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: Master's, 2nd Bologna cycle
Degree awarded: "magister matematike" equiv. to Master's degree in Mathematics
Duration: 2 years (4 semesters)
ECTS-credits: 120
Programme structure: 9 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)

Programme coordinatortop

Prof. Bojan Kuzma, PhD

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

About the programmetop

 
Welcome to Famnit

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.

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 in-depth study of a selected professional field (which may be selected at any university that has introduced the ECTS system).

Short descriptions of courses are available here.

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 MS-07 and MS-18.

Course structure for students enrolled in the academic years 2007/08 - 2017/18 (MS-07)

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.

1ST YEAR (60 ECTS-credits)
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
 
 2ND YEAR (60 ECTS-credits)
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 Public-key Cryptography 9 / 6
Introduction to Symmetric-cipher Cryptography 9 / 6
Probability with Measure (1) 9 / 6
Probability with Measure (2) 9 / 6
Probability 9 / 6
* The student may also select Internally Elective Courses from the list of Internally Elective Courses. However, in this case the courses will be awarded with 6 ECTS-credits (reduced study obligation).

 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 Public-key Cryptography
Introduction to Symmetric-cipher 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:
  • two basic courses from the cores of General, Theoretical or Discrete Mathematics
The student chooses:
  • internally elective courses (student’s choice)
THEORETICAL MATHEMATICS The student chooses:
  • two basic courses from the cores of General, Theoretical or Discrete Mathematics
The student chooses:
  • two internally elective courses from the Analysis core
  • two internally elective courses from the Algebra core
DISCRETE MATHEMATICS The student chooses:
  • two basic courses from the cores of General, Theoretical or Discrete Mathematics
The student chooses:
  • two internally elective courses from the Discrete Mathematics core
  • two internally elective courses (student’s choice)
PROBABILITY AND STATISTICS The student chooses:
  • one basic course from the cores of General, Theoretical or Discrete Mathematics
  • one basic course from the Probability and Statistics core
The student chooses:
  • two internally elective courses from the Probability and Statistics core
  • two internally elective courses (student’s choice)
CRYPTOGRAPHY The student chooses:
  • one basic course from the cores of General, Theoretical or Discrete Mathematics
  • one basic course from the Cryptography core
The student chooses:
  • two internally elective courses from the Cryptography core
  • two internally elective courses (student’s choice)
FINANCIAL MATHEMATICS The student chooses:
  • one basic course from the cores of General, Theoretical or Discrete Mathematics
  • one basic course from the Financial Mathematics core
The student chooses:
  • two internally elective courses from the Financial Mathematics core
  • two internally elective courses (student’s choice)
COMPUTER INTENSIVE METHODS AND APPLICATIONS (CIMA) The student chooses:
  • one basic course from the cores of General, Theoretical or Discrete Mathematics
  • one basic course from the CIMA core
The student chooses:
  • two internally elective courses from the CIMA core
  • two internally elective courses (student’s choice)

Course structure for students enrolled for the first time in the academic year 2018/19 (MS-18)

During their studies, students must take a total of 12 courses (three basic and nine electives), 4 seminars, and prepare and defend their Master’s Thesis.

1ST YEAR (60 ECTS-credits)
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
 
 2ND YEAR (60 ECTS-credits)
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
 Selected Topics in Algebra (1) 6
 Selected Topics in Analysis (1) 6
 Selected Topics in Discrete Mathematics (1) 6
 Selected Topics in Financial Mathematics (1) 6
 Selected Topics in Cryptography (1) 6
 Selected Topics in Mathematical Statistics (1) 6
 Molecular Modeling Course 6
 Selected Topics in Functional Analysis 6

 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 6
Elliptic Curves in Cryptography 6
Healthcare Financing 6
Groups, Covers and Maps 6
Selected Topics in Algebra (2) 6
Selected Topics in Differential Equations 6
Selected Topics in Discrete Mathematics (2) 6
Selected Topics in Complex Analysis 6
Selected Topics in Mathematical Statistics (2) 6
Selected Topics in Numerical Mathematics 6
Selected Topics in Theory of Association Schemes 6
Selected Topics in Theory of Finite Geometries 6
Selected Topics in Number Theory 6
Selected Topics in Topology 6
Selected Topics in Computing Methods and Applications 6
Chaotic Dynamical Systems 6
Characters of Finite Groups 6
Combined Quantum and Classical Methods for Molecular Simulations 6
Mathematical Modelling 6
Mathematical Finances in Real Time 6
Mathematical Topics in a Foreign Language 6
Molecular Dynamics Simulation Methods 6
Molecular Graphics 6
Symmetry and Traversability in Graphs 6
Stochastic Processes 6
Game Theory 6
Coding Theory 6
Theory of Finite Fields 6
Measure Theory 6
Theory of Permutation Groups 6
Introduction to Public-key Cryptography 6
Introduction to Symmetric-cipher Cryptography 6
Probability with Measure (1) 6
Probability with Measure (2) 6
Probability 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 Public-key Cryptography
Introduction to Symmetric-cipher 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:
  • two basic courses from the cores of General, Theoretical or Discrete Mathematics
The student chooses:
  • internally elective courses (student’s choice)
THEORETICAL MATHEMATICS The student chooses:
  • two basic courses from the cores of General, Theoretical or Discrete Mathematics
The student chooses:
  • two internally elective courses from the Analysis core
  • two internally elective courses from the Algebra core
DISCRETE MATHEMATICS The student chooses:
  • two basic courses from the cores of General, Theoretical or Discrete Mathematics
The student chooses:
  • two internally elective courses from the Discrete Mathematics core
  • two internally elective courses (student’s choice)
PROBABILITY AND STATISTICS The student chooses:
  • one basic course from the cores of General, Theoretical or Discrete Mathematics
  • one basic course from Probability and Statistics core
The student chooses:
  • two internally elective courses from the Probability and Statistics core
  • two internally elective courses (student’s choice)
CRYPTOGRAPHY The student chooses:
  • one basic course from the cores of General, Theoretical or Discrete Mathematics
  • one basic course from the Cryptography core
The student chooses:
  • two internally elective courses from the Cryptography core
  • two internally elective courses (student’s choice)
FINANCIAL MATHEMATICS The student chooses:
  • one basic course from the cores of General, Theoretical or Discrete Mathematics
  • one basic course from the Financial Mathematics core
The student chooses:
  • two internally elective courses from the Financial Mathematics core
  • two internally elective courses (student’s choice)
COMPUTER INTENSIVE METHODS AND APPLICATIONS (CIMA) The student chooses:
  • one basic course from the cores of General, Theoretical or Discrete Mathematics
  • one basic course from the CIMA core
The student chooses:
  • two internally elective courses from the CIMA core
  • two internally elective courses (student’s choice)

Admission requirements  top

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.