The graduate study programme Mathematics, specialisation in Pure Mathematics has the goal of offering students appropriate fundaments for the scientific postgraduate doctoral study programme in mathematics. This study programme is directed towards further autonomous research and scientific work. This specialisation, based on the syllabus, enables students to adopt fundamental knowledge and understand results in the area of algebra, mathematical analysis, probability, geometry and topology, including applied mathematics. Though the study programme is primarily directed to further researchers, the programme also provides a good education for all jobs seeking abilities in mathematical modelling, programming, analytical thinking and applied ICT techniques.

LIST OF COURSES | |||||||
---|---|---|---|---|---|---|---|

Year of study: 1. | |||||||

Semester: 1. | |||||||

STATUS | CODE | COURSE | COURSES IN SEMESTER | ECTS | |||

L | S | E | T | ||||

Mandatory | PMM912 | Metric Spaces | 45 | 15 | 6 | ||

PMM811 | Vector Spaces II | 30 | 15 | 5 | |||

PMM216 | Algebra I | 30 | 15 | 5 | |||

PMM913 | Measure and Integral | 30 | 30 | 6 | |||

PMM914 | Vector Analysis | 45 | 15 | 6 | |||

Total mandatory | 180 | 45 | 45 | 28 | |||

Elective | PMM009 | History of Mathematics | 30 | 3 | |||

PMM810 | Diophantine Equations | 30 | 15 | 5 | |||

PMM205 | Cryptography | 30 | 15 | 15 | 5 | ||

PMM217 | Algebraic Number Theory | 45 | 15 | 5 | |||

PMM204 | Mathematical Theory of Computation | 45 | 15 | 5 | |||

PMM922 | Optimization | 30 | 15 | 5 | |||

PMM014 | Constructive Methods in Geometry | 30 | 30 | 5 | |||

PMP106 | Fundamental Concepts in Physics | 30 | 15 | 3 | |||

PMII10 | Introduction to Artificial Intelligence | 30 | 30 | 5 | |||

The students select at least 3 ECTS (1 course). |

LIST OF COURSES | |||||||
---|---|---|---|---|---|---|---|

Year of study: 1. | |||||||

Semester: 2. | |||||||

STATUS | CODE | COURSE | COURSES IN SEMESTER | ECTS | |||

L | S | E | T | ||||

Mandatory | PMM228 | Probability I | 30 | 30 | 6 | ||

PMM215 | Normed Spaces | 45 | 15 | 6 | |||

PMM813 | Algebra II | 30 | 15 | 5 | |||

PMM915 | Partial Differential Equations | 30 | 30 | 6 | |||

PMM120 | Introduction to Differential Geometry | 30 | 30 | 6 | |||

Total mandatory | 165 | 30 | 90 | 29 |

LIST OF COURSES | |||||||
---|---|---|---|---|---|---|---|

Year of study: 2. | |||||||

Semester: 3. | |||||||

STATUS | CODE | COURSE | COURSES IN SEMESTER | ECTS | |||

L | S | E | T | ||||

Mandatory | PMM230 | Statistics | 30 | 30 | 6 | ||

PMM219 | Stochastic Processes | 30 | 30 | 6 | |||

PMM916 | Operators on Normed Spaces | 45 | 15 | 6 | |||

PMM812 | Foundations of Geometry ( if the student HAD passed the course at the undergraduate level, the course is substituted with the prescribed course from the group of elective courses MAThEMATIcs | 45 | 30 | 6 | |||

Total mandatory | 150 | 15 | 90 | 24 | |||

Elective | Elective courses: group Mathematics | ||||||

PMM218 | Topics in Topology | 45 | 15 | 6 | |||

PMM810 | Diophantine Equations | 30 | 15 | 5 | |||

PMM205 | Cryptography | 30 | 15 | 15 | 5 | ||

PMM217 | Algebraic Number Theory | 45 | 15 | 5 | |||

PMM204 | Mathematical Foundation of Computing | 45 | 15 | 5 | |||

PMM922 | Optimization | 30 | 15 | 5 | |||

PMM014 | Constructive Methods in Geometry | 30 | 30 | 5 | |||

PMM919 | Introduction to Lie Groups and Lie Algebras | 45 | 15 | 5 | |||

PMM710 | Mathematics in Action | 5 | |||||

Elective courses: Informatics and Physics | |||||||

PMP106 | Fundamental Concepts in Physics | 30 | 15 | 3 | |||

PMII10 | Introduction to Artificial Intelligence | 30 | 30 | 5 | |||

Minimum 6 ECTS, or 8 ECTS is selected from elective courses (depending on the selected ECTS from elective courses for 1. semester). One or two elective courses is selected for 3. and 4. semester together (minimum one elective course from group Mathematics). |

LIST OF COURSES | |||||||
---|---|---|---|---|---|---|---|

Year of study: 2. | |||||||

Semester: 4. | |||||||

STATUS | CODE | COURSE | COURSES IN SEMESTER | ECTS | |||

L | S | E | T | ||||

Mandatory | PMM918 | Topics in Applied Mathematics | 30 | 30 | 6 | ||

PMM991 | Diploma Thesis | 30 | 22 | ||||

Total mandatory | 30 | 30 | 30 | 28 | |||

Elective | Elective courses: group Mathematics | ||||||

PMM118 | Numerical Analysis | 30 | 30 | 5 | |||

PMM121 | Introduction to Projective Geometry | 30 | 30 | 5 | |||

PMM232 | Probability II | 30 | 30 | 6 | |||

PMM129 | Computability | 30 | 15 | 5 | |||

PMM710 | Mathematics in Action | 5 | |||||

PMM502 | COMPLEX NETWORKS ANALYSIS | 30 | 30 | 5 | |||

PMM504 | STATISTICS IN BIOMEDICINE | 30 | 30 | 5 | |||

Elective courses: group Informatics and Physics | |||||||

PMPN01 | Physics | 30 | 15 | 30 | 6 | ||

PMP009 | History of classical physics | 30 | 3 | ||||

PMP11C | Fundamental Concepts in Quantum Physics | 30 | 15 | 4 | |||

PMID30 | Object Oriented Programming | 30 | 30 | 6 | |||

PMIH20 | Data Minning | 30 | 30 | 5 | |||

Minimum 6 ECTS, or 8 ECTS is selected from elective courses (depending on the ECTS from elective courses for 1. semester). One or two elective courses is selected for 3. and 4. semester together (minimum one elective course from group Mathematics). |

CONDITIONS OF ENROLLMENT AND POTENTIAL DIFFERENTIAL COURSES: | ANY UNDERGRADUATE STUDY OF MATHEMATICS OR MATHEMATICS AND OTHER FIELD WITH AT LEAST 115 ECTS IN MATHEMATICAL COURSES. TOTAL DIFFERENTIAL COURSES CAN NOT EXCEED 30 ECTS. |