PhD in Mathematics & Data Science in Europe

Delivered jointly across three institutions, this doctoral program addresses informatics as a rapidly evolving field grounded in computational science and mathematical modelling, with a focus on artificial intelligence, data analysis, computational intelligence, and signal and image processing. It is aimed at individuals pursuing interdisciplinary research and innovative solutions that drive technological progress.

Core coursework covers the architectures of neural networks, methods for data analysis and visualization, heuristic algorithms, language technologies and information retrieval, mathematical models in informatics, algorithms for parallel and distributed computing along with their complexity analysis, and quantum algorithms. Alongside these subject-specific modules, students build core research competencies through a dedicated set of skills modules, including academic and technical research writing, design thinking in research, digital tools for research writing and publication, research data management, research ethics, grant management for research projects, science communication for public audiences, and systematic literature review methods.

Applicants must hold a master's degree or an equivalent higher education qualification in a field such as informatics, artificial intelligence, mathematics, informatics engineering, physics, mechanical engineering, or electrical and electronic engineering.

Admission is based on a weighted competition score combining the weighted grade point average from the applicant's diploma supplement (35%), their research experience (30%), and a motivation interview (35%). Applicants must reach a minimum competitive score of 8.0 to be admitted. As part of the broader application process, applicants are generally expected to submit materials such as a completed application specifying their preferred research topic, a CV, two letters of recommendation from researchers in the relevant field, evidence of prior scientific publications or an original research paper where publications are not available, a copy of a valid passport or identity document, and proof of payment of the application fee, and all applicants are required to attend an interview with the doctoral admissions committee.

This doctoral program typically spans six semesters (full-time), with an ideal completion time of up to four years. The first three semesters focus on coursework, totaling 40 ECTS: 25 ECTS in mandatory seminars and 15 ECTS in elective subjects. Mandatory courses include Research Seminar I, II, and III, where students explore research methodologies, define their dissertation topics, and develop publication-ready work. Electives cover a wide range of advanced topics such as Machine Learning, Geospatial Analysis, Genetic Programming, Experimental Design, and Business Decision Making with Data Science. After completing coursework, students dedicate their final semesters to the doctoral thesis (140 ECTS).

To apply for the Doctoral Program, candidates must meet one of the legal requirements: hold a Master’s degree or a Bachelor's degree with at least 240 ECTS and a minimum final grade of 16/20, or hold a degree with an academic or scientific curriculum deemed suitable by the Academic Board. Proficiency in English (spoken and written) is also required. The application must include an online form, CV, degree certificates (optional), a letter of intent, and optionally, two recommendation letters. If applying for a scholarship, a research proposal and supervisor's acceptance letter are required. Admission is based on academic grades, curriculum analysis, and possibly an interview.

This PhD program offers advanced research training across several disciplines, including engineering sciences, ICT, mathematical sciences, and natural sciences. It combines theoretical and methodological coursework (minimum 30 ECTS) with supervised original research leading to a doctoral dissertation, trial lecture, and public defense. Specializations include civil and structural engineering, mechatronics, renewable energy, AI, mobile communications, mathematics, mathematics education, molecular biology, and ecology. Each specialization provides tailored courses to support the doctoral work, with research projects often conducted in collaboration with public and private institutions. The program is designed to develop deep expertise and contribute to scientific advancement.

To be eligible for this PhD program, applicants must hold a master’s degree in a relevant subject area from a recognized institution. Admission normally requires a minimum average grade of C or equivalent in the bachelor's degree, and a B or higher for both the master's coursework and thesis. If an applicant does not meet the grade criteria, the hosting research group must justify the candidate’s potential to complete the program, possibly with additional admission conditions. All applicants must demonstrate English proficiency through recognized tests such as TOEFL (minimum 92 iBT or 600 PBT) or IELTS (minimum 6.5), unless exempt under national guidelines.

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.

Delivered in collaboration with two European partner universities, this doctoral program prepares researchers to conduct original studies and advance the field of mathematics, covering differential equations, financial mathematics, and biomedical systems modelling. Students can select their own research direction based on their individual interests and goals.

Core coursework covers algebraic structures and cryptography, data science and reliability theory with statistical modeling, differential equations, dynamical systems and numerical methods, financial mathematics and operations research, mathematical modeling and artificial intelligence applied to biomedical systems, and mathematical operator theory and its applications. Alongside these subject-specific modules, students build core research competencies through a dedicated set of skills modules, including academic and technical research writing, design thinking in research, digital tools for research writing and publication, research data management, research ethics, grant management for research projects, science communication for public audiences, and systematic literature review methods.

Applicants must hold a master's degree or an equivalent higher education qualification, and must also hold a bachelor's degree and diploma supplement. Applicants must submit a research proposal on their selected topic as part of the application.

Admission is based on a weighted competition score combining the weighted grade point average from the applicant's bachelor's diploma supplement (10%) and master's diploma supplement (25%), together accounting for 35% of the score, along with the applicant's research experience (30%) and a motivation interview (35%). Applicants must reach a minimum competitive score of 7.0 to be admitted. As part of the broader application process, applicants are generally expected to submit materials such as a completed application specifying their preferred research topic, a CV, two letters of recommendation from researchers in the relevant field, evidence of prior scientific publications or an original research paper where publications are not available, a copy of a valid passport or identity document, and proof of payment of the application fee, and all applicants are required to attend an interview with the doctoral admissions committee.