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

Name of the study programme is Master in Mathematics Teaching (MP). The aim of the study programme is the education of prospective professor of mathematics in elementary and high schools.

**Type of the Study and the Outcome of the Education Process**

Study programme of Master in Mathematics Teaching belongs to a group of two-year master studies. Total number of ECTS is 120. The syllabus, as well as the forms and methods of teaching enable students to acquire basic mathematical knowledge and to apply mathematical knowledge in teaching mathematics. After completing two years of the study and earning 120 ECTS points, a student receives the professional title of Master in Mathematics.

**Admission Conditions**

To be eligible to enrol in the first year of studies, a candidate should have completed at least three years of undergraduate studies of mathematics with accumulated at least 180 ECTS (for example the study programme M3 offered by the Faculty of Sciences, University of Novi Sad) and should pass an entrance exam in mathematics. Admission of the candidates is based on competition announced by the University of Novi Sad, and the programme is implemented at the Faculty of Sciences. Ranking is made according to the competition criteria. Candidates who finished undergraduate studies of some other academic disciplines have to additionally pass some mathematical subjects to be able to follow courses in this programme. The list of these mathematical subjects will be formed by the Educational-Scientific Council of the Faculty of Sciences, tailored specifically for each of the candidates who finished undergraduate studies other than mathematics.

**The Structure of the Study Programme**

The study programme consists of a group of 13 obligatory courses (83 ETCS) and 25 elective courses (choosing 37 ETCS from 137 ETCS offered). The graduation thesis is obligatory (15 ETCS). The character of this study programme is twofold: students will acquire in-depth theoretical knowledge in main areas of mathematics and gain theoretical and practical knowledge in pedagogical and psychological aspects of mathematics education (teaching and learning mathematics). Hence, the list of obligatory courses contains both theoretical mathematical and educational/didactical courses, preparing the students to be competent and successful mathematics teachers in elementary and high schools. The elective courses are from a wide spectrum of mathematical disciplines and provide a possibility for students to choose those subjects which interest them the most.

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

The studies are carried out through teaching arranged into semesters. Two semesters constitute an academic year. The total duration of studies is two years (four semesters) during which the students need to collect 120 ECTS. Besides theoretical teaching, students also have school practice in some of elementary or high schools.

**Credit Values of Particular Courses**

Each course has a scoring value, which is in line with the load required to complete the individual course.

**Diploma Work**

Graduation thesis is obligatory (15 ETCS).

**Way of Choosing Courses from the Other Study Programmes**

It is possible to choose courses from other study programmes, mainly from the study programme of MA (Mathematics) and MB (Applied mathematics), offered at the Faculty of Sciences.

**Transferring from Another Study Programme**

It is possible to transfer from this study programme to other related programmes by using the credit transfer for the same or similar courses.

The purpose of the study programme of Master in Mathematics Teaching is education of prospective mathematics teachers in elementary and high schools. The maxim is that a competent and successful mathematics teacher needs to have both the reliable subject knowledge and doubtless pedagogical skills.

The objectives of the study include education of prospective mathematics tеаchers who will be able to teach mathematics in elementary and high schools. Students mastering this mathematics programme acquire the ability of logical thinking, formulating hypotheses and drawing conclusions in a formal or formalized way. They will have the skills to successfully transfer the main mathematical ideas to students in elementary and high schools. Through the group of mathematical courses, students get acquainted with the classical mathematical theories, as well as with current trends in mathematics. In addition to the acquired knowledge, such education enables students to become capable of abstraction and logical thinking. The quality of education is guaranteed by the fact that it is performed by professors who are reputable and recognized in the scientific world.

Besides this, through pedagogical and psychological courses the students will gain the necessary competencies of a successful teacher: they will understand the process of learning mathematics, and will be capable to modify the educational tasks and approaches depending on the intellectual, social and motivational diversity in the classroom. Knowledge in the field of information technology that is obtained during the study enables adequate application of modern software necessary for being mathematics teacher in future educational systems.

**General and course-specific competencies of students**

A mathematician who completes this degree program would be able to teach mathematics in elementary schools and in all kinds of high schools, with great theoretical knowledge in mathematics and with pedagogical and other educational skills necessary to plan and conduct the teaching process.

The students will develop their ability of analytical thinking and logical reasoning and will possess skills to perform mathematical modelling and the ability to solve practical problems. They will be capable of solving mathematical problems and tasks that involve handling of real and complex functions, topological, algebraic and combinatorial structures, geometric configurations, probability spaces, and various types of differential equations and basic numerical problems.

**Learning outcomes**

Upon graduation, successful students should possess knowledge on the system of mathematical disciplines and the relationships among them, as well as in-depth understanding of the basic concepts and results of the mentioned mathematical disciplines. This knowledge would allow them to successfully conduct the teaching process in elementary and high schools.

