Mathematics
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Math department's yearly report:
Report 2014
Report 2013
Report 2012
Report 2011
General information
Name of the programme: Mathematics
Type of programme: academic, 1st bologna cycle
Degree awarded: "diplomirani matematik (UN)" equiv. to B.Sc. in Mathematics
Duration: 3 years (6 semesters)
ECTScredits: 180
Programme structure: 29 courses (11 electives) and final project paper (6 ECTS)
Mode of study: fulltime
Language of study: Slovene, English
Programme coordinatortop
For information regarding application, enrolment and other administrative procedures please contact Student Services.
About the programmetop
Mathematics is the only universal language of interpersonal communication, which is present everywhere in the world at all levels of education. It is the foundation of all science and an indispensable tool in the social sciences and economics. Being also the theoretical core of computer science, its influence is growing in all areas of life that will decisively mark the 21st Century. Among them are modern economics, communications, data security, national security, the decoding of the human genome and human brain, etc.
The first half of the study year and the second study year are mainly devoted to learning and consolidation of the fundamentals of analysis, algebra, discrete mathematics and numerical computing.
Along the way the students will learn a set of computer skills and the basics of probability theory. On the labour market within the financial sector, the latter represents an important advantage of mathematical students versus the students which come from management/economy oriented studies. Moreover, the computer oriented courses and ways of thinking that an individual develops while studying mathematics provides a good farewell for employment in programming and related companies. The larger part of the study programme represent elective courses where students learn about various specific areas of pure and applied mathematics. An optional part of the curriculum also has an interdisciplinary outline, which means that students can choose courses where the natural sciences (especially biology, biochemistry) combine with computer science and mathematics. Since virtually every science (at the research level) significantly relies on mathematics, the mathematics undergraduate studies are also suitable for those who will later shift to other sciences. The proof of this is the numerous personnel at the college, which in pursuing their career chose this kind of way.
Scientific excellence and international integration of our professors allows the students to fully pursue their study and research ambitions, inter alia, at UP FAMNIT operates one of the four global leading research centres for algebraic graph theory.
Educational and professional goalstop

To learn and strengthen the foundations of basic areas of mathematics, which are necessary for understanding of specific areas.

To learn about a range of specific mathematical areas, both in theoretical mathematics as well as in applied mathematics.

To learn the "problem solving" way of thinking that distinguishes mathematics and is indispensable in all sciences, economy and everyday life.

To attain a structured way of thinking and a variety of computer skills, which are the foundation for students who after graduation enter the software sector.

To become acquainted with the basics of probability theory, which is a prerequisite for an indepth knowledge of advanced statistical and stochastic topics especially for those students who wish to pursue their career in the financialinsurancebanking sector.

To recognize the connections between different mathematical theories and other natural and social sciences.

To introduce the best students to the research content of individual mathematical disciplines.
Course structuretop
During the studies, students must complete altogether 29 courses (compulsory and electives courses) and prepare a final project. On completing the 1^{st} year, students can opt for one of the following seven study fields: Discrete Mathematics, Financial Mathematics, Cryptography, Computer intensive methods and applications, Statistics, General Mathematics and Theoretical Mathematics.
All courses are awarded with 6 ECTScredits. One ECTScredit encompasses 30 hours of student work. In addition to the student’s presence (at Lecturers, Seminars, Practical Work: inclass, and Practical Work: laboratory) includes also independent work (literature study, preparation for examinations, home assignments, seminar and project work, etc.). The courses require a minimum of 75 and a maximum of 90 hours of student’s presence (contact hours).
From the Academic Year 2017/18 changes of the course plan occurred. Find below the information regarding course structure, elective courses and programme information for 2017/18 marked as Course plan 2017/18 – (MA17).
Course structure and programe information for students enrolled 2007/08 – 2016/17 (MA07)
During the studies, students must complete altogether 29 courses (18 compulsory and 11 electives) and prepare a final project. On completing the 1^{st} year, students can opt for one of the following seven study fields: Discrete Mathematics, Financial Mathematics, Cryptography, Computer intensive methods and applications, Statistics, General Mathematics and Theoretical Mathematics. From the above description it is evident that the study programme provides for a large scope of selectivity. All courses are awarded with 6 ECTScredits. One ECTScredit encompasses 30 hours of student work. In addition to the student’s presence (at Lecturers, Seminars, Practical Work: inclass, and Practical Work: laboratory) includes also independent work (literature study, preparation for examinations, home assignments, seminar and project work, etc.). The courses require a minimum of 75 and a maximum of 90 hours of student’s presence (contact hours).
The internally courses selected may fall within the field of Computer Science.
The student may select 2 out of 11 elective courses from study programmes provided by other institutions of higher education in Slovenia and internationally.
Short descriptions of courses are available here.
Course structure and programe information for students enrolled 2007/08  2016/17
Courses  ECTS 

