# SEE Doctoral Studies in Mathematical Sciences

### Third-cycle Study Programme Rules and Procedures at the Department of Mathematics

In the first semester, all candidates are required to take the course "Research methodology and academic skills" and two courses from the list of offered courses, determined by the Doctoral Council of the Department of Mathematics and in accordance with the broad research interests of the candidate.

In the second semester, each candidate takes three courses from the list of offered courses, determined by the Doctoral Council of the Department of Mathematics and in accordance with the specific research interests of the candidate.

In the third semester, the candidate is obliged to defend the "doctoral seminar" with superviso /potential mentor which carries 30 ECTS and which is directly linked to the work on candidate’s doctoral thesis. Doctoral seminars are not graded, but successful defence is verified in the index.

In the fourth and fifth semester candidate is working on the draft version of the doctoral thesis which is labelled as "Work on doctoral dissertation”, verified by mentor in the index and which carries 30 ECTS per semester, not graded.

In the sixth semester, candidate is entitled to 30 ECTS for development and defence of the doctoral dissertation, which is again verified by mentor. One candidate can take up to two courses per same lecturer.

The candidate is awarded one of the titles provided by the Law, and in accordance with the area of the subject of candidate’s doctoral dissertation (PhD in Mathematics / PhD in Computer Science).

### SEE Doctoral Studies in Mathematical Sciences -The Curriculum

(since academic year 2016/17)

Doctoral's (third cycle) academic study programme

SEMESTER I | |||
---|---|---|---|

COURSE CODE | COURSE TITLE | CONTACT HOURS | ECTS |

EDU 610 | Research methodology and academic skills | 30 | 10 |

-------------- | Elective course 1 | 30 | 10 |

-------------- | Elective course 2 | 30 | 10 |

SEMESTER II | |||
---|---|---|---|

COURSE CODE | COURSE TITLE | CONTACT HOURS | ECTS |

-------------- | Elective course 3 | 30 | 10 |

-------------- | Elective course 4 | 30 | 10 |

-------------- | Elective course 5 | 30 | 10 |

SEMESTER III | |||
---|---|---|---|

COURSE CODE | COURSE TITLE | CONTACT HOURS | ECTS |

-------------- | Work on doctoral dissertation - Doctoral seminar | -------- | 30 |

SEMESTER IV | |||
---|---|---|---|

COURSE CODE | COURSE TITLE | CONTACT HOURS | ECTS |

-------------- | Work on doctoral dissertation | ------- | 30 |

SEMESTER V | |||
---|---|---|---|

COURSE CODE | COURSE TITLE | CONTACT HOURS | ECTS |

-------------- | Work on doctoral dissertation | ------- | 30 |

SEMESTER VI | |||
---|---|---|---|

COURSE CODE | COURSE TITLE | CONTACT HOURS | ECTS |

-------------- | Development and defence of the doctoral dissertation | ------- | 30 |

**PhD in Mathematics / PhD in Computer Science**

### Elective courses:

Elective courses 1 and 2:

- PMAT 605 - Algorithmic Number Theory
- AMAT 605 - Topological dynamical systems
- PMAT 610 - Apstraktna algebra i grafovi
- AMAT 610 - Constraint and Unconstraint Optimization
- CS 605 - Algorithms and data structures II
- AMAT 615 - Dynamical Systems
- PMAT 615 - Finite fields and their applications
- PMAT 620 - Harmonic function theory
- PMAT 625 - Generalized functions
- CS 610 - Intelligent Systems
- PMAT 630 - Statistical Convergence
- PMAT 635 - Integral Operators
- PMAT 640 - Generalized functions and transformations
- PMAT 645 - Algebraic Number Theory
- CS 615 - Computability
- AMAT 620 - Monotone Dynamical Systems
- PMAT 650 - Combinatorics

Elective courses 3, 4 and 5:

- AMAT 655 - Continuous Dynamical Systems
- AMAT 660 - Parameter estimation
- AMAT 665 - Optimal Control and Stochastic Optimization
- CS 655 - High performance computing
- CS 660 - Compiler and Software support for parallel computer architectures
- PMAT 655- Algebraic Combinatorics
- PMAT 660 - Harmonic Analysis
- PMAT 665 - Spectral theory of automorphic forms
- PMAT 670 - Spectral graph theory
- PMAT 675 - Analysis on manifolds
- AMAT 670 - Selected Topics in Cryptography
- PMAT 680 - Hilbert Function Spaces and Pick Interpolation
- PMAT 685 - Analytic Number Theory II
- AMAT 675 - Chaos
- AMAT 685 - Stochastic processes II
- AMAT 680 - Global Optimization
- CS 665 - Complexity