budapest elte mathematics 2018 ecmi educational …

Budapest–ELTE–Mathematics 2018

ECMI Educational Committee

Eötvös Loránd University

(science, humanities, law)

Semmelweis University

(medicine)

Budapest University of

Technology and Economics

(engineering, science)

Corvinus University

(economics)

Budapest, the city of universities

Altogether 22 institutions in higher education,

approx. 150.000 students

ELTE – Faculty of ScienceInstitute of Mathematics

• Tradition of the 1960’s, 70’s and 80’s: international students from third

world countries (teaching language: Hungarian)

• Exchange programs of the 1990’s and 2000’s: Tempus, Erasmus,

Ceepus (teaching language: Hungarian or – mostly on an individual

basis – English)

• New mobility programs: Erasmus+, Campus Mundi, Balassi, Makovecz,

Stipendium Hungaricum (teaching language: Hungarian and English –

in organized fashion)

• International students coming on an individual basis to our English

language programs (MSc, PhD)

• Each term we have about 5-10 Erasmus+ exchange students (staying

one or two semesters) and 5-10 new Stipendium Hungaricum students

(staying for 2-3-4 years)

• Erasmus+ exchange programs with over 25 universities from the Czech

Republic, Finnland, France, Germany, Italy, Netherlands, Poland,

Romania, Slovenia, United Kingdom…

International students in

mathematics at ELTE

English programs in mathematics at ELTE

1) 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.

Basic courses for sudents with different

background.

Approximately 25 students (7 international).

Course selection of a student specializing in

algebraic geometry and differential topology

1) Algebraic and differential topology

2) Algebraic curves

3) Algebraic geometry

4) Algebraic number theory

5) Algebraic topology

6) Chapters in differential geometry

7) Chapters in ring theory

8) Cobordisms

9) Commutative algebra

10) Complex manifolds

11) Differential geometry of manifolds

12) Differential topology

13) Fourier integral

14) Functional analysis 2

15) Groups and representations

16) Homology theory

17) Lie algebras

18) Lie groups

19) Riemannian geometry

20) Rings and algebras

21) Symmetric spaces

22) Topological vector spaces and Banach

algebras

Course selection of a student specializing in

discrete mathematics and optimization

1) Algebraic number theory

2) Algorithms 1

3) Combinatorial algorithms 1

4) Combinatorial algorithms 2

5) Commutative algebra

6) Descriptive set theory

7) Design, analysis and implementation

of algorithms and data structures 1

8) Discrete optimization

9) Groups and representations

10) Markov chains in discrete and

continuous time

11) Numerical modelling and numerical

solving methods of ordinary differential

equations 1

12) Partial differential equations

13) Random graphs

14) Rings and algebras

15) Set theory 1

16) Software engineering Lab IV.

17) Special stochastic processes

18) Topics in group theory

19) Topics in ring theory

20) Universal algebra and lattice theory

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)

MSc diploma works of some of our

international students

Baldur Sigurdsson

(Iceland)

2010

The Milnor fiber

of the singularity

f(x,y)+zg(x,y)=0

(at present

postdoc at the

Basque Center for

Applied Mathematics

BCAM in Bilbao)



Daniel Copeland

(USA)

2014

The multivariable

Alexander polynomial

and Thurston norm

(at present

PhD student at

University of California

San Diego)



Peter Dozio

(Switzerland)

2017

A Study of

Forcings

(at present

teacher of

mathematics in

France)



Nicolo Gusmeroli

(Italy)

2017

Machine

scheduling to

minimize

weighted

completion time

(at present

PhD student at

Alpen-Adria

University

Klagenfurt)



Nour El Houda

Seridi

(Algeria)

2017

Numerical

Solutions of Non-

Linear

Conservation

Laws



Hsinyi Lin

(Taiwan)

2017

Application of

machine learning

in manufacturing

industry

(at present PhD

student at

University of

Maryland, College

Park)



Hao Cui

(China)

2018

Learning

Bayesian

Network

Structure from

Data

(at present PhD

student at CEU)

2) MSc program in applied mathematics (2 years)

Structure similar to the pure math program:

120 credits: courses + research projects + diploma work

5 specializations: 1) general;

2) analysis;

3) computer science;

4) operations research;

5) stochatstics

Full program in Hungarian (2-5) and in English (1).


3) PhD program (4 years) in:• pure mathematics

• applied mathematics

• teaching of mathematics

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.

Comprehensive exam after 2 years.

Report about research progress every year.

Full program in Hungarian and in English.

Approximately 45 students (10 international).


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 students

3) International summer schools organized each year

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

Deadline for application:October 31 to begin in February

June 15 to begin in September

Tuition fee:4160 Euro / semester (MSc)

3000 Euro / semester (PhD)

(reduction for EU citizens)

Funding:Stipendium Hungaricum scholarship

for citizens of certain countries

(about 50 applicants each year,

during the last two periods)

Application procedure

Selection process:Written entrance examination

(sent electronically) +

Skype interview if necessary

(May and June)

budapest elte mathematics 2018 ecmi educational …

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