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

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

FIRST YEAR | Број часова | ||||

1 | МA-02 | Topology | I | 3+3 | 7 |

2 | МA-03 | Rings, Fields and Galois Theory | I | 3+1 | 5 |

3 | МP-01 | Teaching of mathematics 1 | I | 2+2 | 5 |

4 | МP-02 | Evolutionary and educational psychology | I | 3+1 | 5 |

5 | МP-03 | Pedagogy | II | 3+0 | 5 |

6 | МP-04 | Nonstandard mathematical problems | II | 2+2 | 5 |

7 | MP-05 | Teaching of mathematics 2 | II | 2+2 | 5 |

8 | MP-06 | School practice | II | 0+6 | 6 |

Active teaching hours per year– total | 35 | ||||

Total ECTS | 43 | ||||

SECOND YEAR | |||||

1 | МA-07 | Measure and integral | III | 2+2 | 5 |

2 | МP-07 | Mathematical logic | III | 3+1 | 5 |

3 | МA-08 | Theory of Curves and Surfaces | III | 2+2 | 5 |

4 | МP-08 | Numerical Solving of Equations | III | 3+1 | 5 |

5 | MP-09 | Descriptive Geometry | IV | 2+2 | 5 |

6 | MP-10 | Graduation Thesis | IV | 15 | |

Active teaching hours per year– total | 20 | ||||

Total ECTS | 40 |

- Course type: AO-academic and general education, ТМ-theoretical-methodological, SP-scientific-professional, PА-professional applicative
- Course status: O-obligatory, E-elective block
- Teaching hours: L-lecture, E-exercise, АE-auditory exercises, LE-laboratory exercises, OTF-other teaching forms (seminar work, etc.), SRW-study research work

**Elective courses in the Study Program**

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

GROUP A | Група А | Група А | Група А | Група А | Група А |

1 | МB-12 | Selected topics in applied algebra | I or III | 3+1 | 5 |

2 | МA-12 | Theory of algorithms | I or III | 3+1 | 5 |

3 | МA-13 | Theory of formal languages | I or III | 2+2 | 5 |

4 | МA-01 | Partial differential equations | I or III | 4+2 | 7 |

5 | MB-01 | Numerical analysis 2 | I or III | 4+2 | 7 |

6 | MA-06 | Algebraic topology | I or III | 2+2 | 5 |

7 | MB-02 | Stochastic analysis | I or III | 4+2 | 7 |

8 | MB-04 | Seminar in mathematical modelling 1 | I or III | 1+5 | 6 |

9 | MB-14 | Operations research | I or III | 4+2 | 7 |

10 | MB-18 | Seminar in informatics | I or III | 1+3 | 4 |

11 | MA-05 | Functional analysis | II or IV | 3+3 | 7 |

12 | MA-16 | Semigroups | II or IV | 3+1 | 5 |

13 | MA-17 | Set Theory | II or IV | 3+1 | 5 |

14 | MA-18 | Universal algebra | II or IV | 3+1 | 5 |

15 | MB-03 | Numerical methods of linear algebra 2 | II or IV | 4+2 | 7 |

16 | MB-10 | Equations of mathematical physics | II or IV | 3+1 | 5 |

17 | MA-19 | Differential geometry | II or IV | 2+2 | 5 |

18 | MP-11 | Physics 2 | II or IV | 2+2 | 5 |

19 | MA-20 | Numerical solving of partial differential equations | II or IV | 3+1 | 5 |

Active teaching hours– total | 90 | ||||

Total ECTS | Total ECTS | Total ECTS | Total ECTS | Total ECTS | 107 |

GROUP B | |||||

20 | МP-12 | Geometric practicum | I or III | 2+2 | 5 |

21 | МP-13 | Modern teaching aids | I or III | 2+2 | 5 |

Active teaching hours– total | 8 | ||||

Total ECTS | 10 | ||||

GROUP C | |||||

22 | MA-14 | Fixed Point Theory | I or III | 2+2 | 5 |

23 | МA-15 | Operator Theory | I or III | 2+2 | 5 |

24 | МA-10 | Number Theory | II or IV | 2+2 | 5 |

25 | МA-11 | Graph Theory | II or IV | 2+2 | 5 |

Active teaching hours– total | 16 | ||||

Total ECTS | 20 |

- Course type: AO-academic and general education, ТМ-theoretical-methodological, SP-scientific-professional, PА-professional applicative
- Course status: O-obligatory, E-elective block
- Teaching hours: L-lecture, E-exercise, АE-auditory exercises, LE-laboratory exercises, OTF-other teaching forms (seminar work, etc.), SRW-study research work