Algebra I  Matrix Calculus  6 
Algebra II – Linear Algebra  6 
Analysis I – Foundations of Analysis  6 
Analysis II – Infinitesimal Calculus  6 
Discrete Mathematics I – Set Theory  6 
Discrete Mathematics II – Combinatorics  6 
Mathematical Practicum I  6 
Computer Science I  6 
Computer Practicum  6 
Mathematical Topics in English I  6 
2^{ND} YEAR (60 ECTScredits)
Courses  ECTS 

Algebra III – Abstract Algebra  6 
Analysis III – Functions of Many Variables  6 
Physics  6 
Introduction to Numerical Calculations  6 
Computer Science II  6 
Probability  6 
Mathematical Topics in English II  6 
Elective courses  18 
Courses  ECTS 

Mathematical Modelling  6 
Elective courses  48 
Seminar – Final Project Paper  6 
ELECTIVE COURSES
Courses  ECTS 

Algebraic Graph Theory  6 
Algebra IV – Algebraic Structures  6 
Analysis IV – Real Analysis  6 
Differential Equations  6 
Financing the Health System  6 
Functional Analysis  6 
Selected Topics in Discrete Mathematics  6 
Selected Topics in Computing Methods and Applications  6 
Selected Topics in Statistics  6 
Combinatorics  6 
Complex Analysis  6 
Geometry  6 
Cryptography and Computer Safety  6 
Mathematical Methods in Physics  6 
Mathematics: Methods and Art  6 
Molecular Modelling  6 
Optimization Methods  6 
Optimization Methods in Logistics  6 
Introduction to Financial Mathematics  6 
Introduction to Statistics  6 
Permutation Groups  6 
Solving Equations: from alKhwarizmi to Galois  6 
Symmetric Codes  6 
Stochastic Processes  6 
Graph Theory  6 
Game Theory  6 
Coding Theory  6 
Measure Theory  6 
Number Theory  6 
Topology  6 
History and Philosophy of Mathematics  6 
Course structure and programe information for students enrolled from 2017/18 (MA17)
During the studies, students must complete altogether 29 courses (21 compulsory, 6 internal and 2 external electives) and prepare a final project.
Every Academic year the faculty offers a different selection of elective courses from the internal elective courses listed below. The faculty tries to meet student interests and faculty’s resource’s limitations when the final selection of elective courses for next Academic year is published in July.
The coordinator will help students and give them guidance after the first year when choosing the study field and elective courses.
The internally courses selected may fall within the field of Computer Science and Mathematic in Economics and Finance. As mathematical internal courses are also classified the following courses from the study programme Mathematics in Economics and Finance: Fundamentals of Insurance, Financial Mathematics, Stochastic processes I, Game Theory.
The student may select 2 out of 8 elective courses from study programmes provided by other institutions of higher education in Slovenia and internationally.
Short descriptions of courses are available here: Description of courses (MA  17)
Course structure and programe information for students enrolled from 2017/18Courses  ECTS 

Algebra I  Matrix Calculus  6 
Algebra II – Linear Algebra  6 
Analysis I – Foundations of Analysis  6 
Analysis II – Infinitesimal Calculus  6 
Discrete Mathematics I – Set Theory  6 
Discrete Mathematics II – Combinatorics  6 
Mathematical Practicum I  6 
Computer Science I  6 
Computer Practicum  6 
Mathematical Topics in English I  6 
2^{ND} YEAR (60 ECTScredits)
Courses  ECTS 

Algebra III – Abstract Algebra  6 
Analysis III – Functions of Many Variables  6 
Physics  6 
Introduction to Numerical Calculations  6 
Computer Science II  6 
Probability  6 
Mathematical Topics in English II  6 
Algebra IV  Algebraic Structures  6 
Analysis IV  Real Analysis  6 
External elective course  6 
3^{RD} YEAR (60 ECTScredits)
Courses  ECTS 

Mathematical Modelling  6 
Statistics  6 
Internal elective courses  36 
External elective course  6 
Seminar – Final Project Paper  6 
INTERNAL ELECTIVE COURSES
Courses  ECTS 

