The postgraduate PhD study program Mathematics was adopted by the Senate of the Faculty of Natural Sciences and Mathematics on27 May 2008 and by the Senate of the University of Maribor on 16 Dec. 2008. On the basis of Article 51 of the Law on Higher Education (Official Gazette of the Republic of Slovenia, No. 119/06-UPB3) and on the basis of the Measures for the Accreditation of Higher Education Institutions and Study Programmes (Official Gazette of the Republic of Slovenia, No. 101/04), the Council for Higher Education at its 15th meeting on 12 Mar. 2009 gave consent to the programme. The Ministry of Higher Education, Science and Technology issued a decree No. 60392-125/2009/5 on6 May 2009, by which the study programme is included in the register for higher education institutions under the serial number 17. On 20 Oct. 2016, the Council of the National Agency of the Republic of Slovenia for Quality Assurance in Higher Education extended the accreditation of the doctoral study program Mathematics for seven years. On 28 Nov. 2017, the Senate of the University of Maribor approved the renewal of the doctoral study program Mathematics according to the Doctoral School of the University of Maribor’s principles.

A student advances to the second study year if they collect at least 51 ECTS credits by completing 1st year obligations. A student advances to the third study year if they complete all 1st year obligations and collect at least 51 ECTS credits by completing 2nd year obligations. A student advances to the fourth study year if they complete all 2nd year obligations and collect at least 51 ECTS credits by completing 3rd year obligations.

Postdoctoral study.

In the framework of the doctoral study Mathematics candidates are trained for independent research in complex national and international projects; they are also enabled a university academic career. They are employable in research and development institutions, primary and secondary schools, at university level, and as the organizers and heads of various professional training courses in business and in public service.

The summations provide the average values of hours to PhD study program Mathematics. Inconsistencies in the numbers are the result of choice of elective courses. Independent student work per PhD study program Mathematics amounts up to 6990 hours.

In the first and the third semester of study each candidate carries out a lecture in the framework of the research seminar. The theoretical basis for these seminars is the knowledge acquired by the student in the elective courses, and the horizontal and vertical link with the topic of the future doctoral thesis.

Examination and assessment of student learning outcomes is performed in accordance with the criteria and methods defined in the Rules on the Examination and Assessment of Knowledge at the University of Maribor: https://www.um.si/univerza/dokumentni-center/akti/Dopolnitve2013/Pravilnik%20o%20preverjanju%20in%20ocenjevanju%20znanja%20na%20UM%20-%20NPB3,%20AVGUST%202019doc.pdf. Knowledge examination and assessment methods at the University of Maribor are regulated by the Statute of the University of Maribor and the Rules on Examinations and Grading of the University of Maribor, No. A4/2009-41AG (University of Maribor Journal, No. XXVII-6-2009); Amendments to the Rules on Examinations and Grading of the University of Maribor, No. A4/2009-41AG (University of Maribor Journal, No. XXVIII-7-2010); Amendments to the Rules on Examinations and Grading of the University of Maribor, No. A4/2009-41AG (University of Maribor Journal, No. XXX-2-2012); Amendments to the Rules on Examinations and Grading of the University of Maribor, No. A4/2009-41AG (University of Maribor Journal, No. XXXII-5-2014); Rules on Examinations and Grading of the University of Maribor – unofficial consolidated text (2015); Amendments to the Rules on Examinations and Grading of the University of Maribor, No. A4/2009-41AG (2019): https://www.um.si/univerza/dokumentni-center/akti/Dopolnitve2013/Pravilnik%20o%20preverjanju%20in%20ocenjevanju%20znanja%20na%20UM%20-%20NPB3,%20AVGUST%202019doc.pdf. Forms and methods of assessment are defined in Article 5 of the Rules on Examinations and Grading. Criteria and methods for knowledge assessment of individual subjects are part of the Subject Specification, and are publicly available on the faculty’s website: https://www.fnm.um.si/index.php/predstavitev-tudija/podiplomski-tudijski-programi/

- to provide students with in-depth knowledge in the field of mathematics and to introduce to them the width, role, importance, and interdisciplinary nature of this field; - to provide students with the necessary organisational knowledge and expertise on the development and research, both in the field of mathematics as well as in mathematical education; - to introduce modern methods and technologies of work in the field of mathematics and train students to use these methods and technologies, and to follow developmental trends in the profession; - to train candidates for independent internationally competitive research work in the field of education in the given research field and efficient teaching in that field; - to deepen theoretical knowledge in the field of mathematics; and expand the methodological knowledge for solving complex technological, engineering, organizational and developmental tasks and projects.

