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 studies are intended for those students who want to upgrade their knowledge acquired at the previous level.

The courses are based in a way that after they finish, they have more opportunities to choose from: continuation with doctoral studies, employment in the industry or public sector or switching to other sciences, well equipped with the acquired knowledge.

Mostly, the courses are elective and they cover various topical mathematical areas. Of course, detailed understanding of these issues requires some certain prior knowledge of basic mathematical concepts that students learn at the undergraduate studies. Depending on the student's enthusiasm, skills, interests and his ambitions/plans for the future, the student can be introduced in the research mathematics. The latter mainly depends on the help of a supervisor for the master's thesis. There are also some courses from the applied mathematics, which are particularly suitable for the students interested in the financial sector and the second economy.

Educational and professional goals  top

  • To gain and consolidate the in-depth knowledge of the special mathematic areas.
  • The students who intend to continue their study at the doctoral programme are gradually introduced with the research mathematics.
  • The students focused on the economy gain some specific knowledge of the applied mathematics. For example, for those interested in the financial and insurance-banking sector, particularly important are the courses from probability and statistics.
  • To provide students with a thorough understanding of Mathematics; to demonstrate the importance of analytical thought and argumentation, as well as usefulness of various mathematical problem-solving methods.
  • Students will develop and learn to employ mathematical thinking, reasoning and argumentation in diverse mathematical areas. 
  • Students will learn to recognise the connections between different mathematical theories and other natural and social sciences.
  • Students will develop both the capacity to analyse given data in the sense of reaching new conclusions and the sense of teamwork in problem-solving.
  • Students will learn to employ modern technological tools (e.g. calculators, PCs, graphoscopes, projectors, etc.) in solving and demonstrating mathematical problems and concepts.

Course structure top

During the studies, students must take altogether 9 courses (two basic and seven electives), 4 seminars and prepare as well as defend their Master’s Thesis. 

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 the study programmes at other faculties; however, the student may also select a course from among internal courses as their Externally Elective Course. No less than one elective course must be mathematical, and must also be delivered in a foreign language, normally English. 

After the first year, the student decides which study field he/she would like to follow.  Students can opt for one of the following seven study fields (study field): Discrete Mathematics, Financial Mathematics, Cryptography, Computer Intensive Methods and Applications, Probability and Statistics, General Mathematics and Theoretical Mathematics. Based on this decision the student then chooses elective courses.   

Every study field in the study program, aside for the study field of General Mathematics, belongs to a subject core (see the table below). The two basic courses and four internally elective courses student chooses in respect of the selected study field, while the three externally elective courses provide students with the opportunity to expand their knowledge in the selected fields within 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 having introduced the ECTS system). 

Short descriptions of courses are available here.

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 Diferential 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 Foreign Language 9 / 6
Molecular Dynamics Simulation Methods 9 / 6
Molecular Graphics 9 / 6
Computer Security 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 select Internally Elective Courses also 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)
Computer Security
Mathematical Modelling
Stochastic Processes
Probability with Measure (1)
Probability with Measure (2)
CRYPTOGRAPHY Core Algebraic Combinatorics
Elliptic Curves in Cryptography
Computer Security
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)
Computer Security
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 WITH REGARD TO THE STUDY FIELD
Study Field Basic Courses Internally Elective Courses
GENERAL MATHEMATICS The student chooses:
  • two basic courses from the core General, Theoretical or Discrete Mathematics
The student chooses:
  • internally elective courses (student’s choice)
THEORETICAL MATHEMATICS The student chooses:
  • two basic courses from the core General, Theoretical or Discrete Mathematics
The student chooses:
  • two internally elective courses from the core Analysis
  • two internally elective courses from the core Algebra
DISCRETE MATHEMATICS The student chooses:
  • two basic courses from the core General, Theoretical or Discrete Mathematics
The student chooses:
  • two internally elective courses from the core Discrete Mathematics
  • two internally elective courses (student’s choice)
PROBABILITY AND STATISTICS The student chooses:
  • one basic course from the core General, Theoretical or Discrete Mathematics
  • one basic course from the core Probability and Statistics
The student chooses:
  • two internally elective courses from the core Probability and Statistics
  • two internally elective courses (student’s choice)
CRYPTOGRAPHY The student chooses:
  • one basic course from the cores General, Theoretical or Discrete Mathematics
  • one basic course from the core Cryptography
The student chooses:
  • two internally elective courses from the core Cryptography
  • two internally elective courses (student’s choice)
FINANCIAL MATHEMATICS The student chooses:
  • one basic course from the cores General, Theoretical or Discrete Mathematics
  • one basic course from the core Financial Mathematics
The student chooses:
  • two internally elective courses from the core Financial Mathematics
  • two internally elective courses (student’s choice)
COMPUTER INTENSIVE METHODS AND APPLICATIONS (CIMA) The student chooses:
  • one basic course from the cores General, Theoretical or Discrete Mathematics
  • one basic course from the core CIMA
The student chooses:
  • two internally elective courses from the core CIMA
  • 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 of any mathematical study field; or
  • completed a first-cycle study programme of other professional fields, provided that they have, prior to enrolment, fulfilled all study obligations that are deemed essential for the continuation of studies and accumulate 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 (transfers between the programmes). The Senate of the Faculty has the authority to impose mandatory study obligations on individuals applying for transfer, based on their qualifications. 

In 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 the student has 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 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

Advancement Requirements: 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 have a possibility to 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: A student shall be deemed to have completed his/her studies when he/she fulfils all the prescribed study requirements to a total of 120 ECTS-credits. 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. The student publicly presents 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 field of education and research. Graduates can also opt for professional careers not directly related to Mathematics, as the acquired skills of logical reasoning, deliberation, assessment of procedures and results, including analytical approach to problem-solving, also represent the qualities indispensable for executive workers in numerous branches of economy.