# Practical Mathematics (first cycle)

**Study program cycle and type:**

First cycle professional study program.

**Anticipated professional title:**

In Slovenian: diplomirani matematik (VS), diplomirana matematičarka (VS), abbreviated to dipl. mat. (VS)

**Duration:**

3 full years (6 terms) based on 180 ECTS credits

**Primary goals:**

The primary goal of the professional study program in Practical Mathematics is to produce professionals capable of application of their mathematical knowledge in the working process in communications and information technology, technology, logistics, and elsewhere.

**Generic competences developed by the student:**

- ability of critical assessment of solutions,
- ability of application of knowledge,
- ability of professional team work,
- ability to use and follow professional literature,
- ability to follow professional information on the internet,
- ability of written as well as oral presentation of professional reports,
- ability to adjust to new computer environments,
- understanding the role of advanced knowledge of information technologies,
- ability of identification of statistically significant differences,
- ability of lifelong self–education

**Subject specific competences developed by the student:**

- ability of employment of mathematical tools at practical problem solving,
- ability of identification of mathematical processes in professional environment,
- ability of result analysis,
- ability of presentation of results,
- ability of employment of mathematical tools in everyday environment,
- ability of initiation and conduct of software upgrade,
- ability of business process optimization,
- ability of mathematical modelling of technological processes,
- ability of employment of numerical methods at mathematical problem solving

**Employment possibilities:**

Graduates of the professional study program in Practical Mathematics can find employment in

- the information technology sector of the economy (computer programmers, IT developers, system administrators, customer support employees),
- the technology and logistics sector,
- statistical companies at survey planning and statistical data analysis,
- financial institutions at information technology and mathematical support,
- the public sector, and elsewhere.

## Admission requirements and admission limitation measures

Admission to the study program is open to holders of the final examination certificate, the vocational matura certificate or the matura certificate obtained by completion of any four-year high school equivalent program.

If the number of applicants exceeds the maximum availability, the applicants are selected according to their high school achievements weighted in the following way:

- Final examination or vocational matura or matura combined grade - 30 % of points
- Final examination or vocational matura or matura mathematics grade - 30 % of points
- Grade point average in the 3rd and 4th years of high school - 20 % of points
- Mathematics grade in the 3rd and 4th years of high school - 20 % of points

## Validation of competences, knowledge, and skills acquired prior to admission to the study program

Students may apply for validation of their competences acquired previously by means of various forms of education if their competences match those of one or more courses offered within this study program. In a formal written request submitted to the mathematics department at the FMF, the applicant must specify the course(s) whose competences he or she had already mastered, and attach accredited transcripts proving it. When considering the possible validation of competences corresponding to a particular course, the department study committee bases its decision on a comparison of

- the duration of the educational process where the student acquired the competences with the duration of the respective course(s), and
- the scope of the previously acquired competences with the goals of the respective course(s).

If the study committee decides to validate the previously acquired competences, the student is awarded all ECTS credits that correspond to the respective course(s). In the validation process, the study committee follows The rules and guidelines for validation of informally acquired knowledge and skills, accepted by the Senate of The University of Ljubljana on 29 May 2007 (http://www.unilj.si/o_univerzi_v_ljubljani/statut_in_pravilniki.aspx).

## Grading system

The methods for testing the competences, knowledge, and skills are described in the courses syllabi. The basic knowledge testing rules are explained in the Exam guidelines of FMF. Course examinations are either written or oral or both. They can have the form of midterm exams, oral defense of the midterm exams, written exams, oral exams, seminar or project work and oral defense of seminar and project work.

Grading is based on the grading scale determined in the Statute of The University of Ljubljana. All forms of examinations are graded by grades 1-10, out of which 6-10 are passing grades, and 1-5 are failing grades. The following grading scale is most commonly used for grading the score of a written course examination:

Score (in %) | grade |
---|---|

50 - 59 % | 6 |

60 - 69 % | 7 |

70 - 79 % | 8 |

80 - 89 % | 9 |

90 - 100 % | 10 |

## Enrollment requirements

Enrollment in the first study year is granted upon admission.

