Graduates of this academic programme are eligible for employment in computing, technology and logistic sector of the economy, banks and insurance companies, research and planning institutions, technology parks and the public sector.

# Mathematics, First Cycle

Mathematics is much more than arithmetic, mathematics is a science that teaches structured and clear thinking. The distinguishing properties of a mathematician are thus the ability to distinguish between right and wrong and between essential and non-essential, rapid learning and setting up transparent models that describe and solve dilemmas in various fields of work, from social sciences through medicine to engineering.

The principal goal of this study programme is to qualify its graduates for solving hard mathematical problems arising in industry, in the public sector, and in the sciences. At the same time it gives excellent preparation to those wishing to continue their studies in the master’s programme (second cycle) of this and other related fields.

General competences developed by the student:

- abstraction and analysis of problems,
- ability to find and critically evaluate effective solutions,
- ability to apply knowledge in practical situations,
- ability to use and follow professional literature,
- ability to give both written and oral presentations of specialized topics,
- ability to work both individually and as part of an (international) group,
- ability of lifelong self-education.

Subject specific competences developed by the student:

Mathematics is the link between natural sciences, engineering, social sciences and computer sciences. Therefore, a graduate of the academic study programme in Mathematics should be able to:

- model a practical problem mathematically,
- qualitatively analyse the obtained mathematical problems,
- conceive algorithms to solve them,
- implement those algorithms using appropriate programming tools,
- analyze and present the results.

Admission to the study programme is open to either:

a) Holders of the matura certificate (or an equivalent degree from a foreign institution).

b) Holders of the vocational matura certificate obtained in any of the four-year high school programmes (or an equivalent degree from a foreign institution). In this case, additional examination in mathematics on the general matura is required.

c) Holders of the final examination certificate obtained in any of the four-year high school programmes prior to 1 June 1995.

In case the number of applicants exceeds the maximum availability, the applicants are selected according to their final matura (or vocational matura) grade, their mathematics matura (or vocational matura) grade, their grade point average (GPA) in the last two years of high school, and their final mathematics grades in the last two years of high school. These are weighted in the following way.

Applicants under a)

- Matura certificate - grade (30% of points),
- Matura mathematics exam grade (30% of points),
- GPA in the 3rd and 4th years of high school (20% of points),
- Final grade in mathematics in the 3rd and 4th years of high school (20% of points);

Applicants under b):

- Vocational matura grade (20% of points),
- Matura mathematics exam grade (40% of points),
- GPA in the 3rd and 4th years of high school (10% of points),
- Final grade in mathematics in the 3rd and 4th years of high school (30% of points);

Applicants under c):

- Final examination grade (30% of points),
- Mathematics final examination grade or mathematics grade in the 4th year of high school in case of exemption from the final exam (30% of points),
- GPA in the 3rd and 4th years of high school (20% of points),
- Final mathematics grade in the 3rd and 4th years of high school (20% of points).

Types of examination are defined in the learning plans of individual subjects. General rules of examinations are determined by internal regulations of FMF. Types of examinations are: written exercise based midterm exams, oral defense of midterm exams, written exercise based final exams, oral theoretical knowledge exams, seminars and work projects, defense of seminars and work projects. The grading scale used is in accordance with the Statute of the University of Ljubljana. All types of examinations are evaluated with grades from 5-10, where grades 6-10 are considered passing grades and grade 5 is a failing grade.

Enrolment in Year 1 is granted upon admission. For enrolment in the next study year it is necessary to earn 50 ECTS credits from courses and exams in the current study year. In addition to the credit quota, the completions of the following exams are obligatory:

- For enrolment in Year 2: Analysis 1, Algebra 1, Computer practical.
- For enrolment in Year 3: all exams from Year 1, Analysis 2a, Analysis 2b, Algebra 2, Programming 1, Point-set topology, Seminar.

To enrol in Year 2, students must also complete a medical exam.

For re-enrolment in the same study year, a student needs to earn:

- at least half of all possible credits of the current study year (30 ECTS credits), and
- all credits from the previous study years.

Re-enrolment is only possible once. A change of the study programme counts as re-enrolment.

To graduate, students need to complete all exams.

It is possible to transfer from other study programmes. The appropriate year of study as well as other transfer requirements are determined on the basis of the programme the student is transferring from. The exact conditions for finishing the programme are determined by the department study committee.

To graduate, students need to complete all exams.

