Jagiellonian University

What you'll study

The PhD in Mathematics is primarily a research degree centred on producing an original doctoral thesis under the supervision of a faculty member. Candidates normally choose a research area within the broad range of mathematics represented at the university, including but not limited to algebra, analysis, geometry and topology, probability and mathematical statistics, numerical analysis and scientific computing, mathematical physics, and optimisation and control.

Programme components typically include:

• Research project: The main element is an independent research project leading to a doctoral dissertation. Projects are developed with an academic supervisor and may be carried out individually or as part of a research group.
• Advanced seminars: Attendance and participation in specialised seminars and reading groups in the chosen field to deepen theoretical knowledge and stay current with literature.
• Coursework and examinations: Some programmes require a limited set of advanced courses or qualifying examinations to ensure breadth and readiness for research.
• Teaching and training: Opportunities to gain teaching experience by assisting with undergraduate or graduate courses, and professional development courses on research methods, academic writing and presentation skills.
• Conferences and publications: Encouragement and support to present work at conferences and publish in peer-reviewed journals as part of doctoral training.

Doctoral candidates usually follow a flexible timetable negotiated with their supervisor, with regular progress reviews. The degree concludes with submission and public defence of the doctoral thesis in accordance with university regulations.

Entry requirements

Applicants should hold a Master’s degree (or recognised equivalent) in mathematics or a closely related discipline, demonstrating strong academic performance in advanced mathematical topics. Sufficient preparation in the chosen research area is expected.

• Research proposal: A concise research statement or proposal outlining intended research topics and questions helps match applicants with potential supervisors.
• Supervisor support: Identification of or contact with a prospective supervisor in the relevant research area is strongly recommended and often necessary for admission.
• Academic references: Two or more academic references attesting to the applicant’s research ability and preparedness for doctoral study.
• Entrance evaluation: Admission typically involves assessment of academic records, the research proposal, references and an interview or discussion with potential supervisors. Evidence of research aptitude, such as publications or a Master’s thesis, is advantageous.
• Language requirements: Instruction and supervision are available in Polish and in English in many research groups; applicants should demonstrate proficiency in the language of supervision. International applicants are advised to confirm language arrangements with the faculty.

Career prospects

Graduates of the PhD in Mathematics pursue a range of careers where deep analytical and problem-solving skills are valued. Typical paths include:

• Academic research and teaching: University and research institute positions, postdoctoral fellowships, and lecturing roles leading to habilitation and professorship.
• Industry research and development: Roles in engineering, technology, telecommunications, software development and advanced scientific computing.
• Data science and quantitative analytics: Positions in finance, insurance, consulting and technology firms requiring expertise in modelling, statistics and algorithm design.
• Cryptography and security: Work in cybersecurity, cryptographic protocol design and related applied mathematics areas.
• Public sector and policy: Research roles in government agencies, statistical offices and organisations that require quantitative modelling and evidence-based analysis.

Why study at Jagiellonian University

Jagiellonian University, based in Kraków, has a long tradition of mathematical scholarship and an active contemporary research environment. The Faculty of Mathematics and Computer Science hosts several specialised research groups and an Institute of Mathematics that organises seminars, colloquia and international lectures, providing a lively intellectual atmosphere for doctoral study.

Doctoral candidates benefit from close mentoring by experienced researchers, access to doctoral schools and structured training modules, and opportunities to collaborate on interdisciplinary projects across physics, computer science and applied disciplines. The university maintains national and international research collaborations, facilitating conference participation and exchange.

For candidates seeking a balance of historical academic setting and modern research infrastructure, Jagiellonian University offers a supportive environment to develop as an independent researcher and to prepare for careers in academia, industry and the public sector.