Mathematical Sciences

Math department's yearly report:
Report 2014
Report 2013
Report 2012
Report 2011

General information

Name of the programme: Mathematical Sciences
Type of programme: Doctoral, 3rd Bologna cycle
Degree awarded: “doktor znanosti” equiv. to a Doctoral degree
Duration: 3 years (6 semesters)
ECTS-credits: 180
Programme structure: 2 electives, individual research work, seminars, doctoral dissertation
Mode of study: part-time

Programme coordinatortop

Prof. Štefko Miklavič, PhD

For information regarding application, enrolment and other administrative procedures please contact Student Services.

About the programmetop

The study programme is primarily intended for prospective researchers, professors and other academic staff. Each student has a supervisor, who is ordinarily selected before the student’s enrolment. One of the key roles of the supervisor is to present a relevant open problem (or open problems) to the student. While the student is trying to solve the problem (or problems), the supervisor helps, informs the student of similar problems already solved and introduces appropriate techniques from relevant mathematical fields. The solution to these open problems and its publication in the relevant international journals must be a primary goal of each student.

In the first year, there are two elective courses - Advanced Mathematical Course I and Advanced Mathematical Course II. Their purpose is to acquaint students with topics with which they did not become familiar during lower-level studies, but which are indispensable for research in their field. Courses are often suggested by the supervisor and are usually individual to the student. Students regularly present their current research work at research seminars.

The aim of the programme is to encourage students to do the research, and not to burden them with course exams that are not directly related to their research area (the latter is probably a special feature among Slovenian universities). Faculty members are aware of the fact that nowadays Ph.D. students must have some research results immediately after finishing their studies if they want to stay in academia – whether that be abroad or at home.

During their studies, Ph.D. students usually attend various international conferences and conduct research visits, where they present their research results. Often they are involved in the organization of the conferences, summer schools, etc., organized by the Faculty or UP IAM, which is directly connected with the faculty. To a lesser extent, students are also involved in teaching students at lower levels.

Educational and professional goals

• After (or during) the study programme, the student is capable of independent, internationally competitive research work.
• The student publishes articles in reputable international journals listed on the Science Citation Index Expanded. This is also a prerequisite for a successful dissertation defence.
• The student knows his/her research area thoroughly, having the latest information on open problems or the problems that have already been solved.
• During the study programme, the student becomes familiar with the career of a researcher (active participation in international conferences, research visits, etc.).

Course structuretop

The doctoral degree study is provided on an individual basis. The main components of the study programme are the following:

• Advanced mathematical courses covering the research topic chosen by the candidate together with the supervisor
• Research by the candidate
• Seminar presentations
• A minimum of two scientific articles in SCI journals
• Doctoral dissertation and defence

All these activities must add up to 180 ECTS.

Advanced Mathematical Courses (AMC I and AMC II) are the basis of the doctoral student’s Individual Research work and introduce the candidate to problems associated with each of the following fields of Mathematics: Analysis, Algebra, Discrete Mathematics, Financial Mathematics, Cryptography, Computing Intensive Methods Applications, and Statistics.

Students select a supervisor with research interests similar to their own, who mentors their chosen AMC I or AMC II courses and doctoral dissertation. The choice of courses is usually made in consultation with the student’s supervisor. Similar study programmes, within the field of natural sciences, either inside or outside the university, may also be chosen. The University of Primorska provides one such option within their Information Technologies Doctoral programme.

In studying these courses, with the benefit of their supervisor’s input and direction, students acquire the necessary skills to enable them to perform individual research work in any of the above-mentioned fields of Mathematics. Candidates' Individual Research work is shared with their supervisor during their consultations; it is also introduced to teachers, students and others during seminars and concluded by their doctoral dissertation.

A doctoral dissertation represents an original contribution to science and, consequently, has to conform to University rules and regulations on doctoral dissertations. The procedure for preparing a doctoral dissertation is regulated by the Rules on the preparation and defence of the doctoral dissertation at the University of Primorska.

As part of their studies, students are required to write a doctoral dissertation, which must represent a new and important contribution to the body of knowledge in the field of mathematics. Prior to the thesis defence (viva voce), their research must be published (or accepted for publication) in international journals in the field of mathematics, in at least two articles in journals from the SCI list. Detailed criteria are established by the Department of Mathematics of UP FAMNIT.

