# Mathematics (first cycle)

**Study program cycle and type:**

First cycle academic study program.

**Anticipated academic title:**

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

**Duration:**

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

**Basic goals:**

The principal goal of the academic study program in Mathematics is to qualify its graduates for solving hard mathematical problems arising in industry, in the public sector, and in sciences. At the same time, graduates of the program are equipped with the core knowledge necessary for studies in the second cycle.

**Generic competences developed by the student:**

- ability of abstract thinking and problem analysis,
- ability of sorting out effective solutions and of their critical evaluation,
- ability of application of knowledge in practice,
- ability of using and following the expert literature,
- ability to set forth both written and oral presentations of specialized topics,
- ability to work both individually and as part of an (international) team,
- 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 program in Mathematics should be able to:

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

**Employment possibilities:**

Graduates of the academic study program in Mathematics can find employment in:

- the technology and logistic sector of the economy,
- banks and insurance companies,
- research and planning institutions, technology parks, and the public sector.

## Admission requirements and admission limitation measures

Admission to the study program is open to the following:

**a)** Holders of the matura certificate.

**b)** Holders of the vocational matura certificate obtained in any of the four-year high school programs.
In this case, an additional examination in one of the general matura subjects different from those of the
vocational matura is required. Either one of the vocational matura subjects or the additional one must
be mathematics.

**c)** Holders of the final examination certificate obtained in any of the four-year high school programs 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 or vocational 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

## Enrollment requirements

Enrollment in the first study year is granted upon admission.

For enrollment 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 enrollment in the 2nd year: Analysis 1, Algebra 1 and Computer lab,
- for enrollment in the 3rd year: all exams of the 1st year, Analysis 2, Algebra 2, Programming 1, Point-set topology and Seminar 1.

## 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.

## Finishing requirements

To finish the program, students need to complete all exams.

## 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.uni-lj.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 the FMF. Course examinations are either written or oral or both. They can have the form of midterm exams, oral defense of 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 |

## 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 week (in hours),

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

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

**S** = seminars per week (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 |

Analysis 1 | 4 | 4 | 0 | 0 | 9 | 270 | 4 | 4 | 0 | 0 | 9 | 270 | 18 | 540 |

Algebra 1 | 3 | 3 | 0 | 0 | 7 | 210 | 3 | 3 | 0 | 0 | 7 | 210 | 14 | 420 |

Logic and sets | 2 | 2 | 0 | 0 | 6 | 180 | 0 | 0 | 0 | 0 | 0 | 0 | 6 | 180 |

Computer lab | 1 | 0 | 3 | 0 | 6 | 180 | 0 | 0 | 0 | 0 | 0 | 0 | 6 | 180 |

Introduction to programming | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 2 | 0 | 6 | 180 | 6 | 180 |

Physics 1 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 3 | 0 | 0 | 6 | 180 | 6 | 180 |

Elective | 1 | 2 | 0 | 0 | 2 | 60 | 1 | 2 | 0 | 0 | 2 | 60 | 4 | 120 |

Weekly total |
11 | 11 | 3 | 0 | 30 | 900 | 13 | 12 | 2 | 0 | 30 | 900 | 60 | 1800 |

Term total |
165 | 165 | 45 | 0 | 195 | 180 | 30 | 0 |

**Electives**

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

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

Proseminar A | 2 | 2 | 0 | 0 | 2 | 60 | 0 | 2 | 0 | 0 | 2 | 60 | 4 | 120 |

Proseminar B | 0 | 2 | 0 | 0 | 2 | 60 | 2 | 2 | 0 | 0 | 2 | 60 | 4 | 120 |

*Remark: Proseminars A and B are electives. Proseminar A is intended as a review of selected high school topics in mathematics, while Proseminar B should be chosen by students with strong mathematical background. Problem sessions for both Proseminars are a supplement to the other courses in the first year's curriculum.*

