Mathematics

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)
ECTS-credits: 180
Programme structure: 30 courses (9 electives)
Mode of study: full-time
Language of study: Slovene, English

Programme coordinatortop

Prof. Marko Orel, PhD

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-/economy-oriented studies. Moreover, the computer-oriented courses, along with computer-oriented 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 in-depth knowledge of advanced statistical and stochastic topics, especially for those students who wish to pursue careers in the financial-insurance-banking 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 30 courses (21 compulsory and 9 elective courses).

On completing the 2^nd year, students decide which study field they would like to follow.

All courses are awarded 6 ECTS-credits. One ECTS-credit encompasses 30 hours of student work. In addition to the student’s presence (at lectures, seminars,  in-class 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 45 and a maximum of 75 hours of a student’s presence (contact hours).

Based on the chosen study field 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.

Short descriptions of courses are available - HERE.

Year of study	Study obligation	Number	ECTS-credits (ECTS)
			ECTS	ECTS/Year of study
1.	Compulsory Course	10	60	60
2.	Compulsory Course	8	48	60
	Internal Elective Course	1	6
	External Elective Course	1	6
3.	Compulsory Course	2	12	60
	Internal Elective Course	6	36
	External Elective Course	2	12

No.	Course	ECTS	Form of contact hour
			L	T	SE	LW	Total
1.	Algebra I - Matrix Calculus	6	45	30	-	-	75
2.	Algebra II – Linear Algebra	6	45	30	-	-	75
3.	Analysis I – Foundations of Analysis	6	45	30	-	-	75
4.	Analysis II – Infinitesimal Calculus	6	45	30	-	-	75
5.	Discrete Mathematics II – Combinatorics	6	45	30	-	-	75
6.	Mathematical Practicum I	6	-	15	-	30	45
7.	Computer Practicum	6	-	30	-	30	60
8.	Computer Science I	6	45	-	-	30	75
9.	Discrete Mathematics I – Set Theory	6	45	30	-	-	75
10.	Mathematical Topics in English I	6	45	30	-	-	75

Legend:
L = lecture, T = tutorial, SE = seminar, LW = laboratory work
ECTS = ECTS-credits

No.	Course	ECTS	Form of contact hour
			L	T	SE	LW	Total
1.	Algebra III – Abstract Algebra	6	45	30	-	-	75
2.	Analysis III – Functions of Many Variables	6	45	30	-	-	75
3.	Physics	6	45	30	-	-	75
4.	Introduction to Numerical Calculations	6	45	30	-	-	75
5.	Computer Science II	6	45	-	-	30	75
6.	Probability	6	45	30	-	-	75
7.	Algebra IV - Algebraic Structures	6	45	-	30	-	75
8.	Analysis IV - Real Analysis	6	45	-	30	-	75
9.	Internal Elective Course I *	6
10.	External Elective Course I	6

No.	Course	ECTS	Form of contact hour
			L	T	SE	LW	Total
1.	Mathematical Modelling	6	45	30	-	-	75
2.	Statistics	6	45	-	30	-	75
3.	Internal Elective Course II	6
4.	Internal Elective Course III	6
5.	Internal Elective Course IV	6
6.	Internal Elective Course V	6
7.	Internal Elective Course VI	6
8.	Internal Elective Course VII	6
9.	External Elective Course II	6
10.	External Elective Course III	6

No.	Course	ECTS	Form of contact hour
			L	T	SE	LW	Total
1.	Algebraic Graph Theory	6	45	15	-	-	60
2.	Differential Equations	6	45	-	15	-	60
3.	Functional Analysis	6	45	-	15	-	60
4.	Combinatorics	6	45	-	15	-	60
5.	Geometry	6	45	-	15	-	60
6.	Optimization Methods	6	45	-	15	-	60
7.	Permutation Groups	6	45	-	15	-	60
8.	Graph Theory	6	45	15	-	-	60
9.	Measure Theory	6	45	-	15	-	60
10.	Topology	6	45	-	15	-	60
11.	Selected Topics in Computing Methods and Applications	6	45	-	15	-	60
12.	Selected Topics in Statistics	6	45	-	15	-	60
13.	Complex Analysis	6	45	-	15	-	60
14.	Cryptography and Computer Safety	6	45	-	15	-	60
15.	Mathematics: Methods and Art	6	45	-	15	-	60
16.	Molecular Modelling	6	45	-	15	-	60
17.	Optimization Methods in Logistics	6	45	-	15	-	60
18.	Galois Theory	6	45	-	15	-	60
19.	Seminar - Introduction to Research Work	6	45	-	-	-	45
20.	Symmetric-key Cryptography	6	45	-	15	-	60
21.	Coding Theory	6	45	-	15	-	60
22.	Number Theory	6	45	-	15	-	60
23.	History and Philosophy of Mathematics	6	45	15	-	-	60
24.	Mathematical Topics in English II	6	30	30	-	-	60

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.

Course structure and programme information for students enrolled 2007/08 - 2016/17

In the past year changes occurred in the course plan. In the beginning of this section you can find the course plan for students enrolled from the academic year 2017/18.

Here you can find information regarding course structure, compulsory and elective courses, and also short description of courses for students enrolled for the first time in the academic years 2007/08 - 2016/17 (MA-07):

• course structure, short description of courses.

Elective courses and study fieldstop

Elective courses

Elective courses are internal or external elective courses.

Internal elective courses are courses within the study programme; the list of all internal elective courses is available in the section Course structure (Table 5).

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 second year.

Students may select external elective courses from study programmes provided by other institutions of higher education in Slovenia and internationally.

Study fields

After the second year, the student decides which study field he/she would like to follow.

There are 7 study fields: Discrete Mathematics, Financial Mathematics, Cryptography, Computer intensive methods and applications, Statistics, General Mathematics, Theoretical Mathematics.

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.

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).

Study fields and internal elective courses (MA-17):

• 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.

Elective courses and study fields for students enrolled 2007/08 - 2016/17

In the past year changes occurred in the course plan. In the beginning of this section you can find information regarding elective courses and study fields for students enrolled from the academic year 2017/18.

Here you can find information regarding elective courses and study fields for students enrolled for the first time in the academic years 2007/08 - 2016/17 (MA-07).

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 in a 4-year secondary-school programme and a final examination in the general matura subject Mathematics; insofar as the aforementioned subject has already been taken within the framework of the vocational matura examination, applicants must pass any other general matura subject; the selected subject cannot be the same as one of the subjects passed in the framework of the vocational matura;
• successfully completed any four-year secondary-school 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 (40%),
  • 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 (40%).
• applicants under Point b) shall be selected on the basis of:
  • overall vocational matura results (20%),
  • 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 (40%),
  • results in the additional matura subject examination (20%).
• applicants under Point c) shall be selected on the basis of:
  • overall final examination results (40%),
  • 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 (40%).

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 regulations of this field.

The transition between study programmes is the enrolment in the higher year of the study programme, in case of leaving the education at the initial study programme and continuing the study process at another study program of the same degree. The transition takes into account the comparability of the study programmes and the completed study obligations of the candidate in the initial study program.

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 candidates of a related first-cycle study programme or a pre-Bologna reform undergraduate study programme, provided that the following conditions have been met:

• the candidate fulfils the requirements for admission to the study programme of Mathematics
• the completion of the initial study programme which the candidate 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 UP FAMNIT committee. Apart from comparability between both fields of study, the committee shall also consider the 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 candidates 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 enrolment restrictions, 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 ECTS-credits.

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 co-operation, 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

Subject-specific 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.