers are presented at

conferences at a faculty or at national level

• award winning papers very often end up as research papers in scientific

journals

• International Mathematical Competition in

Blagoevgrad, Bulgaria, organized by University

College London: IMO style competition for

individuals and teams (the team of ELTE is usually

among the top 5 university teams)

Special programs for students3) International summer schools organized each year

http://www.math.elte.hu/summerschool

Further information

Website of the Institute of Mathematics:

http://www.math.elte.hu/en

Enjoy your stay in Budapest!

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