Algebraic Graph Theory  6 
Differential Equations  6 
Financing the Health System  6 
Functional Analysis  6 
Selected Topics in Discrete Mathematics  6 
Selected Topics in Computing Methods and Applications  6 
Selected Topics in Statistics  6 
Combinatorics  6 
Complex Analysis  6 
Geometry  6 
Cryptography and Computer Safety  6 
Mathematical Methods in Physics  6 
Mathematics: Methods and Art  6 
Molecular Modelling  6 
Optimization Methods  6 
Optimization Methods in Logistics  6 
Permutation Groups  6 
Solving Equations: from alKhwarizmi to Galois  6 
Symmetric Codes  6 
Graph Theory  6 
Coding Theory  6 
Measure Theory  6 
Number Theory  6 
Topology  6 
History and Philosophy of Mathematics  6 
Study fieldstop
After first year, the student decides which study field he/she would like to follow. There are seven study fields: Discrete Mathematics, Financial Mathematics, Cryptography, Computer intensive methods and applications, Statistics, General Mathematics and Theoretical Mathematics.
Every study field in the study program, aside for the study field of General Mathematics, belongs to a subject core (i.e. Discrete Mathematics Core, Financial Mathematics Core, Cryptography Core, Computer Intensive Methods and Applications Core, Statistics Core or Theory of Mathematics Core) as shown below.
Every Academic year the faculty offers a different selection of elective courses from the internal elective courses listed. The faculty tries to meet student interests and faculty’s resource’s limitations when the final selection of elective courses for next Academic year is published in July. The coordinator will help students and give them guidance after the first year when choosing the study field and elective courses.
From the Academic year 2017/18 changes of the course plan occurred. Find below the information regarding elective courses and programme fields for 2017/18 marked as Study fields and internal elective courses for students enrolled from 2017/18 (MA17).
Study fields and internal elective courses for students enrolled 2007/08  2016/17 (MA07)
After first year, the student decides which study field he/she would like to follow. There are seven study fields: Discrete Mathematics, Financial Mathematics, Cryptography, Computer intensive methods and applications, Statistics, General Mathematics and Theoretical Mathematics.
Based on this decision the student then chooses elective courses. These must include at least 6 mathematical subjects, 4 of which must be from the core of subjects which belong to the chosen study field (i.e. a student which decides to specialize in statistics must choose at least 4 subjects from the Statistics core).
The study field General Mathematics is an exception in the sense that the student can choose 6 of his/her favourite mathematical subjects.
Every study field in the study program, aside for the study field of General Mathematics, belongs to a subject core (i.e. Discrete Mathematics Core, Financial Mathematics Core, Cryptography Core, Computer Intensive Methods and Applications Core, Statistics Core or Theory of Mathematics Core) as shown in the following table:
STUDY FIELDS AND INTERNAL ELECTIVE COURSES (MA07)
Courses Cores  Courses 

DISCRETE MATHEMATICS  Algebraic Graph Theory 
Selected Topics from Discrete Mathematics  
Finite Geometries  
Optimization Methods  
Graph Theory  
FINANCIAL MATHEMATICS  Introduction to Financial Mathematics 
Programming III Concurrent Programming  
Game Theory  
Financing the Health System  
Introduction to Statistics  
CRIPTOGRAPHY  Algebra IV Algebraic Structures 
Cryptography and Computer Safety  
Symmetric Codes  
Coding Theory  
Number Theory  
COMPUTER INTENSIVE METHODS AND APPLICATIONS 
Differential Equations 
Mathematical Methods in Physics  
Molecular Modelling  
Selected Topics in Computing Methods and Applications  
Introduction to Bioinformatics  
STATISTICS  Combinatorics 
Programming III Concurrent Programming  
Introduction to Statistics  
Selected Topics from Statistics  
Stochastic Processes  
THEORETICAL MATHEMATICS  Algebra IV Algebraic Structures 
Analysis IV Real Analysis  
Functional Analysis  
Permutation Groups  
Number Theory  
Topology 
Study fields and internal elective courses for students enrolled from 2017/18 (MA17)
After first year, the student decides which study field he/she would like to follow. There are seven study fields: Discrete Mathematics, Financial Mathematics, Cryptography, Computer intensive methods and applications, Statistics, General Mathematics and Theoretical Mathematics. Every study field in the study program, aside for the study field of General Mathematics, belongs to a subject core (i.e. Discrete Mathematics Core, Financial Mathematics Core, Cryptography Core, Computer Intensive Methods and Applications Core, Statistics Core or Theory of Mathematics Core) as shown in the following table.
Every Academic year the faculty offers elective courses from the field of General Mathematics. If the student would like to follow onother study field (after 1^{st} year) and consequently select the elective courses of the belonging subject core he/she has to consult the coordinator before the enrolment in next year.
Based on this decision the student then chooses internal elective courses. These must include at least 5 mathematical subjects, 4 of which must be from the core of subjects which belong to the chosen study field (i.e. a student which decides to specialize in statistics must choose at least 4 subjects from the Statistics core). The study field General Mathematics is an exception in the sense that the student can choose 5 of his/her favourite mathematical subjects.
As mathematical internal courses are also classified the following courses from the study programme Mathematics in Economics and Finance: Fundamentals of Insurance, Financial Mathematics, Stochastic processes I, Game Theory.
STUDY FIELDS AND INTERNAL ELECTIVE COURSES (MA17)
Courses Cores  Courses 

