Name of the programme: Mathematical Sciences
Type of programme: Master's, 2nd Bologna cycle
Degree awarded: "magister matematike" equiv. to Master's degree in Mathematics
Duration: 2 years (4 semesters)
Programme structure: 12 courses (72 ECTS), 4 seminars (24 ECTS), Master's Thesis (24 ECTS)
Mode of study: full-time
Language of study: Slovene, English (in English from 2016/17)
For information regarding application, enrolment and other administrative procedures please contact Student Services.
About the programmetop
The master’s programme is intended for those students who want to further their knowledge of mathematics acquired at the undergraduate level.
The courses are designed in such a way that, upon completion of the degree, students have several opportunities to choose from: continuation with doctoral studies, employment in industry or the public sector, or switching to other sciences, well equipped with the knowledge they have gained.
The courses are mostly elective and cover various topical mathematical areas. Of course, detailed understanding of these topics requires a certain knowledge of basic mathematical concepts that students learn at the undergraduate level (see Admission requirements below). Depending on the students' enthusiasm, skills, interests and ambitions/plans for the future, they can be introduced to research mathematics. The latter mainly depends on the help of a supervisor for the master's thesis. There are also some courses offered in applied mathematics which are particularly suitable for students interested in the financial sector and the secondary sector (manufacturing and industry).
Educational and professional goals top
Students gain and consolidate an in-depth knowledge of the special mathematical areas.
Students who intend to continue their studies in the doctoral programme are gradually introduced to research mathematics.
Students interested in financial mathematics gain some specific knowledge of applied mathematics. For example, probability and statistics courses are particularly important for those interested in the finance, insurance or banking sectors.
Students are provided with a thorough understanding of mathematics and taught the importance of analytical thought and argumentation, as well as the usefulness of various mathematical problem-solving methods.
Students develop and learn to employ mathematical thinking, reasoning and argumentation in diverse mathematical areas.
Students learn to recognise the connections between different mathematical theories and other natural and social sciences.
Students develop the capacity to analyse given data in the sense of both reaching new conclusions and of teamwork in problem-solving.
Students learn to employ modern technological tools (e.g. calculators, PCs, graphoscopes, projectors) in solving and demonstrating mathematical problems and concepts.
The study programme lasts two years (120 ECTS), comprising courses, seminars and preparation and defence of the master’s thesis.
Courses are divided into basic courses, internal elective and external elective courses (Table 1). During their studies, students must take 3 basic courses, 6 internal elective courses and 3 external elective courses.
The Seminar (study obligation in the 1st and 2nd year of study) contains the following obligations: in the 1st year, students must deliver at least one lecture or presentation, while in the 2nd year they attend lectures at the Mathematical Research Seminar of the faculty.
Students choose the study field by enrolling. Students choose basic courses and internal elective courses related to their selected study field.
Short descriptions of courses are available here.
|Year of study||Study obligation||ECTS-credits (ECTS)|
|ECTS||ECTS/Year of study|
|1.||Basic Course I||6||60|
|Basic Course II||6|
|Basic Course III||6|
|Internal Elective Course I||6|
|Internal Elective Course II||6|
|Internal Elective Course III||6|
|External Elective Course I||6|
|External Elective Course II||6|
|2.||Internal Elective Course IV||6||60|
|Internal Elective Course V||6|
|Internal Elective Course VI||6|
|External Elective Course III||6|
Table 2: Basic Courses (MS-18)
(The list shows all basic courses of the study programme. Every academic year, the Faculty offers a different (shorter) selection of basic courses.)
|No.||Course||ECTS||Form of contact hour|
|1.||Selected Topics in Algebra (1)||6||45||-||15||60|
|2.||Selected Topics in Analysis (1)||6||45||-||15||60|
|3.||Selected Topics in Discrete Mathematics (1)||6||45||15||-||60|
|4.||Selected Topics in Financial Mathematics (1)||6||45||15||-||60|
|5.||Selected Topics in Cryptography (1)||6||45||15||-||60|
|6.||Selected Topics in Mathematical Statistics (1)||6||45||15||-||60|
|7.||Molecular Modeling Course||6||45||15||60|
|8.||Selected Topics in Functional Analysis||6||45||15||-||60|
L = lecture, SE = seminar, T = tutorial
ECTS = ECTS-credits
Table 3: Internal Elective Courses (MS-18)
(The list shows all internal elective courses of the study programme. Every academic year, the Faculty offers a different (shorter) selection of elective courses.)
