Ph.D. in Discrete Mathematics


Program Description


Pavol Jozef Safarik University Faculty of Science

Ph.D. program description

The Ph.D. program Discrete Mathematics is a research-based study program with an emphasis on two areas. Graph theory direction concentrates mainly on chromatic graph theory, the structure of graphs, topological graph theory, cycles in graphs, graph labelings, graph algorithms and applications of graph theory. The algebraic branch deals with universal algebras, lattices, and ordered structures. Students work on the most recent research topics and tackle difficult open problems. They have a possibility to participate actively in international collaboration, present their results at international conferences and publish in leading scientific journals. Institute of Mathematics that implements this Ph.D. program has a long tradition in research and rich international collaboration. KOSDIM - the discrete mathematics group is recognized as one of the top European research teams in the area.

Admission requirements

All applicants to a Doctor of Philosophy (Ph.D.) program at the Faculty of Science must meet the admission requirements for entry. We welcome graduates in the field of Mathematics, Computer Science, but also in related scientific disciplines. The applicants should support their interest with relevant background in Mathematics, which they acquired either during the previous study or in a professional activity. Personal contact with the potential supervisor by email or phone is advisable to consult the focus of the thesis.

The focus of the thesis can be modified during the study to more accurately reflect the content of the thesis. The number of new doctoral positions is limited to 2-4 places per year.

The applicants must provide the following materials to be considered for the Ph.D. graduate program:

  • Motivation letter
  • Complete and printed online application form
  • Transcripts of records of the Master's studies
  • Certified copy of a Master's Diploma - notary verified
  • CV including a list of publications and unpublished work
  • Documents regarding professional experience (if applicable)
  • Application fee (scanned copy of the bank transfer receipt)
  • Letter of recommendation (optional)
  • Ph.D. project proposal (max. 5 pages, A4)

All qualified applicants will be invited to the admission committee hearing in June. The applicants can ask for a Skype call instead. During the approximately 30-minute meeting, the applicant introduces himself/herself (education, experience, results) and presents his/her preliminary research plan based on the abstract of the Ph.D. theme published in the admission call and his/her knowledge of the research area.

Our selection criteria:

  1. Personal skills, knowledge, motivation, and ability to work on the topic. (40%)
  2. Study results and other activities such as participation in science fairs, scientific competitions, publications, conferences. (40%)
  3. The Institute of Mathematics priorities such as ongoing and planned projects, number of Ph.D. students of the selected supervisor, etc. (20%)

Admission Fees and Funding

Application forms need to be submitted either by post or online.  The application fee for doctoral study programs is 50 EUR (by post) or 30 EUR (online).

The doctoral study is financially supported by providing funding (a stipend) for students. Each year the University allocates a certain number of Ph.D. positions for each doctoral study program. These positions are eligible for funding of ca. 10,000 EUR annually per student. More applicants for the Ph.D. study than this number of funded positions can be admitted only as self-payers. The self-paid study is subject to a tuition fee of 5,000 EUR per academic year (2,500 EUR per semester) and no state funding is applicable. The study is taught in Slovak or English with no impact on tuition fees at the Faculty of Science.

We also welcome students within mobility exchange schemes such as Erasmus+, Ceepus, SAIA, Cotutelle, and others following the conditions of the schemes and the candidates should contact the International Relations and Scientific Research Office before sending an application.

How is the study organized?

The standard duration of the study is four years. Normally, submissions are due by June and the study commences in September.

The doctoral degree is based on coursework and research that leads to a dissertation. The coursework includes compulsory and selective compulsory courses dedicated to expanding the student’s knowledge in various disciplines of discrete mathematics with a special emphasis on the dissertation subject. In the research part, the students work closely with their Ph.D. supervisor within a scientific seminar where they discuss the scientific issues with other senior researchers and peer colleagues. Further, the research involves the preparation of publications, research projects, citations, and others.

The successful finish of the doctoral study expects acquiring skills and scientific expertise to publish the achieved results in international peer-reviewed research journals. Students will learn these skills in the process of supervision and communication with other colleagues at the Institute. Students meet with their supervisors on a regular basis and they are required to report their progress annually.

Both components of the study start since the first year of study and, typically, the study part is finished within the second year. By the end of the second year of the program, the student has to pass a written and oral state examination demonstrating the ability to independently conduct research. Writing the dissertation expects to detail the results of a substantial and original research project. The study ends with the public defense of the dissertation thesis.

Ph.D. graduate profile

The graduate has a wide range of theoretical and empirical knowledge of discrete mathematics, capable to propose discrete mathematical models for various scientific and practical tasks and find their solutions (optimal or approximate) applying developed programming skills.

The graduate knows the principles of scientific work and research, including publishing in international scientific journals and presentation of scientific results. He or she can formulate research questions and solve them creatively with appropriate methodological procedures. The graduate has an excellent overview of the contemporary state-of-the-art.

Graduates of the Discrete Mathematics Ph.D. program are highly relevant on the job market especially for institutions focusing on research and development, universities, governmental institutions and business involving data analysis, design and management of grids and networks, software development, finance, and insurance tasks.

Career Prospects

Ph.D. graduates in Discrete Mathematics have excellent career opportunities in academia, research, software engineering, economics, government, and other kinds of public and private sector positions. Our graduates work in high-level academic and corporate positions in companies such as LaBRI Bordeaux, Google Zurich, Gazprom Marketing & Trading London, Privatbank Bratislava, IBM Košice.

Last updated Mar 2020

About the School

Founded in 1963, the Faculty of Science, has educated over 6 000 graduates of both, joint and single degree study. Currently, over 350 Bachelor’s, Masters’s, and Doctoral students graduate each year i ... Read More

Founded in 1963, the Faculty of Science, has educated over 6 000 graduates of both, joint and single degree study. Currently, over 350 Bachelor’s, Masters’s, and Doctoral students graduate each year in disciplines that impact lives today and will shape our future. Read less