**Name and the Goals of the Study Programme**

Master study programme of Mathematics (MA) represents master studies in the field of pure (theoretical) mathematics at the University of Novi Sad, which is conducted at the Faculty of Sciences. The goal of the study programme *Mathematics *is an education of mathematician-researchers, and their further improving in scientific-research work, which also involves creating of young scientists at universities, scientific institutes and other institutions and facilities in which realization and modeling of practical problems involves using of advanced mathematical structures.

**Professional Title, Academic, or Scientific Title**

Finishing it, student acquires a title *Master in Mathematics*.

**The Structure of the Study Programme**

There are 8 compulsory courses and the Master thesis, which are defined by the curriculum of the programme. Elective courses are divided into 5 groups. First four groups consist of two courses, and student has to choose at least one from them. By this conducted choices, finished student has learned basics from each of the area of Mathematics. Fifth group consists of 17 courses, and each student has to choose at least 2. This choice allows him to specialize in one of the area of Mathematics.

**The Time Allotted for the Realization of Particular Study Forms**

Master study programme *Mathematics *(MA) lasts 2 years with the total credit value of 120 ECTS.

**Prerequisites for the Registration for Particular Courses or Group of Courses**

By choosing this programme, student orients himself toward extensive study of sophisticated theoretical results (and by that to direct him/her towards the profession of a mathematician-researcher). Student can extend his/her knowledge by several highly-specialized courses, some of which are inherited from the master study programme MB: *Applied mathematics*. These elective courses are independent by its contents, and therefore, there are no extra requirements for attending them, exception being the year of study to ensure logical continuation of knowledge obtained in compulsory courses. Each course has an adequate amount of ECTS credits, and the total number of classes.

The purpose of the study programme of Mathematics stands for education of mathematician-researchers and their further advancement in scientific-research work. This also involves creating the young scientists at universities, scientific institutes and other institutions and facilities, where realization and modelling of practical problems involves using advanced mathematical structures.

The goal of the master study programme of Mathematics is obtaining more advanced, but still basic knowledge of all the major sub-disciplines out of the area of theoretical mathematics, including in particular: Calculus (with applications to geometry and physics), topology, abstract algebra, discrete mathematics, basic mathematical logic, and selected topics of numerical mathematics and statistics. Another goal is a deeper and broader study of the basic theoretical results of modern mathematics, as the initial phase of introducing the young mathematicians to scientific research in the field of mathematics. However, the intention of this programme is to develop the highest level of abstract, analytical and synthetic mental abilities, independence and initiative in solving mathematical problems, as well as a critical attitude towards the studied topics.

**General and Course-specific Competencies of Students**

Depending on the module selected, a Master in Mathematics will be able to do research, and advance in further self-development in the field of mathematics and other sciences. These include both scientific research activities at universities and research institutes, and participation in the implementation of development projects and other businesses, since it is expected that the flexibility, adaptability to new situations, and ability to apply theoretical knowledge, should be the main features of the Master in Mathematics. These professionals should be able to use computers in their work.

**Learning Outcomes**

Upon completing the programme, successful students should master the basic concepts and theoretical principles of mathematical sciences, and should be well trained in all the skills necessary for mathematical research.

**A Distribution of the Courses into Semesters and Academic Years**

No. | Course Code | Course Title | Semester | Course Status | Active teaching hours | ECTS | |

L | E | ||||||

FIRST YEAR | |||||||

1 | MA01 | Partial Differential Equations | I | O | 4 | 2 | 7,5 |

2 | MA02 | Algebra 3 | I | O | 4 | 2 | 7,5 |

3 | MB01 | Numerical Methods of Linear Algebra 1 | I | O | 3 | 3 | 7,5 |

4 | MB02 | Numerical Analisys 2 | I | O | 4 | 2 | 7,5 |

5 | MA03 | Operator Theory | II | O | 3 | 1 | 5 |

6 | MA04 | Programming 2 | II | O | 3 | 3 | 7,5 |

ECTS per year – total | 42,5 | ||||||

SECOND YEAR | |||||||

1 | MA05 | Measure and Integral | III | O | 2 | 2 | 5 |

2 | MA06 | Theory of Curves and Surfaces | III | O | 3 | 1 | 5 |

3 | MAZR | Master Thesis | IV | O | 20 | ||

ECTS per year – total | 30 | ||||||

ECTS – total | 72,5 |

- Course status: O-obligatory
- Teaching hours: L-lecture, E-exercise

**Elective courses in the Study Program**

No. | Course Code | Course Title | Semester | Course Status | Active teaching hours | ECTS | |

L | E | ||||||

Elective group 1 | |||||||

1 | MA11 | Number Theory | S | EG | 2 | 2 | 5 |

2 | MA12 | Graph Theory | S | EG | 2 | 2 | 5 |

Elective group 2 | |||||||

1 | MB22 | Equations of Mathematical Physics | S | EG | 3 | 1 | 5 |

2 | MB43 | Numerical Solving of Partial Differential Equations | S | EG | 3 | 1 | 5 |

Elective group 3 | |||||||

1 | MA31 | Advanced Mathematical Logic | W | EG | 3 | 1 | 5 |

2 | MA32 | Foundations of Algebraic Geometry | S | EG | 3 | 1 | 5 |

Elective group 4 | |||||||

1 | MA41 | Algebraic Topology | W | EG | 2 | 2 | 5 |

2 | MA42 | Advanced Topics in Functional Analisys | W | EG | 3 | 1 | 5 |

Elective group 5 | |||||||

1 | MB32 | Selected Topics in Applied Algebra | W | EG | 3 | 1 | 5 |

2 | MB33 | Selected Topics in Applied Analisys | W | EG | 3 | 1 | 5 |

3 | MB36 | Operations Research | W | EG | 4 | 2 | 7,5 |

4 | MB38 | Optimization | W | EG | 2 | 2 | 5 |

5 | MB52 | Projective Geometry | W | EG | 2 | 2 | 5 |

6 | MB53 | Theory of Algorithms | W | EG | 3 | 1 | 5 |

7 | MB54 | Fixed Point Theory | W | EG | 2 | 2 | 5 |

8 | MB24 | Mechanics of Continuous Environments | W | EG | 3 | 2 | 6 |

9 | MA61 | Differentional Geometry | S | EG | 3 | 1 | 5 |

10 | MA62 | Combinatorial Geometry | S | EG | 2 | 2 | 5 |

11 | MB04 | Numerical Methods of Linear Algebra 2 | S | EG | 3 | 3 | 7,5 |

12 | MA63 | Semigroups | S | EG | 3 | 1 | 5 |

12 | MB03 | Stochastic Analysis | S | EG | 4 | 2 | 7,5 |

14 | MB45 | Decision Theory | S | EG | 2 | 2 | 5 |

15 | MA64 | Set Theory | S | EG | 3 | 1 | 5 |

16 | MA65 | Theory of Formal Languages | S | EG | 2 | 2 | 5 |

17 | MA66 | Universal Algebra | S | EG | 3 | 1 | 5 |

- Student has to choose at least 1 course from Elective groups 1, 2, 3, and 4, and at least 2 courses from Elective group 5.
- Course status: EG-elective group
- Teaching hours: L-lecture, E-exercise