Mathematical Sciences
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General information
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)
ECTScredits: 120
Programme structure: 9 courses (72 ECTS), 4 seminars (24 ECTS), Master's Thesis (24 ECTS)
Mode of study: fulltime
Language of study: Slovene, English (in English from 2016/17)
Programme coordinatortop
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 indepth 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 problemsolving 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 problemsolving.

Students learn to employ modern technological tools (e.g. calculators, PCs, graphoscopes, projectors) in solving and demonstrating mathematical problems and concepts.
Course structuretop
Courses are divided into basic courses, internal elective and external elective courses.
The elective courses are divided into Internally and Externally elective courses. Internally Elective Courses are courses from the mathematical field of expertise. Externally 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 courses as their Externally Elective Course. At least one elective course must be mathematical, and must also be delivered in a foreign language, normally English.
After the first year, students decide which study field they would like to follow. Students can opt for one of the following seven study fields: Discrete Mathematics, Financial Mathematics, Cryptography, Computer Intensive Methods and Applications, Probability and Statistics, General Mathematics and Theoretical Mathematics. Based on this decision, students then choose elective courses.
Every study field in the Mathematics programme, aside from the study field of General Mathematics, belongs to a subject core (see the table below). Students choose basic courses and internally elective courses related to their selected study field, while the externally 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 indepth study of a selected professional field (which may be selected at any university that has introduced the ECTS system).
From the academic year 2018/19, a revised study programme will be implemented. Presented below is a course structure for students enrolled in the academic years 2007/08  2017/18 and a course structure for students enrolled for the first time in the academic year 2018/19. For reference, the course structures are named as MS07 and MS18.
Course structure for students enrolled in the academic years 2007/08  2017/18 (MS07)
During their studies, students must take a total of 9 courses (two basic and seven electives), 4 seminars, and prepare and defend their Master’s Thesis.
Short descriptions of courses are available here.
Courses  ECTS 

Basic Course I  9 
Basic Course II  9 
Elective Course I – Internally Selected  9 
Elective Course II – Internally Selected  9 
Elective Course III – Externally Selected  6 
Elective Course IV – Externally Selected  6 
Seminar I  6 
Seminar II  6 
2^{ND} YEAR (60 ECTScredits)
Courses  ECTS 

Elective Course V – Internally Selected  9 
Elective Course VI – Internally Selected  9 
Elective Course VII – Externally Selected  6 
Seminar III  6 
Seminar IV  6 
Master’s Thesis  24 
BASIC COURSES
Courses  ECTS 

Selected Topics in Algebra (1)  9 
Selected Topics in Analysis (1)  9 
Selected Topics in Discrete Mathematics (1)  9 
Selected Topics in Financial Mathematics (1)  9 
Selected Topics in Cryptography (1)  9 
Selected Topics in Mathematical Statistics (1)  9 
Molecular Modeling Course  9 
Selected Topics in Functional Analysis  9 
BASIC COURSES – CORES
Cores  Courses 

General, Theoretical and Discrete Mathematics Core  Selected Topics in Analysis (1) 
Selected Topics in Algebra (1)  
Selected Topics in Discrete Mathematics (1)  
Selected Topics in Functional Analysis  
Probability and Statistics Core  Selected Topics in Mathematical Statistics (1) 
Cryptography Core  Selected Topics in Cryptography (1) 
Financial Mathematics Core  Selected Topics in Financial Mathematics (1) 
Computer Intensive Methods and Applications Core  Molecular Modelling Course 
INTERNALLY SELECTED ELECTIVE COURSES
Courses  ECTS* 

