# Theoretical Mathematics

Theoretical Mathematics – The Curriculum

(academic year 2016/17)

Master's (second cycle) academic study programme

COURSE CODE | COURSE TITLE | SEMESTER I | ECTS |
---|---|---|---|

AMAT 420 | Partial Differential Equations | 3+2+0 | 8 |

PMAT 435 | Harmonic Analysis | 3+2+0 | 7 |

PMAT 440 | Commutative Algebra | 3+2+0 | 8 |

PMAT 445 | Special Functions | 3+2+0 | 7 |

COURSE CODE | COURSE TITLE | SEMESTER II | ECTS |
---|---|---|---|

PMAT 470 | Functional Analysis | 3+2+0 | 8 |

PMAT 480 | Differential Geometry | 3+2+0 | 7 |

PMAT 485 | Group Representation Theory | 3+2+0 | 7 |

PMAT 490 | Analytic Number Theory | 3+2+0 | 8 |

COURSE CODE | COURSE TITLE | SEMESTER III | ECTS |
---|---|---|---|

PMAT 510 | Algebraic Curves | 3+2+0 | 8 |

PMAT 520 | Algebraic Number Theory | 3+2+0 | 8 |

-------------- | Elective Course 1 | ---------------- | min 7 |

-------------- | Elective Course 2 | ----------------- | min 7 |

COURSE CODE | COURSE TITLE | SEMESTER IV | ECTS |
---|---|---|---|

AMAT 560 | Master Thesis | 20+0+0 | 30 |

**Master of Mathematics**

### Elective Courses

COURSE CODE | COURSE TITLE | P+AV+LV | ECTS |
---|---|---|---|

AMAT 525 | Integral Equations with Applications | 3+2+0 | 7 |

AMAT 535 | Integer and Combinatorial Optimization | 3+2+0 | 7 |

AMAT 430 | Nonlinear Optimization | 3+2+0 | 7 |

AMAT 510 | Integral Transformations with Applications | 3+2+0 | 8 |

AMAT 530 | Mathematical Physics | 3+2+0 | 7 |

PMAT 545 | Nonlinear Functional Analysis | 3+2+0 | 7 |

PMAT 537 | Selected Topics in Combinatorics | 3+2+0 | 7 |

PMAT 525 | Topological groups | 3+2+0 | 7 |

PMAT 530 | p-adic analysis | 3+2+0 | 7 |

PMAT 535 | Introduction to Algebraic Topology | 3+2+0 | 7 |

PMAT 540 | Selected Topics in Number Theory | 3+2+0 | 7 |

CS 410 | Coding and Information Theory | 3+2+0 | 8 |

### Rules of II cycle studies

Classes for each direction of studies are carried out over the four terms: I, II, II and IV semester. In each of the first three semesters student has 4 subjects and the fourth semester is dedicated for the work on master's thesis.Each of the subjects is one-semester subject, usually carries from 7 to 9 ECTS and is represented with 5 classes per week of effective teaching and auditorial and/or laboratory exercises, depending on the nature of the course. All subjects from the first and second semester are obligatory as well as two subjects from the third semester.

Two subjects from the third semester are elective and related to the topic of the thesis. Two elective courses and master's thesis (which carries 30 ECTS) together carry a minimum of 47 credits, which is more than 1/3 of the total number of ECTS for the entire second cycle education. Therefore, they define the degree based on the wishes and individual preferences of each student. Compulsory courses carry a total of 76 ECTS, which is 2/3 of the total ECTS for the entire second cycle education. They determine the direction of study program.

Prior to the third semester enrolment, student (in writing) opt for elective courses from the comprehensive list of elective courses for each direction of studies. Also, before enrolling in the third semester, each student, in consultation with the teacher (future thesis mentor) and with the consent of the Council of the Department chooses topic of the thesis (in writing).