**KLASIUS-SRV**: Academic higher education (first Bologna cycle)/Academic higher education (first Bologna cycle)**ISCED**: Mathematics and statistics**KLASIUS-P**: Mathematics (broad programmes)**KLASIUS-P-16**: Mathematics**Frascati**: Natural Sciences**SOK level**: 7**EOK level**: 6**EOVK level**: First cycle

### Curriculum

**P** = lecture and seminar hours per week

**V** = theoretical and laboratory exercise hours per week

**ECTS** = credit points

compulsory | |||
---|---|---|---|

1. sem. | 2. sem. | ||

Course | ECTS | P/V | P/V |

Algebra 1 | 14 | 3/3 | 3/3 |

Analysis 1 | 18 | 4/4 | 4/4 |

Physics 1 | 6 | 0/0 | 3/3 |

Elective course | 4 | 1/2 | 1/2 |

Logic and sets | 6 | 2/2 | 0/0 |

Computer laboratory | 6 | 1/3 | 0/0 |

Introduction to programming | 6 | 0/0 | 2/3 |

compulsory | |||
---|---|---|---|

1. sem. | 2. sem. | ||

Course | ECTS | P/V | P/V |

Algebra 2 | 10 | 2/2 | 2/2 |

Analysis 2a | 8 | 4/3 | 0/0 |

Analysis 2b | 8 | 0/0 | 4/3 |

Discrete mathematics 1 | 5 | 0/0 | 2/2 |

Physics 2 | 6 | 4/2 | 0/0 |

Elective course 1 | 5 | 0/0 | 2/2 |

Elective course 2 | 5 | 0/0 | 2/2 |

Programming 1 | 5 | 2/2 | 0/0 |

Seminar | 3 | 0/0 | 2/0 |

Point-set topology | 5 | 2/2 | 0/0 |

compulsory | |||
---|---|---|---|

1. sem. | 2. sem. | ||

Course | ECTS | P/V | P/V |

Analysis 3 | 6 | 3/3 | 0/0 |

Analysis 4 | 6 | 0/0 | 3/3 |

Diploma seminar | 7 | 2/0 | 2/0 |

Elective courses | 15 | 0/0 | 6/6 |

Elective courses | 5 | 2/2 | 0/0 |

Mechanics 1 | 5 | 2/2 | 0/0 |

Statistics | 5 | 0/0 | 3/2.53 |

Introduction to numerical methods | 6 | 3/3 | 0/0 |

Probability | 5 | 2.47/2.53 | 0/0 |

electives | |||
---|---|---|---|

1. sem. | 2. sem. | ||

Course | ECTS | P/V | P/V |

Introductory seminar A | 4 | 2/2 | 0/2 |

Introductory seminar B | 4 | 0/2 | 2/2 |

electives | |||
---|---|---|---|

1. sem. | 2. sem. | ||

Course | ECTS | P/V | P/V |

Affine and projective geometry | 5 | 0/0 | 2/2 |

Algebraic curves | 5 | 0/0 | 2/2 |

Programming 2 | 5 | 0/0 | 2/2 |

Introduction to geometric topology | 5 | 0/0 | 2/2 |

Electives Group B1 | |||
---|---|---|---|

1. sem. | 2. sem. | ||

Course | ECTS | P/V | P/V |

Mathematical modelling | 5 | 0/0 | 2/2 |

Mechanics 2 | 5 | 0/0 | 2/2 |

Numerical linear algebra | 5 | 0/0 | 2/2 |

Electives Group B2 | |||
---|---|---|---|

1. sem. | 2. sem. | ||

Course | ECTS | P/V | P/V |

Discrete mathematics 2 | 5 | 0/0 | 2/2 |

Optimization 1 | 5 | 2/2 | 0/0 |

Data structures and algorithms 1 | 5 | 2/2 | 0/0 |

Data structures and algorithms 2 | 5 | 0/0 | 2/2 |

Coding theory and cryptography | 5 | 0/0 | 2/2 |

Electives Group B | |||
---|---|---|---|

1. sem. | 2. sem. | ||

Course | ECTS | P/V | P/V |

Algebra 3 | 5 | 0/0 | 2/2 |

Elementary geometry | 6 | 3/2 | 0/0 |

Elementary number theory | 6 | 0/0 | 3/2 |

Financial mathematics 1 | 5 | 0/0 | 2/2 |

Topics in data analysis | 5 | 0/0 | 2/2 |

Fundamentals of databases | 5 | 0/0 | 2/2 |

Stochastic processes 1 | 5 | 0/0 | 2/2 |

Game theory | 6 | 3/3 | 0/0 |

Introduction to differential geometry | 5 | 2/2 | 0/0 |