DISCRETE MATHEMATICS  Algebraic Graph Theory 
Selected Topics from Discrete Mathematics  
Finite Geometries  
Optimization Methods  
Graph Theory  
FINANCIAL MATHEMATICS  Financial Mathematics 
Programming III Concurrent Programming  
Game Theory  
Financing the Health System  
CRIPTOGRAPHY  Cryptography and Computer Safety 
Symmetric Codes  
Coding Theory  
Number Theory  
COMPUTER INTENSIVE METHODS AND APPLICATIONS 
Differential Equations 
Mathematical Methods in Physics  
Molecular Modelling  
Selected Topics in Computing Methods and Applications  
Introduction to Bioinformatics  
STATISTICS  Combinatorics 
Programming III Concurrent Programming  
Selected Topics from Statistics  
Stochastic Processes  
THEORETICAL MATHEMATICS  Functional Analysis 
Permutation Groups  
Number Theory  
Topology 
Admission requirementstop
Admission to the first year of study shall be granted to applicants having:

passed the matura examination; or

passed the vocational matura examination (poklicna matura) and a final examination in the matura subject Mathematics, in so far the aforementioned subjects have already been taken within the framework of the vocational matura examination, applicants must pass any other matura subject; or

successfully completed any fouryear secondaryschool programme before 1 June 1995.
In case of enrolment limitations, applicants shall be selected in accordance with the following criteria:

applicants under Point a) shall be selected on the basis of:

overall matura results (60%),

overall results in the 3^{rd} and 4^{th} year of secondary school (20%),

results in the subject Mathematics in the 3^{rd} and 4^{th} year of secondary school (20%),


applicants under Point b) shall be selected on the basis of:

overall vocational matura results (30%),

overall results in the 3^{rd} and 4^{th} year of secondary school (30%),

results in the subject Mathematics in the 3^{rd} and 4^{th} year of secondary school (20%),

results in the additional matura subject examination (20%),


applicants under Point c) shall be selected on the basis of:

overall final examination results (60%),

overall results in the 3^{rd} and 4^{th} year of secondary school (20%),

results in the subject Mathematics in the 3^{rd} and 4^{th} year of secondary school (20%).

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.
Access to Year 2 or Year 3 of the study programme of Mathematics on the basis of the Criteria for Transferring between Study Programmes is granted to students of a related firstcycle study programme or a prereform undergraduate study 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 Mathematics;

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 Mathematics; and

other conditions in accordance with the Criteria for Transferring between Study Programmes have also been met (a comparable course structure, course requirements completed).
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.
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 Mathematics.
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
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 year only once during their study period.
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 180 ECTScredits. Students must obtain a positive assessment for the Final Project Paper completed within the framework of the Seminar.
Graduate competenciestop
General competencies

The ability to analyze, synthesize and predict solutions and consequences of the factors related to the discipline of mathematics.

Critical assessment of the developments in the field of mathematics.

Development of communication skills.

Skills of cooperation, team work and project work.

The ability to autonomously seek knowledge and to integrate it with the existing knowledge.

The ability to seek and interpret new information and to place it into the context of the discipline of mathematics.

Autonomy in professional work.
Subjectspecific competencies

The ability to describe a given situation with the correct use of mathematical symbols and notations.

The ability to explain their own understanding of mathematical concepts and principles.

The ability to solve mathematical and other problems with the use of modern technology.

The ability to use the algorithmic approach  to solve a given problem by developing an algorithm.

The ability to perform a numerical, graphical and algebraic analysis of a given problem.

The ability to deduce new logical conclusions from the information given.

The ability to tackle a given mathematical problem with confidence and find its solution.
Graduate employment opportunitiestop
Graduates have abundant employment possibilities. The study will provide them with the knowledge indispensable for work and promotion, as well as opportunities for employment in the pedagogical and research field, e.g.: 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.