Doctoral Programme Mathematics and Physics

The main objective of the study programme in Mathematics and Physics is to produce highly qualified researchers and experts capable of conducting independent research and development in the fields of physics, astrophysics, nuclear physics, meteorology, mathematics, and physics and matematics education, at a level comparable to and competitive with current top-quality research pursued in the most advanced parts of the world. In this regard, independent research towards the doctoral thesis, which is the main component of the doctoral study programme, develops in-depth knowledge in the area of immediate specialization. This is supplemented by the organized part of the study programme, which develops the broader knowledge that is indispensable for any young researcher to be able to efficiently respond to rapid development and change in modern science, or for them to participate in larger interdisciplinary research teams.

• Capacity for abstraction and problem analysis
• Gathering, critical evaluation and synthesis of data, measurements and solutions
• Identification of data needed for obtaining new knowledge
• Forming new knowledge on the basis of existing theories and available data
• Use of knowledge in practice (especially in modern technologies)
• Capacity for interdisciplinary integration of scientific knowledge
• Capacity for both autonomous research and development, and for working in an (international) group
• Communicating scientific knowledge to the general public
• Ability to use modern research methods and procedures
• Ability to critically evaluate and present one’s own results
• Capacity for further independent education, research and following of the literature

• In-depth understanding of the physical laws of nature
• Combining the basic laws of nature and observable properties of the world
• Ability to creatively identify physical problems and analyse them
• Capacity for the mathematical formulation of physical problems
• Deduction of the physical basis of practical problems
• Ability to model problems
• Advanced physical experimental skills
• Critical evaluation of the results of measurements and their use in the construction of models
• Understanding the principles of operation of technical devices on the basis of fundamental laws
• Presentation of physical methods and results adapted to the target public
• Ability to convey knowledge of physics
• Thorough understanding of the results of research in the field of interest
• Independence in research
• Capacity for abstraction of practical problems
• Capacity for critical and independent work and for consultation in the field of physics education.

Candidates can enrol in the doctoral study programme if they have successfully completed:

• A second-cycle (i.e., masters) study programme.
• A university-level degree programme accredited before 11.6.2004.
• A study programme for specialisation following completion of a profession-oriented higher education programme. In this case, the relevant doctoral studies board (either mathematics or physics) will determine any additional study requirements that need to be fulfilled. These requirements may be tailored to the individual, or they may involve between 30 and 60 ECTS points of additional courses to study.
• A profession-oriented study programme that is either regulated by directives of the European Union or is a masters programme, and which carries at least 300 ECTS credit points.
• A Masters level study programme or a study programme for specialization, having previously completed another University-level degree programme. In accordance with the law, such candidates may request up to 60 ECTS credit points in recognition of their previous education.

Enrolment in the doctoral study programme in Mathematics and Physics is open also to graduates of foreign universities. In accordance with the Statutes of the University of Ljubljana, the equivalence of previous education acquired abroad is established as part of the process of recognition of foreign education for the continuation of education at University of Ljubljana.

In the case of a size-limited enrolment process, the selection of the candidates will be based on:

• The average mark in previous studies (15%)
• The mark for the diploma or masters work (5%)
• The score achieved in a written selection exam (80%) in physics or mathematics. The score from this exam can be partially (up to 40%) be replaced by the candidate’s research and professional achievements in the area of the study programme.

Note: By the end of the application deadline, the candidate must have an agreement with a higher education teacher or researcher to act as mentor / co-mentor for their doctoral studies. The written consent of the mentor / co-mentor must then be submitted at the time of enrolment, together with a short high-level outline of the planned research topic of the doctorate.

A student can be awarded credit for knowledge acquired in different forms of previous education that corresponds in content to courses in the study programme. Decisions concerning the recognition of such knowledge are made by the Department of Physics and Department of Mathematics Study Boards at FMF, on the basis of the student's written application with attached testimonials and other documents confirming successful acquisition of such knowledge and its content.

In awarding credit for an individual course, the Study Board will use the following criteria:

• comparability of the scope of previous education with the scope of the course for which credit is awarded,
• correspondence of the content of previous education to the content of the course for which credit is awarded.

In cases in which the Study Board determines that the acquired knowledge can be recognised, it is accredited with the number of ECTS points attached to the corresponding courses.

The assessment methods follow the Statutes of the University of Ljubljana, and are listed in the curricula.

Subprogramme Physics:

For enrolment in the second year of study, students must make a successful presentation of the theme of doctoral dissertation and they must collect a total of at least 48 ECTS from organized forms of study. For enrolment into the third year, the student must collect at least 90 ECTS, of which 60 are required to be from organized forms of study (the compulsory course for the selected module, elective courses, courses from external study programmes, international summer schools, etcetera). In addition, prior to enrolment in the third year of study, the opinion of Commission for monitoring the doctoral student (KSDŠ) that the dissertation topic is suitable for a doctoral dissertation must be confirmed by the Senate of the Faculty (UL FMF). For enrolment into the fourth year of study, the student must meet all study requirements for the first three years, and obtain approval of the subject of the doctoral dissertation from the Senate of UL.

Subprogramme Mathematics:

For enrolment in the second year of study, students must make a successful presentation of the theme of doctoral dissertation and they must collect a total of at least 48 ECTS from organized forms of study. For enrolment into the third year, the student must collect at least 90 ECTS, of which 48 are required to be from organized forms of study (the compulsory course for the selected module, elective courses, courses from external study programmes, international summer schools, etcetera). In addition, prior to enrolment in the third year of study, the opinion of Commission for monitoring the doctoral student (KSDŠ) that the dissertation topic is suitable for a doctoral dissertation must be confirmed by the Senate of the Faculty (UL FMF). For enrolment into the fourth year of study, the student must meet all study requirements for the first three years, and obtain approval of the subject of the doctoral dissertation from the Senate of UL.