|No.||Course||ECTS||Form of contact hour|
|2||Elliptic Curves in Cryptography||6||45||-||-||45|
|5||Geometry and Topology||3||45||-||-||45|
|6||Geometric Measure Theory||3||30||-||-||30|
|7||Geometric Aspects in Discrete Dynamical Systems||6||30||-||15||45|
|8||Geometrical Optimization Problems||3||30||-||-||30|
|9||Groups, Covers and Maps||6||45||-||-||45|
|10||Selected Topics in Algebra (2)||6||45||-||-||45|
|11||Selected Topics in Partial Differential Equations||6||45||-||-||45|
|12||Selected Topics in Dynamical Systems||6||45||-||15||60|
|13||Selected Topics in Discrete Mathematics (2)||6||45||-||-||45|
|14||Selected Topics in Complex Analysis||6||45||-||-||45|
|15||Selected Topics in Mathematical Statistics (2)||6||45||-||-||45|
|16||Selected Topics in Numerical Mathematics||6||45||-||-||45|
|17||Selected Topics in Theory of Association Schemes||6||45||-||-||45|
|18||Selected Topics in Theory of Finite Geometries||6||45||-||-||45|
|19||Selected Topics in Number Theory||6||45||-||-||45|
|20||Selected Topics in Topology||6||30||-||30||60|
|21||Selected Topics in Computing Methods and Applications||6||45||-||-||45|
|22||Chaotic Dynamical Systems||6||45||-||-||45|
|23||Characters of Finite Groups||6||45||-||-||45|
|24||Combinatorial and Convex Geometries||6||45||-||-||45|
|25||Combined Quantum and Classical Methods for Molecular Simulations||6||45||-||-||45|
|26||Cryptographic Hash Functions and Block Chains||6||30||15||-||45|
|27||Lie Groups and Lie Algebras||3||30||-||-||30|
|29||Mathematical Finances in Real Time||6||45||-||-||45|
|30||Mathematical Topics in a Foreign Language||6||45||-||-||45|
|31||Molecular Dynamics Simulation Methods||6||45||-||-||45|
|33||Computer Aided Geometric Design||3||30||-||-||30|
|34||Symmetry and Traversability in Graphs||6||45||-||-||45|
|38||Theory of Finite Fields||6||45||-||-||45|
|40||Theory of Permutation Groups||6||45||-||-||45|
|42||Introduction to Public-key Cryptography||6||45||-||-||45|
|43||Introduction to Symmetric-cipher Cryptography||6||45||-||-||45|
|44||Probability with Measure (1)||6||45||-||-||45|
|45||Probability with Measure (2)||6||45||-||-||45|
|47||History and Methodology of the Subject||3||30||-||-||30|
Course structure and programme information for students enrolled 2007/08 - 2017/18
In the past year changes occurred in the course plan. In the beginning of this section you can find the course plan for students enrolled from the academic year 2018/19.
Here you can find information regarding course structure, compulsory and elective courses, and also short description of courses for students enrolled for the first time in the academic years 2007/08 - 2017/18 (MS-07):
The elective courses are divided into internal and external elective courses:
INTERNAL elective courses are courses from the mathematical field of expertise and are presented in the Table 3;
EXTERNAL elective courses may be chosen from the areas of social sciences, humanities and natural sciences, and from study programmes at other faculties; however, students may also select a course from internal elective courses as their external elective course.
Every academic year, the Faculty offers a different selection of elective courses from the internal elective courses listed. The Faculty tries to meet student interests within the limits of the Faculty’s resources. The final selection of elective courses for the next academic year is published in July. The coordinator will help guide students when choosing their study field and elective courses after the second year.
Students choose the study field by enrolling.
Every study field, aside from the study field of General Mathematics, belongs to a subject core. Students choose basic courses and internal elective courses related to their selected study field, while the external elective courses provide students with the opportunity to expand their knowledge in selected fields within the Social Sciences, Humanities and Natural Sciences, and/or enable an in-depth study of a selected professional field (which may be selected at any university that has introduced the ECTS system).
Students can opt for one of the following eight study fields:
Study fields for students enrolled 2007/08 - 2017/18
In the past year changes occurred in the course plan. In the beginning of this section you can find information regarding elective courses and study fields for students enrolled from the academic year 2018/19.
HERE you can find information regarding elective courses and study fields for students enrolled for the first time in the academic years 2007/08 - 2017/18 (MS-07).
