PhD in Mathematics — Program Description

General Data

Title: Doctoral School in Mathematics
Degree: PhD in Mathematics
Faculty: Faculty of Science
Institute: Institute of Mathematics
Language: English
Duration: 8 semesters
ECTS credits: 240

Program Content

Short description

The PhD School in Mathematics of Eötvös Loránd University was founded in 2001. The topics covered by the PhD Program comprise most of pure mathematics, including also computer science, combinatorial optimization, statistical and mathematical physics, as well as most of applied mathematics including the full spectrum of operations research, numerical analysis and statistics.

The program is research oriented: apart from attending specialized courses, our students usually start their research work by the end of the first year. Thus by the end of the program most of them already obtain results which are published (or accepted for publication) in internationally renowned journals. At the end of each year the students report about their research progress. More details on the requirements are given in Structure below.

Strength of the program

The Institute of Mathematics employs close to one hundred full time or part time professors working in various fields of mathematics. The advisors of the PhD School are internationally renowned experts of their fields. We collaborate with several research institutes and universities both in and outside Hungary, and regularly have visitors from abroad doing research or giving courses. Of particular interest is the fact that many researchers in the internationally renowned Hungarian school of combinatorics have started their career at our university and many of them still have position at the Institute of Mathematics. For example the Wolf, Kyoto and Abel Prize winner Prof. László Lovász is a professor at our university. Another recent Abel prize winner, Prof. Endre Szemerédi is also a graduate of our school. But one could also recall the Ostrowski Prize of Prof. Miklós Laczkovich (professor of our university), the Gödel Prize of Prof. László Babai (former professor), the Coxeter Prize of Prof. Balázs Szegedy (a graduate of our university) etc.

Structure

Program requirements

  • course work
  • research work and annual reports
  • comprehensive examination
  • at least two reviewed papers, accepted for publication
  • thesis

For details, see the table of term-by-term requirements or the overview.

Research topics

Each year several research topics are offered (see the current list).

Complex exam

A prerequisite for the complex exam that the candidate should have obtained at least 108 credits (see the table of term-by-term requirements). The deadline for registering for the complex exam is March 31 (for the exam in June).

The complex exam consists of two parts:

  1. Theoretical part. Choose two subject areas (one as a main subject and one as a secondary subject)  – see the topics and requirements of the complex examination. An oral examination has to be taken from the chosen subjects.
  2. Dissertation part. This part consists of an oral presentation about the research of the candidate,
    • showing familiarity with the literature;
    • presenting the obtained research results;
    • explaining plans for future research during the second half of the  studies;
    • sketching a timing for preparing the dissertation.

    Note that an overview about the dissretation part of the exam has to be submitted in writing prior to the exam. This document has to contain information about the studies, publications and plans for writing the dissertation . The doucment has to be signed by the candidate and by the supervisor. The signed document should be forwarded by April 30 in pdf form as an attachment to an E-mail message sent to klaudia.szalay@ttk.elte.hu and adressed to the leader of the doctoral school.

Course requirements

To fulfill the course requirements, courses can be chosen in the following areas, depending on the research interest of the candidate:

  • Algebra
  • Number Theory
  • Real, Complex and Functional Analysis
  • Differential Equations, Dynamical Systems
  • Partial Differential Equations
  • Numerical Analysis
  • Stochastics
  • Probability and Statistics
  • Graph Theory
  • Combinatorics
  • Operations Research, Optimization
  • Geometry
  • Topology
  • Algorithms, Cryptography
  • Set Theory and Mathematical Logic

Admission for the Academic Year 2025/2026

Tuition and other fees, deadlines

EU/EEA students non-EU/EEA students
Tuition fee/semester 1,000,000 HUF (if research is performed at ELTE)

300,000 HUF (if research is perfomed outside ELTE)

 4000 EUR (if research is perfomed at ELTE)

1500 EUR (if research is perfomed outside ELTE)
Application fee (first year only)  9000 HUF 9000 HUF
Deadline for application – September intake: 31/05/2026
Different deadlines may be in effect if you apply for funding.

Funding

Admission requirements, language requirements

A master’s degree in mathematics (or in a related field) is a requirement. A reasonable command of English language is also needed (most international certificates will be accepted). Students applying to the program should choose a research topic (see above) and contact their potential supervisor about the conditions of their admittance. Please, note that a necessary condition to be admitted to the school is to obtain a declaration from the future supervisor about the commitment for joint research. (This holds also for SH applicants.)

The final decision will depend on the ranking after the admission procedure. Criteria for ranking will include:

  • previous university achievements (examinations, comprehensive examinations, qualification of degree)
  • achievements related to previous research work (awards obtained in students’ academic circles, publications in the particular professional area)
  • feasibility of the research program
  • (online) interview

Application procedure

The next few steps should be done by those individual candidates who do not wish to apply for the Stipendium Hungaricum scholarship. (Applicants of the scholarship program should follow the instructions of the Tempus Foundation.)

  • Among other things you will need the scanned version of the following documents:
    • degree certificates (BSc, MSc), together with English (or Hungarian) translation
    • transcript of records (BSc, MSc), together with English (or Hungarian) translation
    • CV, containing data about past professional activities (education, employment history), awards, list of publications etc.
    • motivation letter, describing main lines of interest within mathematics
    • research plan (list one or more potential research topics)
    • 2 letters of recommendation by people qualified to judge the applicants professional potentials and/or achievements
    • copy of the main page of the passport, together with a passport photo
    • copy of the transfer of application fee
    • English language certificate, proving reasonable command of the language
    • name of potential advisor who has agreed to supervise the applicant (please, enclose the letter/E-mail reply of the professor)
  • For further details about the application procedure please visit the following links:
    • contact the admistration of Faulty of Science, handling doctoral issues;
    • application iformation for doctoral students of Faculty of Science (in Hungarian and in English);
    • detailed information about admission for ELTE students at felvi.hu (in Hungarian and in English).

Online Information session about the program

An online information session (“webinar”) was organized on May 6, 2021 at 13.00 CET.

Contact

Name E-mail
School leader Prof. Tibor Jordán tibor.jordan@ttk.elte.hu
Program leader in pure mathematics Prof. Dömötör Pálvölgyi domotor.palvolgyi@ttk.elte.hu
Program leader in appplied mathematics Prof. János Karátson janos.karatson@ttk.elte.hu
International coordinator Prof. István Ágoston istvan.agoston@ttk.elte.hu
Program administrator Ms. Klaudia Szalay klaudia.szalay@ttk.elte.hu
International coordinator (Faculty of Science) Mr. Péter Molnár sh@ttk.elte.hu (Stipendium Hungaricum)
inter@ttk.elte.hu (international affairs)

 

Appendix 1.