Study Pure Mathematics in Europe

This master's program provides advanced training in Mathematics, offering two distinct tracks: the Research Option and the Professional Option. The Research Option prepares students for doctoral studies or academic careers through in-depth coursework in pure mathematics, logic, topology, number theory, and advanced algebra. The Professional Option focuses on applying mathematical methods to real-world problems, including courses in financial mathematics, numerical analysis, statistics, and optimization. Students take core and elective courses, choose a minor from areas like statistics or applied mathematics, and complete a master’s thesis. The curriculum includes topics such as algebraic geometry, quantum theory, cryptography, differential equations, and mathematical modeling.

This master's program welcomes applicants holding degrees in Mathematics or related disciplines obtained outside the Flemish Community, with each case evaluated individually. Students must demonstrate English proficiency through TOEFL, IELTS, or Cambridge exams unless they earned a prior degree entirely taught in English in Australia, English-speaking Canada, Ireland, New Zealand, the United Kingdom, or the United States, or possess a Belgian diploma. Applicants must also provide detailed course descriptions and grading information unless exempt through institutional partnerships or degrees from top 200 universities. The final admission decision is made by the Admissions Board based on the provided academic and language credentials.

This PhD program introduces students to high-level research in mathematics, covering most of pure mathematics, including combinatorial optimization, computer science, and statistical and mathematical physics, as well as most of applied mathematics, spanning operations research, numerical analysis, and statistics. It offers three specializations: pure mathematics, applied mathematics, and didactics of mathematics.

The program is strongly research-oriented: students typically begin their own research by the end of the first year, generally producing results published or accepted for publication in internationally recognized journals by the time they finish, and they report on their progress annually. A comprehensive examination is required at the end of the second year, and the program overall combines coursework, research work with annual reporting, the comprehensive examination, at least two accepted research papers, and a thesis. Coursework is drawn from areas including algebra, number theory, real, complex, and functional analysis, differential equations and dynamical systems, partial differential equations, numerical analysis, stochastics, probability and statistics, graph theory, combinatorics, operations research and optimization, geometry, topology, algorithms and cryptography, and set theory and mathematical logic, selected according to each student's research interests. The institute collaborates with research institutes and universities both in and outside Hungary and regularly hosts visiting researchers and instructors from abroad.

Many graduates go on to postdoctoral positions worldwide, and a large number obtain tenure or tenure-track positions at universities or research institutes; others pursue research careers in non-academic settings, including large international research institutions tied to high-tech development or the economic and financial sectors. Typical roles include research mathematician, university professor, system analyst in a financial institution such as a bank, investment firm, or insurance company, roles in high-tech industry, and mathematics teacher.

Applicants must hold a master's degree in mathematics or a related field. Before applying, it is optional but helpful to secure the agreement of a potential advisor willing to supervise the research; a motivation letter describing the applicant's main interests within mathematics and a research plan outlining potential topics are also required. Limited state-funded scholarships are available to eligible EU and non-EU applicants.

An internationally accredited English language examination at a minimum of B2 CEFR level is required, such as a TOEFL iBT score of at least 72 or an IELTS score of at least 5.5; alternatively, applicants may submit an official certificate from their previous institution confirming that their prior degree was completed entirely in English.

Required documents include an application form, the master's degree certificate, a transcript of records, a CV, a research plan, a motivation letter, two letters of recommendation, and a language certificate; a bachelor's degree certificate, a passport copy and photo, and a medical certificate may also be requested. For the entrance exam, applicants select a general subject area, such as algebra and number theory, geometry and topology, discrete mathematics, analysis, applied analysis, probability and statistics, operations research, or set theory and mathematical logic, then complete a timed written test in that area, sometimes followed by an oral interview. Final rankings combine this evaluation with an assessment of the applicant's academic record, including prior achievements, research accomplishments, and the feasibility of their proposed research.