Transfer to the doctoral (third-cycle) programme in Mathematics and Physics is possible:

• From other doctoral (third-cycle) programmes of UL. The candidate must fulfil the requirements for enrolment in the doctoral (third-cycle) programme in Mathematics and Physics. On the basis of credit points awarded for exams taken in the previous study programme, the FMF Study Board may require a candidate to take bridging exams (corresponding to up to 60 ECTS points) and decide in which year of study he/she may enrol.
• Under the same conditions as in the previous paragraph, transfer is possible also from comparable programmes at other universities if the candidate meets the requirements for enrolment in the doctoral (third-cycle) programme in Mathematics and Physics.

The requirements for completion of study and acquisition of the title Doctor of Science are that the candidate successfully meets all study requirements laid down in the programme and successfully defends the doctoral dissertation, amounting to a total of 240 ECTS. That is the student must fulfil all requirements for organised study (amounting to 60 ECTS), as well as for individual research work including the preparation and defence of the doctoral dissertation (amounting to 180 ECTS). The candidate must also publish or have accepted for publication at least one scientific article from the field of the dissertation in one of the journals from group I - III, as defined in the FMF Interpretation of the Criteria for Election of University Teachers, Researchers and Research Associates, as approved at the UL Senate on 22.11.2016. If it is not possible for the candidate to be the first author of the publication, the mentor should provide written confirmation of the significance of the candidate’s contribution. The research article must be published or accepted for publication prior to the doctoral dissertation being submitted for evaluation. For the student to complete the doctorate, the dissertation and its defence must receive positive evaluations from the examining committee.

International cooperation:

FMF participates in the following professional organizations:

• AAPT (American Association of Physics Teachers)
• AGU (American Geophysical Union)
• AMPERE (Association for Microwave Power in Europe for Research and Education)
• AMS (American Meteorological Society)
• AMS (The American Mathematical Society)
• APS (American Physical Society)
• Biophysical Society
• EAS (European Astronomical Society)
• ECMI (The European Consortium for Mathematics in Industry)
• EMS (The European Mathematical Society)
• ENEN (European Nuclear Education Network)
• EPS (European physical society)
• FuseNet Association
• HOPE (Horizons in Physics Education)
• ILCS (The International Liquid Crystal Society)
• IOP (Institute of Physics)
• MAA (The Mathematical Association of America)
• SIAM (The Society for Industrial and Applied Mathematics)

FMF collaborates with numerous academic and research institutions. For example:

• CERN (Conseil Européen pour la Recherche Nucléaire)
• ETH (Eidgenössische Technische Hochschule Zürich)
• LANL (Los Alamos National Laboratory)
• Ludwig-Maximilians-Universität München
• MIT (Massachusetts Institute of Technology)
• University of Oxford
• Stanford University
• University of Cambridge
• University of California
• Weizmann institute, Izrael

FMF international cooperation: https://www.fmf.uni-lj.si/en/research/

The mobility of students and teachers is supported by the Erasmus programme:

• KLASIUS-SRV: Education leading to doctorate of science (third Bologna cycle)/Doctorate of science (third Bologna cycle)
• ISCED: Teacher training and education science, Physical sciences, Mathematics and statistics
• KLASIUS-P: Science (broad programmes)
• KLASIUS-P-16: Physics, Mathematics
• Frascati: Natural Sciences
• SOK level: 10
• EOK level: 8
• EOVK level: Third cycle

• Physics
• Physics Education
• Meteorology
• Nuclear Engineering

Organized forms of study (60 ECTS)

• courses (30 ECTS): (compulsory module course, selective courses)
• other organized activities (30 ECTS): (individual study, preparation and presentation of disposition, compulsory seminar)

Research work, preparation of doctoral dissertation and defence (180 ECTS)

The research work is concluded with a dissertation and its defence, and with the publication of at least one scientific article from the field of the dissertation in one of the journals from groups I - III, as defined in the FMF Interpretation of the Criteria for Election of University Teachers, Researchers and Research Associates. The candidate should be the first author of the publication. If this is not possible, the supervisor should provide a declaration that the contribution of the candidate to the publication is important.

A detailed syllabus

Organized forms of study: 60 ECTS

• Compulsory course of the module: 12 ECTS
• Individual study: 9 ECTS
• Preparation and presentation of dissertation theme: 15 ECTS
• Compulsory seminar: 6 ECTS
• Elective courses: 18 ECTS

Individual research, preparation of doctoral dissertation and defence: 180 ECTS

Total: 240 ECTS

Compulsory courses (group A) with lecturers (regarding modules):

• Selected Topics in Contemporary Physics  (Prof. dr. Boštjan Golob)
• Selected Topics in Physics Education Research  (Prof. dr. Gorazd Planinšič)
• Selected Topics in Atmospheric Sciences  (Assoc. prof. dr. Nedjeljka Žagar)
• Selected Topics in Reactor Physics and Engineering (Prof. dr. Iztok Tiselj)
  

Elective courses (group B) with lecturers:

• Specialized Seminar on Theoretical Physics (Prof. dr. Primož Ziherl)
• Specialized Seminar on Experimental Physics (Prof. dr. Denis Arčon)
• Specialized Seminar on Physics Education Research (Prof. dr. Gorazd Planinšič)
• Specialized Seminar in Atmospheric Sciences (Asst. prof. dr. Gregor Skok)
• Specialized Seminar on Nuclear Physics and Engineering (Asst. prof. dr. Luka Snoj)
• Summer schools and other organized education (3-6 ECTS),
• Courses on other UL doctoral programmes or other universities (up to 12 ECTS).

The choice of courses must be supported by the supervisor and approved by the FMF Department of Physics Study Board.