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

Study programme of Bachelor Academic Studies in Mathematics Teaching (code: M4).

**Admission Conditions**

Programme curriculum comprises 29 compulsory courses that are accepted world-wide as the core of basic academic education of every mathematician, including 8 courses from the category of methodical-psychological-pedagogical subjects (MPP courses). Courses include the basics of calculus (functions of real and complex variables, differential equations, functional analysis), topology, algebra, arithmetic, discrete mathematics, geometry (analytical, absolute, Euclidean, hyperbolic), numerical mathematics, probability theory and statistics. Students’ knowledge is broadened through 32 specialized general and mathematical courses. Three of them are from the group of MPP courses, while four courses fall into the category of highly specialized mathematical subjects available in the final year of study.

**The Structure of the Study Programme**

Programme curriculum comprises 29 compulsory courses that are accepted world-wide as the core of basic academic education of every mathematician, including 8 courses from the category of methodical-psychological-pedagogical subjects (MPP courses).

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

Their duration is 4 years (8 semesters),

**Credit Values of Particular Courses**

The total value credit score is 240 ECTS, and upon completion, a student acquires a degree of Bachelor with Honours in Mathematics Teaching.

An adequate number of ECTS and teaching hours, have been assigned to each course. Teaching is mainly performed on frontal lectures, with an appropriate use of modern visual aids. Due to the specific nature of mathematics as a science, most of the exercises have theoretical character where previously presented theoretical principles are practised and typical problems and their solutions analyzed, after which students independently apply the techniques adopted. In a number of courses (mostly in computer science, numerical mathematics and other applied disciplines), the use of computers is provided as part of exercises and other forms of students research work. This study programme provides collecting of 40 ECTS in the MPP courses, and additional 6 ECTS in school practice, which qualify a student for teaching mathematics in schools upon completing the studies.

The purpose and the role of this programme is to provide an adequate base of knowledge required to successfully undertake the master academic studies in the field of pure mathematics or teaching of mathematics. In addition, due to sufficient number of courses in the MPP group, this study programme educates future teachers capable of applying modern methodological principles and techniques of educational technology in the preparation and teaching of mathematics in primary and secondary schools.

- Introduction to the foundations of mathematical disciplines, roles and relationships between subfields of mathematics, as well as basic objects, concepts and methods of the disciplines studied;
- Acquisition of basic knowledge of key mathematical theories and structures, with special emphasis on the theory of functions, differential equations, topology, general and linear algebra, group theory, rings and fields, combinatorics, axiomatic approach to geometry and the basics of numerical mathematics and probability theory and statistics;
- Preparation for further knowledge upgrade, as a theoretical basis for adopting the more advanced and complex mathematical theories, but also as a basis for applying the acquired knowledge in mathematical modelling of practical problems and methodical transformation of contents learned in the classroom practice;
- High level of development of the abstract, as well as analytical and synthetic logical thinking and mathematical understanding of the different levels of abstraction;
- Developing initiative and ability to independently solve problems and critical approach to the analysis of the logical correctness of solutions to mathematical problems;
- Adoption and practice of methodological, didactic and psychological processes necessary for successful teaching of mathematics in schools, and the acquisition and practice routines in that direction.

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

Students who complete this study programme will be able to address all aspects of solving basic mathematical problems and tasks that involve real and complex functions, topological, algebraic and combinatorial structures, geometric objects and configurations, probability spaces, and the (exact) solution of basic types of differential equations and basic numerical and statistical problems. In addition, students will be able to systematically, visibly and clearly reinterpret the most important theoretical concepts in these areas and apply them in simple modelling situations from practice. Graduate student earns 40 ECTS from a group of psychological, pedagogical and methodological disciplines, and with an additional 6 ECTS from school practice, he/she is legally qualified to engage in educational work and teaching of mathematics in primary and secondary schools with modern teaching methods and methodical, didactic and psychological processes. The general culture of a student who completes this degree program also consists of knowledge from the history of mathematics. Besides performing basic operations on the computer, graduate student is skilled in software implementation of the basic forms of the problems considered.

**Learning outcomes**

Upon graduation, successful students will acquire an idea of a system of mathematical disciplines and the relationships among them, and fundamentally understand the basic concepts and results of a branch of mathematics mentioned in the objectives of this study programme. This knowledge will allow him/her to successfully adopt more complex and sophisticated mathematical contents as well as application of knowledge acquired, primarily.