Algebraic Combinatorics  9 / 6 
Elliptic Curves in Cryptography  9 / 6 
Healthcare Financing  9 / 6 
Groups, Covers and Maps  9 / 6 
Selected Topics in Algebra (2)  9 / 6 
Selected Topics in Differential Equations  9 / 6 
Selected Topics in Discrete Mathematics (2)  9 / 6 
Selected Topics in Complex Analysis  9 / 6 
Selected Topics in Mathematical Statistics (2)  9 / 6 
Selected Topics in Numerical Mathematics  9 / 6 
Selected Topics in Theory of Association Schemes  9 / 6 
Selected Topics in Theory of Finite Geometries  9 / 6 
Selected Topics in Number Theory  9 / 6 
Selected Topics in Topology  9 / 6 
Selected Topics in Computing Methods and Applications  9 / 6 
Chaotic Dynamical Systems  9 / 6 
Characters of Finite Groups  9 / 6 
Combined Quantum and Classical Methods for Molecular Simulations  9 / 6 
Mathematical Modelling  9 / 6 
Mathematical Finances in Real Time  9 / 6 
Mathematical Topics in a Foreign Language  9 / 6 
Molecular Dynamics Simulation Methods  9 / 6 
Molecular Graphics  9 / 6 
Symmetry and Traversability in Graphs  9 / 6 
Stochastic Processes  9 / 6 
Game Theory  9 / 6 
Coding Theory  9 / 6 
Theory of Finite Fields  9 / 6 
Measure Theory  9 / 6 
Theory of Permutation Groups  9 / 6 
Introduction to Publickey Cryptography  9 / 6 
Introduction to Symmetriccipher Cryptography  9 / 6 
Probability with Measure (1)  9 / 6 
Probability with Measure (2)  9 / 6 
Probability  9 / 6 
INTERNALLY ELECTIVE COURSES – CORES
Cores  Courses 

ALGEBRA Core  Algebraic Combinatorics 
Selected Topics in Algebra (2)  
Selected Topics in Number Theory  
Characters of Finite Groups  
Theory of Finite Fields  
Theory of Permutation Groups  
ANALYSIS Core  Selected Topics in Analysis (2) 
Selected Topics in Complex Analysis  
Selected Topics in Numerical Mathematics  
Selected Topics in Topology  
Chaotic Dynamical Systems  
DISCRETE MATHEMATICS Core  Algebraic Combinatorics 
Groups, Covers and Maps  
Selected Topics in Discrete Mathematics (2)  
Selected Topics in Theory of Association Schemes  
Selected Topics in Theory of Finite Geometries  
Symmetry and Traversability in Graphs  
Theory of Finite Fields  
PROBABILITY AND STATISTICS Core  Selected Topics in Mathematical Statistics (2) 
Mathematical Modelling  
Stochastic Processes  
Probability with Measure (1)  
Probability with Measure (2)  
CRYPTOGRAPHY Core  Algebraic Combinatorics 
Elliptic Curves in Cryptography  
Coding Theory  
Theory of Finite Fields  
Introduction to Publickey Cryptography  
Introduction to Symmetriccipher Cryptography  
FINANCIAL MATHEMATICS Core  Healthcare Financing 
Selected Topics in Mathematical Statistics (1)  
Mathematical Modelling  
Mathematical Finances in Real Time  
Game Theory  
COMPUTER INTENSIVE METHODS AND APPLICATIONS (CIMA) Core  Selected Topics in Discrete Mathematics (1) 
Selected Topics in Numerical Mathematics  
Selected Topics in Computing Methods and Applications  
Combined Quantum and Classical Methods for Molecular Simulations  
Selected Topics in Mathematical Statistics (1)  
Molecular Dynamics Simulation Methods  
Molecular Graphics 
LIST OF BASIC AND INTERNALLY ELECTIVE COURSES IN THE STUDY FIELDS
Study Field  Basic Courses  Internally Elective Courses 

GENERAL MATHEMATICS  The student chooses:

The student chooses:

THEORETICAL MATHEMATICS  The student chooses:

The student chooses:

DISCRETE MATHEMATICS  The student chooses:

The student chooses:

PROBABILITY AND STATISTICS  The student chooses:

The student chooses:

CRYPTOGRAPHY  The student chooses:

The student chooses:

FINANCIAL MATHEMATICS  The student chooses:

The student chooses:

COMPUTER INTENSIVE METHODS AND APPLICATIONS (CIMA)  The student chooses:

The student chooses:

Course structure for students enrolled for the first time in the academic year 2018/19 (MS18)
During their studies, students must take a total of 12 courses (three basic and nine elective courses), 4 seminars, and prepare and defend their Master’s Thesis.
A student who chooses the study field Geometry and Applications, in the process of preparing the Master’s Thesis, should pass the comprehensive examination with the chosen mentor; the exam covers the basic mathematical topics in the field of analysis, abstract algebra and geometry.
Short descriptions of courses are available here.
Courses  ECTS 