Admission to the 1st year shall be granted to applicants having:
completed a first-cycle study programme in any mathematical study field; or
completed a first-cycle study programme in other professional fields, provided that they have, prior to enrolment, fulfilled all study obligations that are deemed essential for the continuation of studies in the Master's study programme in Mathematics and accumulated at least 30 credits. The applicants may fulfil these obligations during their first-cycle studies, under training programmes, or by taking examinations prior to enrolment in the study programme Mathematical Sciences.
Applicants having completed a four-year (single-discipline or two-discipline) academic study programme in Mathematics or Mathematics-related study fields may directly enrol in the 2nd year of study (see information on transfers between the programmes below). The Senate of the Faculty has the authority to impose mandatory study obligations on individuals applying for transfer, based on their qualifications.
In the case of enrolment limitations, applicants shall be selected on the basis of the average grade obtained in the undergraduate studies.
Admission may also be gained by an applicant having completed a comparable study abroad. Prior to enrolment the applicant must apply for the recognition of completed education.
Continuation of studies according to the transfer criteriatop
Transfers between study programmes are possible on the basis of the Higher Education Act, Criteria for Transferring between Study Programmes and in accordance with other provisions regulating this field.
Transferring between study programmes means a cessation of studies in the first study programme and the continuation of studies in the second study programme. The first study programme is the programme from which the student is transferring. The second study programme is the programme to which the student is transferring. Applications for transfers shall be considered on the grounds of the level of comparability between study programmes and those study requirements which students have already completed in their first study programme.
Entry into Year 2 of the Master’s programme of Mathematical Sciences on the basis of the Criteria for Transferring between Study Programmes is granted to students of a related second-cycle study programme or a pre-reform undergraduate programme (adopted prior to 11 June 2004), provided that the following conditions have been met:
the student fulfils the requirements for admission to the study programme of Mathematical Sciences;
completion of the first study programme which the student is transferring from ensures the acquisition of comparable competencies as those envisaged by the study programme of Mathematical Sciences; and
other conditions in accordance with the Criteria for Transferring between Study Programmes have also been met (a comparable course structure, course requirements completed).
Entry into Year 2 of the Master’s programme of Mathematical Sciences on the basis of the Criteria for Transferring between Study Programmes is also open to graduates of a related undergraduate non-Bologna degree programme adopted before 11 June 2004.
Individual applications for transfer shall be considered by the relevant committee of UP FAMNIT. Apart from comparability between both fields of study, the committee shall also consider comparability between the study programmes, in accordance with the Criteria for Transferring between Study Programmes. The applicant may also be required to complete differential exams as defined by the relevant Faculty committee.
Enrolment on the basis of the Criteria for Transferring between Study Programmes is also open to students of a related study programme abroad who have been, in the process of recognition of their studies abroad, legally granted the right to continue their educational training in the study programme of Mathematical Sciences.
In the case of limited enrolment, applicants shall be selected on the basis of the average grade obtained during the study programme they are transferring from.
Advancement requirements top
For enrolment in the next study year it is necessary to collect at least 42 ECTS-credits from courses and exams in the current study year. The Study Committee of the Faculty may permit a student who has not fulfilled all study obligations for the particular year to enrol to the next year. The student is obliged to submit a formal written request to the Study Committee. The progress may be approved if a student could not fulfil the obligations for justifiable reasons. Students may repeat a year only once during the study period. A minimum of 18 ECTS-credits in courses from the current year of study are required in order to repeat the year.
Requirements for the Completion of Studies
Students shall be deemed to have completed their studies when they fulfil all the prescribed study requirements to a total of 120 ECTS-credits, including the Master's Thesis. With the Master's Thesis, the student demonstrates expertise and knowledge in the selected study programme, a critical understanding of theories, concepts and principles (basic as well as advanced), originality and creativity in the use and application of knowledge, and the capacity to analyse a problem and form suitable solutions. The theme of the Master’s Thesis must relate to the field of the selected study programme. Students publicly present the theme of their Master’s Thesis at a seminar (verbal presentation), normally twice, and at least once prior to a final defence of the Master’s Thesis.
Graduate employment opportunities top
Graduates will be able to obtain employment in organisations dealing with Computer and Information Science (computer and related companies and institutions), Statistics (Statistical Office, insurance companies, banks), Mathematical Finance (insurance companies, banks, stock exchange, brokerage firms), Gambling Theory (lottery, sports lottery), as well as in the fields of education and research. Graduates can also opt for professional careers not directly related to Mathematics, as the skills acquired in logical reasoning, deliberation, assessment of procedures and results, including an analytical approach to problem-solving, represent qualities indispensable for executive workers in numerous branches of the economy.