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.


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), but other topics may be available in agreement with the potential supervisors.

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 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 2023/2024

Tuition and other fees, deadlines

EU/EEA students non-EU/EEA students
Tuition fee/semester 1910 (EUR) 3000 (EUR)
Application fee (first year only)  160 (EUR) 160 (EUR)
Registration fee 60 (EUR) 60 (EUR)
Deadline for application – September intake: 31/05/2023
Different deadlines may be in effect if you apply for 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). Criteria for ranking at the admission procedure 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

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.)

  • Fill the online application form at 
  • Send the saved version of the form also to
  • Send the scanned versions 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
    • (optional:) name of potential advisor who has agreed to supervise the applicant (please, enclose the letter/E-mail reply of the professor)

Entrance examination (for all international applicants)

  • For the entrance examination the applicants should choose a general area (in accordance with the desired area of research during the PhD program) from those listed below and send their choice together with the exam paper.
    • A written test will be sent (via e-mail) to the applicant, covering basic fields of mathematics. In a limited amount of time the applicant will have to send back the solutions. In some cases a skype interview will follow. For details, see the  subjects and conditions of the written entrance exam.
    • The tentative time for writing the exam (spring 2023) is
      • April 8 (Saturday) at 8 a.m. and 3 p.m. Hungarian time (depending on the geometric location) – TO BE CONFIRMED (for SH candidates)
      • second half of June for individual applicants

  • International students from EU countries who wish to apply for state funding may be required to appear for an interview (in person or via Skype) in June or July.

Online Information session about the program

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


Name E-mail
School leader Prof. Tibor Jordán
Program leader in pure mathematics Prof. Tamás Szőnyi
Program leader in appplied mathematics Prof. János Karátson
Program coordinator Prof. István Ágoston
Program administrator Ms. Klaudia Szalay
International coordinator (Faculty of Science) Ms. Éva Nagy (Stipendium Hungaricum) (international affairs)


Appendix 1.

Academic regulations of doctoral studies at ELTE