Basic Course I  6 
Basic Course II  6 
Basic Course III  6 
Elective Course I – Internally Selected  6 
Elective Course II – Internally Selected  6 
Elective Course III – Internally Selected  6 
Elective Course IV – Externally Selected  6 
Elective Course V – Externally Selected  6 
Seminar I  6 
Seminar II  6 
2^{ND} YEAR (60 ECTScredits)
Courses  ECTS 

Elective Course VI – Internally Selected  6 
Elective Course VII – Internally Selected  6 
Elective Course VIII – Internally Selected  6 
Elective Course IX – Externally Selected  6 
Seminar III  6 
Seminar IV  6 
Master’s Thesis  24 
BASIC COURSES
Courses  ECTS  Forms of contact hours  

L  S  T  Total  
Selected Topics in Algebra (1)  6  45    15  60  
Selected Topics in Analysis (1)  6  45    15  60  
Selected Topics in Discrete Mathematics (1)  6  45  15    60  
Selected Topics in Financial Mathematics (1)  6  45  15    60  
Selected Topics in Cryptography (1)  6  45  15    60  
Selected Topics in Mathematical Statistics (1)  6  45  15    60  
Molecular Modeling Course  6  45  15    60  
Selected Topics in Functional Analysis  6  45  15    60  
Mathematical Practicum  6      60  60 
L = lectures, S = seminars, T = tutorials
ECTS = ECTS credits
BASIC COURSES – CORES
Cores  Courses 

General, Theoretical and Discrete Mathematics Core  Selected Topics in Analysis (1) 
Selected Topics in Algebra (1)  
Selected Topics in Discrete Mathematics (1)  
Selected Topics in Functional Analysis  
Probability and Statistics Core  Selected Topics in Mathematical Statistics (1) 
Cryptography Core  Selected Topics in Cryptography (1) 
Financial Mathematics Core  Selected Topics in Financial Mathematics (1) 
Computer Intensive Methods and Applications Core  Molecular Modelling Course 
Geometry and Applications Core  Selected Topics in Algebra (1) 
Selected Topics in Analysis (1)  
Mathematical Practicum 
INTERNALLY SELECTED ELECTIVE COURSES
Courses  ECTS  Forms of contact hours  

L  T  Total  
Algebraic Combinatorics  6  45    45  
Elliptic Curves in Cryptography  6  45    45  
Healthcare Financing  6  45    45  
Groups, Covers and Maps  6  45    45  
Selected Topics in Algebra (2)  6  45    45  
Selected Topics in Partial Differential Equations  6  45    45  
Selected Topics in Discrete Mathematics (2)  6  45    45  
Selected Topics in Complex Analysis  6  45    45  
Selected Topics in Mathematical Statistics (2)  6  45    45  
Selected Topics in Numerical Mathematics  6  45    45  
Selected Topics in Theory of Association Schemes  6  45    45  
Selected Topics in Theory of Finite Geometries  6  45    45  
Selected Topics in Number Theory  6  45    45  
Selected Topics in Topology  6  30  30  60  
Selected Topics in Computing Methods and Applications  6  45    45  
Chaotic Dynamical Systems  6  45    45  
Characters of Finite Groups  6  45    45  
Combined Quantum and Classical Methods for Molecular Simulations  6  45    45  
Mathematical Modelling  6  45    45  
Mathematical Finances in Real Time  6  45    45  
Mathematical Topics in a Foreign Language  6  45    45  
Molecular Dynamics Simulation Methods  6  45    45  
Molecular Graphics  6  45    45  
Symmetry and Traversability in Graphs  6  45    45  
Stochastic Processes  6  45    45  
Game Theory  6  45    45  
Coding Theory  6  45    45  
Theory of Finite Fields  6  45    45  
Measure Theory  6  45    45  
Theory of Permutation Groups  6  45    45  
Introduction to Publickey Cryptography  6  45    45  
Introduction to Symmetriccipher Cryptography  6  45    45  
Probability with Measure (1)  6  45    45  
Probability with Measure (2)  6  45    45  
Probability  6  45    45  
Philosophy  3  30    30  
Geometry and Topology  3  45    45  
Geometric Measure Theory  3  30    30  
Geometric Aspects in Discrete Dynamical Systems  6  30  15  45  
Geometrical Optimization Problems  3  30    30  
Selected Topics in Dynamical Systems  6  45  15  60  
Combinatorial and Convex Geometries  6  45    45  
Lie Groups and Lie Algebras  3  30    30  
Computer Aided Geometric Design  3  30    30  
Project Management  3  30    30  
History and Methodology of the Subject  3  30    30 
INTERNALLY ELECTIVE COURSES – CORES
Cores  Courses 

