- Bachelor's academic study programme Mathematics 3+
- Bachelor's academic study programme Financial mathematics 3+
- Integrated Master's study programme Pedagogical mathematics 5+0
- Interdisciplinary Bachelor's academic study programme Computer science and mathematics 3+
- Professional study programme Practical mathematics 3+

# Mathematics (academic year 2017/18)

## Doctoral programme

Coordinator: prof. dr. A. SimpsonThe Doctoral Programme in Mathematics is a third cycle Bologna degree with 180 ECTS credits. Students are required to have finished a second cycle Bologna degree (or equivalent) in mathematics or a related field. The objective of the doctoral programme is to prepare the students for independent mathematical research at the highest level.

The programme consists of the course work and the individual research under the supervision of an advisor, resulting in a doctoral thesis. The official duration of the programme is 6 semesters (3 years), however most of the students complete the programme within 4 years.

To graduate, students have to complete the following:

**Course work**During the three years, a student has to take five one-semester courses, three of which have to be taken from the list of the courses for which lectures are organised, while the other two can be reading courses. Reading courses can be supervised by any lecturer at our department. Students, with the help of their advisors, should make arrangements for the reading courses with the lecturers individually, preferably no later than in November. Primož Potočnik, the coordinator of the doctoral programme, should be notified about the choice.**Predoctoral exam**During the first year, the student has to pass a predoctoral exam, the role of which is to check the understanding of basic mathematical concepts. For a student with a solid background, no additional preparation is needed. Here are some examples of the predoctoral exam from 2015 (spring 2015, autumn 2015).**Individual study, research, seminars, and doctoral thesis**The major part of the programme is the individual study and research that the student undertakes under the supervision of an advisor. (The advisor has to be chosen by, or assigned to, the student during the first semester.) The progress is periodically reported within one of the research seminars. Individual research should eventually lead to original mathematical results, which are then presented in the doctoral thesis. Publication of at least one article in an international mathematical journal is required before the defense of the thesis takes place.

## Curriculum

Year 1 | |
---|---|

ECTS | |

Three electives | 18 |

Predoctoral exam | 6 |

Individual study 1 | 6 |

Seminar 1 | 6 |

Research 1 | 24 |

Year 2 | |

Two electives | 12 |

Individual study 2 | 6 |

Seminar 2 | 6 |

Research 2 | 36 |

Year 3 | |

Research 3 | 54 |

Thesis defence | 6 |

A student has to select at least 60 credits every year.

Courses offered in the academic year 2017/18 will be **Topics in discrete mathematics: graph colorings** (lecturer Škrekovski, autumn semester) and **Topics in analysis: operator ideals and their applications** (lecturer Kostenko, spring semester).

### All electives in Years 1 and 2

## Module Mathematics education

At the Department of Mathematics, we also offer the doctoral programme Mathematics education. We expect candidates with excellent mathematical abilities and an exceptional love of teaching. The programme is specific, and we would encourage candidates to get in touch before enrolling. The department study committee will assign courses and suggest an advisor. The coordinator is doc. dr. D. Kobal.