Courses	ECTS
1ST YEAR	60
Elective course – Advanced Mathematical Course I	12
Elective course – Advanced Mathematical Course II	12
Individual Research Work	24
Seminar	12
2ND YEAR	60
Individual Research Work	24
Doctoral Dissertation	24
Seminar	12
3RD YEAR	60
Seminar	12
Doctoral Dissertation	48

Advanced Mathematical Courses (AMC)	ECTS
AMC – Algebra I	12
AMC - Algebra II	12
AMC – Analysis I	12
AMC – Analysis II	12
AMC – Discrete Mathematics I	12
AMC – Discrete Mathematics II	12
AMC – Financial Mathematics I	12
AMC – Financial Mathematics II	12
AMC – Cryptography I	12
AMC – Cryptography II	12
AMC – Computing Intensive Methods and Applications I	12
AMC – Computing Intensive Methods and Applications II	12
AMC – Statistics I	12
AMC – Statistics II	12

Admission requirementstop

Admission to the 1^st year shall be granted to applicants having:

• A Master's degree in Mathematics (“Bologna” study programme); or
• A Master's degree in studies similar to Mathematics (Computer and Information Sciences, Information Science and Mathematics, Natural Sciences) who have met the necessary additional requirements (i.e. passed differential exams in Algebra and Analysis).

In the case of enrolment limitations, applicants shall be selected on the basis of their performance demonstrated in Master's studies (average grade, Master’s thesis grade).

Admission may also be gained by an applicant having completed a comparable study abroad. Prior to enrolment the applicant must apply for 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 regulations of this field.

The transition between study programmes is the enrolment in the higher year of the study programme, in case of leaving the education at the initial study programme and continuing the study process at another study program of the same degree. The transition takes into account the comparability of the study programmes and the completed study obligations of the candidate in the initial study program.

Access to year 2 or year 3 of the doctoral degree programme of Mathematical Sciences on the basis of the Criteria for Transferring between Study Programmes is open to candidates of a related third-cycle doctoral degree programme, provided that the following conditions have been met:

• the candidate fulfils the requirements for admission to the study programme of Mathematical Sciences;
• completion of the first study programme which the candidate 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 doctoral degree programme of Mathematical Sciences on the basis of the Criteria for Transferring between Study Programmes is also open to graduates of a related pre-Bologna reform Master’s degree programme.

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 candidates 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 requirementstop

Students may advance to the higher year upon acquiring 40 ECTS-credits in the current study year and to fulfil all the study obligations for the previous 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 in the next year, but a student has to acquire at least 30 ECTS-credits.

In the 1^st year, students complete two courses within the cluster of in-depth mathematical contents which they select in consultation with their supervisor.

The two courses above provide the basis for individual research work (2^nd and 3^rd year) on which students are to report to their supervisor. Individual research work is presented at department seminars attended by students, teachers and other interested persons. The contents of the seminars (two each year) relate to the above-mentioned courses from the cluster in-depth mathematical contents. Individual research work is completed through the preparation of the Doctoral dissertation, presenting an authentic contribution to science.

Prior to the thesis defence (viva voce), the student's research must be published (or accepted for publication) in international journals in the field of mathematics, in at least two articles in journals from the SCI list. Detailed criteria are established by the Department of Mathematics of UP FAMNIT.

Graduates' competenciestop

General competencies

• The ability to analyze, synthesize and predict solutions and consequences of the factors related to the discipline of mathematics.
• The ability to place mathematics into a broader social context.
• The ability to critically reflect on social events in general.
• The ability to critically assess the developments in the field of mathematics.
• The ability to work within a wider social community.
• The ability to autonomously search for and acquire professional knowledge and to integrate it with the existing knowledge.
• Autonomy in professional and scientific research.

Subject-specific competencies

• The ability to apply the mathematical and computer apparatus in concrete research.
• The ability to place mathematics into a broader social context.
• The ability of autonomous engagement in international mathematical circles.
• The ability of in-depth analysis of the development of their area of ​​expertise.
• The ability to communicate within a global mathematical science and society.
• The ability to design a hierarchy enabling decomposition of a problem into sub problems and engineering of the integration of partial solutions.

Graduate employment opportunitiestop

Graduates are equipped for either independent research or other development projects demanding exacting knowledge, at the national or international level, and are also capable of working on university projects, in scientific institutes or in other research and development organisations. The in-depth knowledge acquired in both theoretical and applied mathematics also enables graduates to seek employment outside the academic environment, i.e. in insurance companies, banks, stockbroking agencies, statistical offices, and in economic environments where the need for survival and development in competitive market economies requires people capable of rational thinking, in-depth analysis and substantial decision making skills - in short, mathematicians.

Tuition feetop

• The TUITION FEE for each year of study is determined in the Price list UP FAMNIT.
• The CO-FUNDING OF DOCTORAL STUDIES will be open to all students who meet the requirements from the Decree on co-Financing of doctoral studies and Criteria for the selection of candidates for co-funding tuition fees in doctoral studies at the University of Primorska. More information is available here.