For enrollment in the next study year, it is necessary to earn 54 ECTS credits from courses and exams in the current study year. In addition, all exams of the first study year must have been completed to be allowed enrollment in the third study year.

## Re-enrollment requirements

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

**a)** at least half of all possible credits of the current study year (30 ECTS credits), and

**b)** all credits from the previous study years.

Re-enrollment is only possible once in the course of studies. A change of the study program as result of disability of enrollment in the next study year is automatically counted as re-enrollment.

## Curriculum

The spreadsheet data are given for both the winter and the summer term.

Each term comprises 15 weeks of classes.

Abbreviations:

**L** = lectures per semester (in hours),

**P** = problem sessions per semester (in hours),

**Lab** = lab classes per semester (in hours),

**S** = seminars per semester (in hours),

**ECTS** = ECTS credits worth,

**TSW** = estimated total student workload (in hours).

#### 1st year

Winter term | Summer term | Total | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Course | L | P | Lab | S | ECTS | TSW | L | P | Lab | S | ECTS | TSW | ECTS | TSW |

Mathematics 1 | 60 | 60 | 0 | 0 | 9 | 270 | 60 | 60 | 0 | 0 | 9 | 270 | 18 | 540 |

Linear algebra | 45 | 45 | 0 | 0 | 7 | 210 | 45 | 45 | 0 | 0 | 7 | 210 | 14 | 420 |

Computer lab | 15 | 0 | 30 | 0 | 3 | 90 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 90 |

Introduction to programming | 15 | 0 | 30 | 0 | 3 | 90 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 90 |

Programming 1 | 0 | 0 | 0 | 0 | 0 | 0 | 15 | 0 | 45 | 0 | 4 | 120 | 4 | 120 |

Mathematics in practice | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 15 | 15 | 0 | 4 | 120 | 4 | 120 |

Introduction to physics | 45 | 0 | 0 | 0 | 3 | 90 | 0 | 0 | 45 | 0 | 2 | 60 | 5 | 150 |

Cognate elective | 30 | 30 | 0 | 0 | 5 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 150 |

Cognate elective | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 15 | 0 | 0 | 4 | 120 | 4 | 120 |

Term total | 210 | 135 | 60 | 0 | 30 | 900 | 180 | 135 | 105 | 0 | 30 | 900 | 60 | 1800 |

**Cognate elective course**

The department of Mathematics at the FMF offers a foreign language course:

Winter term | Summer term | Total | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Course | L | P | Lab | S | ECTS | TSW | L | P | Lab | S | ECTS | TSW | ECTS | TSW |

Foreign language - English | 30 | 15 | 0 | 0 | 5 | 150 | 30 | 15 | 0 | 0 | 4 | 120 | 9 | 270 |

*In addition to the foreign language - English, students may take a cognate course from the curriculum of any 1st cycle professional study program offered at the University of Ljubljana, for example the VPEŠ program at the Faculty of Economics or the 1st cycle professional programs offered at technical faculties.*

#### 2nd year

Winter term | Summer term | Total | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Course | L | P | Lab | S | ECTS | TSW | L | P | Lab | S | ECTS | TSW | ECTS | TSW |

Mathematics 2 | 45 | 45 | 0 | 0 | 6 | 180 | 45 | 45 | 0 | 0 | 6 | 180 | 12 | 360 |

Numerical methods 1 | 30 | 15 | 15 | 0 | 5 | 150 | 30 | 15 | 15 | 0 | 5 | 150 | 10 | 300 |

Computer tools in mathematics | 15 | 0 | 30 | 0 | 3 | 90 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 90 |

Programming 2 | 30 | 0 | 30 | 0 | 5 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 150 |