ALGEBRA Core  Algebraic Combinatorics 
Selected Topics in Algebra (2)  
Selected Topics in Number Theory  
Characters of Finite Groups  
Theory of Finite Fields  
Theory of Permutation Groups  
ANALYSIS Core  Selected Topics in Analysis (2) 
Selected Topics in Complex Analysis  
Selected Topics in Numerical Mathematics  
Selected Topics in Topology  
Chaotic Dynamical Systems  
DISCRETE MATHEMATICS Core  Algebraic Combinatorics 
Groups, Covers and Maps  
Selected Topics in Discrete Mathematics (2)  
Selected Topics in Theory of Association Schemes  
Selected Topics in Theory of Finite Geometries  
Symmetry and Traversability in Graphs  
Theory of Finite Fields  
PROBABILITY AND STATISTICS Core  Selected Topics in Mathematical Statistics (2) 
Mathematical Modelling  
Stochastic Processes  
Probability with Measure (1)  
Probability with Measure (2)  
CRYPTOGRAPHY Core  Algebraic Combinatorics 
Elliptic Curves in Cryptography  
Coding Theory  
Theory of Finite Fields  
Introduction to Publickey Cryptography  
Introduction to Symmetriccipher Cryptography  
FINANCIAL MATHEMATICS Core  Healthcare Financing 
Selected Topics in Mathematical Statistics (1)  
Mathematical Modelling  
Mathematical Finances in Real Time  
Game Theory  
COMPUTER INTENSIVE METHODS AND APPLICATIONS (CIMA) Core  Selected Topics in Discrete Mathematics (1) 
Selected Topics in Numerical Mathematics  
Selected Topics in Computing Methods and Applications  
Combined Quantum and Classical Methods for Molecular Simulations  
Selected Topics in Mathematical Statistics (1)  
Molecular Dynamics Simulation Methods  
Molecular Graphics  
GEOMETRY AND APPLICATIONS Core  Geometry and Topology 
Geometric Measure Theory  
Geometric Aspects in Discrete Dynamical Systems  
Geometrical Optimization Problems  
Selected Topics in Complex Analysis  
Selected Topics in Topology  
Selected Topics in Dynamical Systems  
Combinatorial and Convex Geometries  
Lie Groups and Lie Algebras  
Computer Aided Geometric Design  
History and Methodology of the Subject  
Project Management  
Philosophy 
LIST OF BASIC AND INTERNALLY ELECTIVE COURSES IN THE STUDY FIELDS
Study Field  Basic Courses  Internally Elective Courses 

GENERAL MATHEMATICS  The student chooses:

The student chooses:

THEORETICAL MATHEMATICS  The student chooses:

The student chooses:

DISCRETE MATHEMATICS  The student chooses:

The student chooses:

PROBABILITY AND STATISTICS  The student chooses:

The student chooses:

CRYPTOGRAPHY  The student chooses:

The student chooses:

FINANCIAL MATHEMATICS  The student chooses:

The student chooses:

COMPUTER INTENSIVE METHODS AND APPLICATIONS (CIMA)  The student chooses:

The student chooses:

GEOMETRY AND APPLICATIONS  The student chooses:

The student chooses:

Admission requirements top

completed a firstcycle study programme in any mathematical study field; or

completed a firstcycle 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 firstcycle studies, under training programmes, or by taking examinations prior to enrolment in the study programme Mathematical Sciences.
Applicants having completed a fouryear (singlediscipline or twodiscipline) academic study programme in Mathematics or Mathematicsrelated 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 secondcycle study programme or a prereform 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 nonBologna 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 ECTScredits 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 ECTScredits in courses from the current year of study are required in order to repeat the year.