Ph.D. in Discrete Mathematics

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.

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.