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 and at all levels of education. It is the foundation of all science and an indispensable tool in the social sciences and economics. As the theoretical core of computer science, its influence is growing in all areas of life that will decisively mark the 21st Century. Among these are modern economics, communications, data security, national security, and the decoding of the human genome and human brain.
The first half of the study year and the second study year are mainly devoted to the learning and consolidation of the fundamentals of analysis, algebra, discrete mathematics and numerical computing.
Along the way, students will learn a set of computer skills and the basics of probability theory. Within the labour market for the financial sector, the latter represents an important advantage for mathematics students versus students who come from management/economyoriented studies. Moreover, the computeroriented courses, along with computeroriented ways of thinking that an individual develops while studying mathematics, provide a good foundation for employment in programming and related companies. The larger part of the study programme represents 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 and biochemistry) combine with computer science and mathematics. Since virtually every science (at the research level) significantly relies on mathematics, mathematics undergraduate studies are also suitable for those who will later shift to other sciences. Proof of this are the numerous personnel in the college who chose this path in pursuing their careers.
Scientific excellence and international integration among our professors allows students to fully pursue their study and research ambitions; inter alia, one of the four global leading research centres for algebraic graph theory operates at UP FAMNIT.
Educational and professional goalstop

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

To learn about a range of specific mathematical areas, in both theoretical mathematics and applied mathematics

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

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

To become acquainted with the basics of probability theory, which is a prerequisite for indepth knowledge of advanced statistical and stochastic topics, especially for those students who wish to pursue careers 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 their studies, students must complete a total of 29 courses (compulsory and elective 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 or Theoretical Mathematics.
All courses are awarded 6 ECTScredits. One ECTScredit encompasses 30 hours of student work. In addition to the student’s presence (at lectures, seminars, inclass and laboratory practical work), this also includes 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 a student’s presence (contact hours).
From the Academic Year 2017/18 changes occurred in the course plan. See below for the link to 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 their studies, students must complete a total of 30 courses (18 compulsory and 12 electives) and prepare a final project.
In 2017 changes occurred in the course plan:

students enrolled for the first time in the 3rd year of study in the academic year 2017/18 have to prepare a final project paper;

while students enrolled for the first time in the 3rd year of study starting from the academic year 2018/19 choose instead a ninth elective course (6 ECTScredits). In the 3rd year of study they have to pass 1 compulsory, 7 internal elective and 2 external elective courses.
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 6 ECTScredits.
The internal 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.
Courses  ECTS  Forms of contact hours  

L  S  T  LW  Total  
Algebra I  Matrix Calculus  6  60    30    90 
Algebra II – Linear Algebra  6  60    30    90 
Analysis I – Foundations of Analysis  6  60    30    90 
Analysis II – Infinitesimal Calculus  6  60    30    90 
Discrete Mathematics I – Set Theory  6  60    30    90 
Discrete Mathematics II – Combinatorics  6  60    30    90 
Mathematical Practicum I  6  45      45  90 
Computer Science I  6  45      45  90 
Computer Practicum  6      30  60  90 
Mathematical Topics in English I  6  60    30    90 
ECTS = ECTS credits
2^{ND} YEAR (60 ECTScredits), MA07
Courses  ECTS  Forms of contact hours  

L  S  T  LW  Total  
Algebra III – Abstract Algebra  6  60    30    90 
Analysis III – Functions of Many Variables  6  60    30    90 
Physics  6  60    30    90 
Introduction to Numerical Calculations  6  60    30    90 
Computer Science II  6  45      45  90 
Probability  6  60    30    90 
Mathematical Topics in English II  6  60    30    90 
Elective course  Internal Elective I  6  
Elective course  Internal Elective II  6  
Elective course  External Elective I  6 
3^{RD} YEAR (60 ECTScredits), MA07
Courses  ECTS  Forms of contact hours  