Algebra and discrete mathematics | 45 | 45 | 0 | 0 | 6 | 180 | 0 | 0 | 0 | 0 | 0 | 0 | 6 | 180 |

Probability | 30 | 30 | 0 | 0 | 5 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 150 |

Statistics | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 15 | 15 | 0 | 5 | 150 | 5 | 150 |

Mathematical tools in physics | 0 | 0 | 0 | 0 | 0 | 0 | 45 | 0 | 45 | 0 | 6 | 180 | 6 | 180 |

Communication in mathematics | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 3 | 90 | 3 | 90 |

Differential equations | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 30 | 0 | 0 | 5 | 150 | 5 | 150 |

Term total | 195 | 135 | 75 | 0 | 30 | 900 | 180 | 105 | 75 | 30 | 30 | 900 | 60 | 1800 |

#### 3rd year

Winter term | Summer term | Total | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Course | L | P | Lab | S | ECTS | TSW | L | P | Lab | S | ECTS | TSW | ECTS | TSW |

Partial differential equations | 30 | 30 | 0 | 0 | 5 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 150 |

Optimization | 45 | 45 | 0 | 0 | 6 | 180 | 0 | 0 | 0 | 0 | 0 | 0 | 6 | 180 |

Computer science 1 | 30 | 0 | 45 | 0 | 5 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 150 |

Mechanics | 30 | 15 | 15 | 0 | 5 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 150 |

Project work | 0 | 0 | 0 | 30 | 4 | 120 | 0 | 0 | 0 | 0 | 0 | 0 | 4 | 120 |

Work experience | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 15 | 450 | 15 | 450 |

Elective 1 | 20 | 15 | 15 | 0 | 5 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 150 |

Elective 2 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 15 | 15 | 0 | 5 | 150 | 5 | 150 |

Elective 3 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 15 | 15 | 0 | 5 | 150 | 5 | 150 |

Elective 4 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 15 | 15 | 0 | 5 | 150 | 5 | 150 |

Term total | 165 | 105 | 75 | 30 | 30 | 900 | 90 | 45 | 45 | 30 | 30 | 900 | 60 | 1800 |

**Electives**

Winter term | Summer term | Total | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Course | Group | L | P | Lab | S | ECTS | TSW | L | P | Lab | S | ECTS | TSW | ECTS | TSW |

Geometry of curves and surfaces | 30 | 30 | 0 | 0 | 5 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 150 | |

Numerical methods 2 | 30 | 15 | 15 | 0 | 5 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 150 | |

Programming 3 | 30 | 0 | 45 | 0 | 5 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 150 | |

Topics in physics | 30 | 0 | 30 | 0 | 5 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 150 | |

Numerical methods 3 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 15 | 15 | 0 | 5 | 150 | 5 | 150 | |

Mathematical modelling | I1 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 15 | 15 | 0 | 5 | 150 | 5 | 150 |

System modelling and management | I1 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 15 | 15 | 0 | 5 | 150 | 5 | 150 |

Dynamical modelling | I1 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 15 | 15 | 0 | 5 | 150 | 5 | 150 |

Discrete modelling | I1 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 15 | 15 | 0 | 5 | 150 | 5 | 150 |

Databases | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 0 | 30 | 0 | 5 | 150 | 5 | 150 | |

Computer science 2 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 0 | 45 | 0 | 5 | 150 | 5 | 150 | |

Discrete mathematics 2 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 30 | 0 | 0 | 5 | 150 | 5 | 150 | |

Computer security | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 15 | 15 | 0 | 5 | 150 | 5 | 150 |

*Remark: Each student opts for at least four of the electives listed in the above table: at least one in the winter and at least three in the summer term. Of those, at least one must belong to group I1.*

*Students studying at a foreign institution as part of the Socrates-Erasmus exchange program can transfer up to 30 ECTS credits
awarded at that institution in the case of a single term exchange or 60 ECTS credits in the case of a full year exchange.*