University of Primorska Faculty of Mathematics, Natural Sciences and Information Technologies
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Mathematical Sciences

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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

Assoc. Prof. Štefko Miklavič, PhD

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

About the programmetop

 
Welcome to Famnit

The study is primarily intended for prospective researchers, professors and other academia 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 his student. While student is trying to solve the problem (or problems), the supervisor helps him, informs him of similar problems already solved and introduces some techniques from a given mathematical field. 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 those issues which are indispensable for the research in his field, but the student did not familiarize with them at the lower levels of his study. Courses are often suggested by the supervisor and are usually individual. The student regularly presents his current research work at the research seminars.

The aim of the study is to encourage the student to do the research, and not to burden him with the exams of the courses that are not directly related with his research area (the latter is probably quite special in Slovenia). The faculty staff is aware of the fact that nowadays the Ph.D. students must have some research results immediately after finishing their studies if they want to stay in the academia – whether that be abroad or at home.

During the study, Ph.D. students usually attend various international conferences and 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 the 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 studies, the student is capable of independent, internationally competitive research work.
  • The student publishes articles in the reputable international journals listed on the Science Citation Index Expanded. This is also a prerequisite for a successful dissertation defence.
  • The student knows his research area in a way that he has the latest information on open problems or the problems that have already been solved.
  • During the study, the student becomes familiar with the researcher's way of life (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 their 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 the 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.

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. The candidate’s 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.

As part of their studies, students are required to write a doctoral dissertation, which is to 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
 
 ELECTIVE COURSES - ADVANCED MATHEMATICAL COURSES 
 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 1st year shall be granted to applicants having:

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

In case of enrolment limitations, applicants shall be selected on the basis their performance demonstrated in Masters 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 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 the student has already completed in their first study programme.

Entry into 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 students of a related third-cycle doctoral degree programme or a pre-reform Master’s 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 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 Master’s 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 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

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

The two courses above provide the basis for individual research work (2nd and 3rd year) on which students are to report to their supervisor. Individual research work is presented at (department’s) 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 shall be completed by the preparation of the Doctoral dissertation presenting an authentic contribution to science.

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.

Graduate employment opportunitiestop

Graduates are equipped for either independent research or other developing projects demanding exacting knowledge, at national or international level, and are also capable of working on university projects, in scientific institutes or other research and developing organisations. Knowledge achieved through the study of Theoretical and Applied Mathematics also enables the candidate to be involved outside the academic environment, i.e. insurance companies, banks, stock broking agencies, statistical offices, and in economical environments where awareness, existence and development in competitive market economies requires people capable of rational thinking, in depth analysis and substantial decision making, which is the domain of all mathematicians.