L  S  T  LW  Total  
Mathematical Modelling  6  60    30    90 
Elective course  Internal Elective III  6  
Elective course  Internal Elective IV  6  
Elective course  Internal Elective V  6  
Elective course  Internal Elective VI  6  
Elective course  Internal Elective VII  6  
Elective course  Internal Elective VIII  6  
Elective course  Internal Elective IX  6  
Elective course  External Elective II  6  
Seminar – Final Project Paper *  6    30      30 
* In 2017 changes occurred in the course plan:
 students enrolled for the first time in the 3rd year of study in the academic year 2017/18 have to prepare a final project paper;
 while students enrolled for the first time in the 3rd year of study starting from the academic year 2018/19 choose instead a third external elective course (6 ECTScredits). In the 3rd year of study they have to pass 1 compulsory, 7 internal elective and 2 external elective courses.
INTERNAL ELECTIVE COURSES (MA07)
(The list shows all internal elective courses of the study programme. Every Academic year, the Faculty offers a different selection of elective courses.)
Courses  ECTS  Forms of contact hours  

L  S  T  LW  Total  
Algebraic Graph Theory  6  45    30    75 
Algebra IV – Algebraic Structures  6  45  30      75 
Analysis IV – Real Analysis  6  45  30      75 
Differential Equations  6  45  30      75 
Functional Analysis  6  45  30      75 
Combinatorics  6  45  30      75 
Geometry  6  45  30      75 
Optimization Methods  6  45  30      75 
Introduction to Statistics  6  45  30      75 
Permutation Groups  6  45  30      75 
Stochastic Processes  6  45  30      75 
Graph Theory  6  45    30    75 
Game Theory  6  45  30      75 
Measure Theory  6  45  30      75 
Topology  6  45  30      75 
Financing the Health System  6  45  30      75 
Selected Topics in Discrete Mathematics  6  45  30      75 
Selected Topics in Computing Methods and Applications  6  45  30      75 
Selected Topics in Statistics  6  45  30      75 
Complex Analysis  6  45  30      75 
Cryptography and Computer Safety  6  45  30      75 
Mathematical Methods in Physics  6  45    30    75 
Mathematics: Methods and Art  6  45  30      75 
Molecular Modelling  6  45  30      75 
Optimization Methods in Logistics  6  45  30      75 
Introduction to Financial Mathematics  6  45  30      75 
Solving Equations: from alKhwarizmi to Galois  6  45  30      75 
Symmetric Codes  6  45  30      75 
Coding Theory  6  45  30      75 
Number Theory  6  45  30      75 
History and Philosophy of Mathematics  6  45    30    75 
Course structure and programe information for students enrolled from 2017/18 (MA17)
During their studies, students must complete a total of 30 courses (21 compulsory, 6 internal and 3 external electives).
Every academic year, the Faculty offers a different selection of elective courses from among the internal elective courses listed below. The Faculty tries to meet student interests within the limits of Faculty resources when the final selection of elective courses for the next academic year is published in July.
The coordinator provides students with guidance when choosing their study field and elective courses after the first year.
The internal courses selected may fall within the field of Computer Science and Mathematics in Economics and Finance. The following courses from the study programme Mathematics in Economics and Finance are also classified as mathematical internal courses: Fundamentals of Insurance, Financial Mathematics, Stochastic processes I, Game Theory.
Students may select 3 out of 9 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)
Courses  ECTS  Forms of contact hours  

L  S  T  LW  Total  
Algebra I  Matrix Calculus  6  60    30    90 
Algebra II – Linear Algebra  6  60    30    90 
Analysis I – Foundations of Analysis  6  60    30    90 
Analysis II – Infinitesimal Calculus  6  60    30    90 
Discrete Mathematics I – Set Theory  6  60    30    90 
Discrete Mathematics II – Combinatorics  6  60    30    90 
Mathematical Practicum I  6  45      45  90 
Computer Science I  6  45      45  90 
Computer Practicum  6      30  60  90 
Mathematical Topics in English I  6  60    30    90 
2^{ND} YEAR (60 ECTScredits), MA17
Courses  ECTS  Forms of contact hours  