- ability of systemic thinking; - control of critical and self-critical assessment; - ability and willingness to work in a cooperative group in the domestic and international environment and the ability to use theoretical knowledge in solving practical problems; - in-depth knowledge of experimental and other methods demonstrating scientific theories; - the ability to search for various sources of knowledge in solving professional problems; - ethical reflection and commitment to professional ethics in the fields of engineering and training; - initiative and autonomy in decision-making and management of professional and scientific projects.

- superior understanding of theoretical and methodological concepts in the field of mathematics and mathematical applications in the natural and social sciences; - capacity to use supreme knowledge in individual specialized areas of mathematics; - training for individual and group work in solving the most challenging problems in specific areas of mathematics as well as a variety of mathematical applications using known solutions and discovering new or adapting existing solutions in the international sphere; - training for cutting-edge research work in specific areas of theoretical mathematics and applicative fields, and for individual generating of new knowledge (innovation); - ability to use and create new methods, and to customize existing mathematical research methods in predicted or changed (new) circumstances; - ability to manage scientific research projects in the field of mathematics and related applicative areas; - supreme capacity for independent and group discovery and creating new sources of knowledge in specific scientific areas of theoretical and applied mathematics; - supreme capacity for independent and team adaptation of mathematical knowledge to solving topical problems in specific work areas, where this knowledge useful; - ability to present the results of specific mathematical scientific research at scientific and professional conferences and in scientific and professional journals; - in-depth knowledge of specific educational work in the field of mathematics in different periods of time and in different educational systems.

Candidates who completed the following may apply for the 3rd Cycle Study Programme Mathematics: - a 2nd Cycle Study Programme; - an undergraduate academic study programme adopted prior to 11 June 2004; - a 1st Cycle Higher Education Study Programme adopted prior to 11 June 2004, and a Specialization Study Programme, after having passed additional study obligations corresponding to 45 ECTS (upon a proposal of the Department of Mathematics and Computer Sciences) in the spcific areas of Mathematical Analysis, Algebra, Discrete Mathematics, Geomtery, Topology, Probability and Statistics; - a study program educating for professions regulated by EU directives, or other Single Major 2nd cycle Study Programme ranked with 300 ECTS. To increase the success of further studies, the Faculty recommends university-level prior education in the fields of Mathematics or Natural Sciences.

In the event of limited enrolment, the Faculty shall publish the selection criteria in accordance with Article 41 of the Higher Education Act. In the selection procedure, candidates shall be ranked according to: grade point average (20%), the grade awarded for their MA thesis (40%), and the grade awarded for their elective exam (40%), focused on basic mathematical contents, the knowledge of which is crucial for a succsessful doctoral study according to the given study programme.

According to the Criteria for transitions, a transfer to the 3rd Cycle Study Programme Mathematics is possible for candidates enrolled in the study programmes from the fields of Mathematics, who ensure the acquisition of comparable competences at the end of their studies, and for whom at least half of the ECTS obligations from the first study programme are recognised according to the Criteria for recognition. The relevant Commission of the Member determines the missing obligations which the students have to fulfill if they want to graduate according to the new study program.

Students of 3rd Cycle Study Programmes can obtain full recognition of the knowledge and skills acquired through various forms of formal education before enrolment, which the student demonstrates with relevant qualifications (certificates, degrees, diplomas and other documents). The recognition process shall take into account the following criteria: the assessment of the achieved knowledge and skills must be based on the educational goals of the study program; the relevant skills must be properly documented and at an appropriate level of complexity; the acquired knowledge and skills are recognized regardless of where and when the student acquired them. The process of identification, verification and recognition of knowledge and skills entails the submission of an application, amendments to the application, consideration of the application at the competent authority of the member faculty, the issuing of a decision, and the procedure for the appeal of a candidate against the issued decision. The faculty recognises the knowledge and skills of the candidates if, in terms of their scope, content and complexity, these correspond fully or partially to the general or subject-specific competences determined by the study programme in which the candidates wish to enrol or are enrolled. Recognition of knowledge and skills is defined in the RULES ON THE RECOGNITION OF KNOWLEDGE AND SKILLS IN THE STUDY PROGRAMMES OF THE UNIVERSITY OF MARIBOR No. 012/2019/2: https://www.um.si/univerza/dokumentni-center/akti/GlavniDokumenti2013/Pravilnik%20o%20priznavanju%20znanj%20in%20spretnosti%20v%20%C5%A1tudijskih%20programih%20UM%20%C5%A1t.%20012-2019-2.pdf.

A student completes his/her studies once they have completed all obligations laid down in the study programme, having collected at least 240 ECTS, and successfully defended their doctoral thesis.