#### 2nd year

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

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

Analysis 2 | 4 | 3 | 0 | 0 | 8 | 240 | 4 | 3 | 0 | 0 | 6 | 180 | 14 | 420 |

Physics 2 | 3 | 3 | 0 | 0 | 6 | 180 | 0 | 0 | 0 | 0 | 0 | 0 | 6 | 180 |

Algebra 2 | 3 | 2 | 0 | 0 | 6 | 180 | 0 | 0 | 0 | 0 | 0 | 0 | 6 | 180 |

Algebra 3 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 2 | 0 | 0 | 6 | 180 | 6 | 180 |

Programming 1 | 2 | 0 | 2 | 0 | 5 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 150 |

Point-set topology | 2 | 2 | 0 | 0 | 5 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 150 |

Seminar 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 3 | 90 | 3 | 90 |

Elective 1 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

Elective 2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

Elective 3 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

Weekly total | 14 | 10 | 2 | 0 | 30 | 900 | 13 | 11 | 0 | 3 | 30 | 900 | 60 | 1800 |

Term total | 210 | 150 | 30 | 0 | 195 | 165 | 0 | 30 |

**Electives**

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

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

Discrete mathematics 1 | B1 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

Programming 2 | B1 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 2 | 0 | 5 | 150 | 5 | 150 |

Algebraic curves | B2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

Introduction to geometric topology | B2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

Affine and projective geometry | B | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

Coding theory and cryptography | B | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

*Remark: Electives are divided into groups B1, B2, and B. Each student opts for three electives. Of those, at least one must belong to group B1, and at least one to group B2.*

#### 3rd year

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

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

Analysis 3 | 3 | 3 | 0 | 0 | 6 | 180 | 0 | 0 | 0 | 0 | 0 | 0 | 6 | 180 |

Analysis 4 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 3 | 0 | 0 | 6 | 180 | 6 | 180 |

Introduction to numerical methods | 3 | 3 | 0 | 0 | 6 | 180 | 0 | 0 | 0 | 0 | 0 | 0 | 6 | 180 |

Probability and statistics | 2 | 2 | 0 | 0 | 5 | 150 | 2 | 2 | 0 | 0 | 5 | 150 | 10 | 300 |

Seminar 2 | 0 | 0 | 0 | 2 | 3 | 90 | 0 | 0 | 0 | 1 | 1 | 30 | 4 | 120 |

Mechanics 1 | 2 | 2 | 0 | 0 | 5 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 150 |

Specific elective 1 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

Specific elective 2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

Specific elective 3 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

Specific elective 4 | 2 | 2 | 0 | 0 | 5 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 150 |

General elective | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 3 | 90 | 3 | 90 |

Weekly total | 12 | 12 | 0 | 2 | 30 | 900 | 13 | 11 | 0 | 1 | 30 | 900 | 60 | 1800 |

Term total | 180 | 180 | 0 | 30 | 195 | 165 | 0 | 15 |

**Specific electives**

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

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

Numerical linear algebra | B1 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

Mechanics 2 | B1 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

Mathematical modelling | B1 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

Data structures and algorithms 1 | B2 | 2 | 1 | 1 | 0 | 5 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 150 |

Data structures and algorithms 2 | B2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 1 | 1 | 0 | 5 | 150 | 5 | 150 |

Coding theory and cryptography | B2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

Discrete mathematics 2 | B2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

Optimization 1 | B2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

Database basics | B | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 2 | 0 | 5 | 150 | 5 | 150 |

Financial mathematics 1 | B | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

Game theory | B | 3 | 3 | 0 | 0 | 6 | 180 | 0 | 0 | 0 | 0 | 0 | 0 | 6 | 180 |

Affine and projective geometry | B | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 5 | 150 | 5 | 150 |

Introduction to differential geometry | B | 2 | 2 | 0 | 0 | 5 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 150 |

*Remarks:
*

*Each student opts for at least four electives, at least one (5 ECTS credits worth) in the winter term, and at least three (15 ECTS credits worth) in the summer term. Of the four, one elective must belong to group B1 and one to group B2. Repetition of previous year's electives is not possible.**Electives can also be chosen from among the courses offered in the second cycle of this program, subject to approval by the department study committee.**The 3 ECTS credits corresponding to the general elective course can be earned by completing exams within other study programs.**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.*