L  S  T  LW  Total  
Algebra III – Abstract Algebra  6  60    30    90 
Analysis III – Functions of Many Variables  6  60    30    90 
Physics  6  60    30    90 
Introduction to Numerical Calculations  6  60    30    90 
Computer Science II  6  45      45  90 
Probability  6  60    30    90 
Mathematical Topics in English II  6  60    30    90 
Algebra IV  Algebraic Structures  6  45  30      75 
Analysis IV  Real Analysis  6  45  30      75 
Elective Course  External Elective I  6 
3^{RD} YEAR (60 ECTScredits), MA17
Courses  ECTS  Forms of contact hours  

L  S  T  LW  Total  
Mathematical Modelling  6  60    30    90 
Statistics  6  45  30      75 
Elective Course  Internal Elective I  6  
Elective Course  Internal Elective II  6  
Elective Course  Internal Elective III  6  
Elective Course  Internal Elective IV  6  
Elective Course  Internal Elective V  6  
Elective Course  Internal Elective VI  6  
Elective Course  External Elective II  6  
Elective Course  External Elective III  6  
(The list shows all internal elective courses of the study programme. Every academic year, the Faculty offers a different selection of elective courses.)
Courses  ECTS  Forms of contact hours  

L  S  T  LW  Total  
Algebraic Graph Theory  6  45    30    75 
Differential Equations  6  45  30      75 
Functional Analysis  6  45  30      75 
Combinatorics  6  45  30      75 
Geometry  6  45  30      75 
Optimization Methods  6  45  30      75 
Permutation Groups  6  45  30      75 
Graph Theory  6  45    30    75 
Measure Theory  6  45  30      75 
Topology  6  45  30      75 
Financing the Health System  6  45  30      75 
Selected Topics in Discrete Mathematics  6  45  30      75 
Selected Topics in Computing Methods and Applications  6  45  30      75 
Selected Topics in Statistics  6  45  30      75 
Complex Analysis  6  45  30      75 
Cryptography and Computer Safety  6  45  30      75 
Mathematical Methods in Physics  6  45    30    75 
Mathematics: Methods and Art  6  45  30      75 
Molecular Modelling  6  45  30      75 
Optimization Methods in Logistics  6  45  30      75 
Solving Equations: from alKhwarizmi to Galois  6  45  30      75 
Symmetric Codes  6  45  30      75 
Coding Theory  6  45  30      75 
Number Theory  6  45  30      75 
History and Philosophy of Mathematics  6  45    30    75 
Financial Mathematics (study programme Mathematics in Economics and Finance)  6  
Stochastic Processes I (study programme Mathematics in Economics and Finance)  6  
Fundamentals of Insurance (study programme Mathematics in Economics and Finance)  6  
Game Theory (study programme Mathematics in Economics and Finance)  6 
Study fieldstop
After the first year, students decide which study field they 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 programme, apart from 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 within the limits of the Faculty’s resources. The final selection of elective courses for the next Academic year is published in July. The coordinator will help guide students when choosing their study field and elective courses after the first year.
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, apart from 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):

Discrete Mathematics (courses core): 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, 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 the 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):

Discrete Mathematics (courses core): 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  insofar as 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 the 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 the 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

other conditions have also been met, in accordance with the Criteria for Transferring between Study Programmes (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 the case of enrolment limitations, 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 in the next year. The student is obliged to submit a formal written request to the Study Committee. Progress to the next year may be approved if a student could not fulfil the obligations for justifiable reasons. Students may only repeat a year once during their study period.
Requirements for the Completion of Studies
Students shall be deemed to have completed their studies when they fulfil all the prescribed study requirements for 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 factors related to the discipline of mathematics

Critical assessment of developments in the field of mathematics

Development of communication skills

Skills of cooperation, team work and project work

The ability to independently seek knowledge and to integrate it with 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 in mathematics have abundant employment possibilities. Their studies will provide them with knowledge and skills that are indispensable for work and promotion in any field, and more specifically with opportunities for employment in business and research fields, 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), and Gambling Theory (lottery, sports lottery), as well as in the field of education.