**The curriculum scheme**

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

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

No. | Course Code | Course Title | Semester | Lectures | Exercises | OFT | ||||

FIRST YEAR | ||||||||||

1 | М4-01 | Elementary Mathematics 1 | I | TM | C | 2 | 2 | 5 | ||

2 | М4-02 | Introduction to Analysis | I | SP | C | 4 | 3 | 8 | ||

3 | М4-03 | Algebra 1 | I | SP | C | 3 | 3 | 8 | ||

4 | М4-04 | Programming 1 | I | АG | C | 3 | 3 | 8 | ||

5 | М4-05 | Analysis 1 | II | SP | C | 3 | 3 | 8 | ||

6 | М4-06 | Algebra 2 | II | SP | C | 3 | 3 | 8 | ||

7 | М4-07 | Analytic Geometry | II | SP | C | 2 | 2 | 5 | ||

Active teaching hours per year– total | 39 | |||||||||

SECOND YEAR | ||||||||||

1 | М4-08 | Analysis 2 | III | SP | C | 4 | 3 | 8 | ||

2 | М4-09 | Linear Algebra | III | SP | C | 4 | 3 | 8 | ||

3 | М4-10 | Foundations of Geometry 1 | III | SP | C | 4 | 4 | 8 | ||

4 | М4-11 | Combinatorics | IV | SP | C | 3 | 2 | 6 | ||

5 | М4-12 | Complex Analysis | IV | SP | C | 3 | 3 | 7 | ||

6 | М4-13 | Foundations of Geometry 2 | IV | SP | C | 2 | 2 | 5 | ||

Active teaching hours per year– total | 37 | |||||||||

THIRD YEAR | ||||||||||

1 | М4-14 | Ordinary Differential Equations | V | SP | C | 3 | 3 | 7 | ||

2 | М4-15 | Probability | V | SP | C | 3 | 3 | 7 | ||

3 | М4-16 | Numerical Analysis 1 | V | SP | C | 3 | 4 | 8 | ||

4 | PMF01 | Development and Pedagogical Psychology | V | TM | C | 3 | 1 | 5 | ||

5 | М4-17 | Statistics | VI | PА | C | 3 | 3 | 7 | ||

6 | М4-18 | Group Theory | VI | SP | C | 3 | 3 | 7 | ||

7 | PMF03 | Pedagogy | VI | ТМ | C | 4 | 0 | 5 | ||

8 | М4-19 | History of Mathematics | VI | ТМ | C | 3 | 1 | 5 | ||

Active teaching hours per year– total | 43 | |||||||||

FOURTH YEAR | ||||||||||

1 | М4-20 | Topology | VII | SP | C | 3 | 3 | 7 | ||

2 | М4-21 | Rings, Fields and Galois Theory | VII | SP | C | 3 | 1 | 5 | ||

3 | М4-22 | Physics 1 | VII | SP | C | 2 | 2 | 5 | ||

4 | М4-23 | Teaching of Mathematics 1 | VII | ТМ | C | 2 | 2 | 5 | ||

5 | М4-24 | Functional Analysis | VIII | SP | C | 3 | 3 | 7 | ||

6 | М4-25 | Nonstandard Mathematical Problems | VIII | ТМ | C | 2 | 2 | 5 | ||

7 | М4-26 | Teaching of Mathematics 2 | VIII | ТМ | C | 2 | 2 | 5 | ||

8 | М4-27 | School Practice | VIII | PА | C | 0 | 0 | 6 | 6 | |

Active teaching hours per year – total | 32 | |||||||||

Total: 82 | Total: 69 | Total: 0 | ||||||||

Active teaching hours – total | 151 | |||||||||

ECTS – total | 188 |

- 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 | Course Type | Course Status | Active teaching hours | ECTS | |||

No. | Course Code | Course Title | Lectures | Exercises | OFT | SRW | ECTS | ||

GROUP A (elective on first three years) | |||||||||

1 | М-01 | Boolean Algebras and Optimisation | SP | EB | 2 | 3 | 6 | ||

2 | М-02 | English 1 | АG | EB | 2 | 0 | 4 | ||

3 | М-03 | Optimization | SP | EB | 2 | 3 | 6 | ||

4 | М-04 | Projective Geometry | SP | EB | 2 | 2 | 5 | ||

5 | М-05 | Accounting | АG | EB | 3 | 2 | 6 | ||

6 | М-06 | Fourier Analysis | SP | EB | 2 | 2 | 5 | ||

7 | М3-21 | Mathematical Principles of Economics | АG | EB | 4 | 0 | 5 | ||

8 | М3-23 | Finance 1 | PА | EB | 3 | 3 | 7 | ||

9 | М-07 | Databases 1 | PА | EB | 2 | 3 | 6 | ||

10 | FDОK5О12 | Electromagnetism | АG | EB | 3 | 1 | 3 | 7 | |

11 | FDОK1О12 | Mechanics | АG | EB | 3 | 1 | 2 | 8 | |

12 | FDOI2I12 | Fluid Mechanics | АG | EB | 3 | 1 | 1 | 6 | |

13 | М-08 | Elementary Mathematics 2 | ТМ | EB | 2 | 2 | 5 | ||

14 | М-09 | English 2 | АG | EB | 2 | 0 | 4 | ||

15 | М-10 | Combinatorial Geometry | SP | EB | 2 | 2 | 5 | ||

16 | М-11 | Modelling of Dynamical Systems | PА | EB | 2 | 2 | 5 | ||

17 | М3-24 | Numerical Methods of Linear Algebra 1 | SP | EB | 3 | 4 | 8 | ||

18 | М-12 | Business Informatics | PА | EB | 2 | 4 | 7 | ||

19 | М-13 | Programming 2 | PА | EB | 3 | 3 | 7 | ||

20 | М-14 | Audit | PА | EB | 3 | 3 | 7 | ||

21 | М-15 | Sociology | АG | EB | 2 | 0 | 4 | ||

22 | М-16 | Theory of Automata | SP | EB | 2 | 2 | 5 | ||

23 | М3-22 | Financial Mathematics 1 | PА | EB | 3 | 4 | 8 | ||

24 | FDOK8О12 | Foundations of Electronics | АG | EB | 3 | 1 | 2 | 7 | |

25 | М3-26 | Theoretical Mechanics | SP | EB | 2 | 2 | 5 | ||

26 | М3-25 | Тhermodynamics | АG | EB | 3 | 3 | 7 | ||

GROUP B (elective on fourth year) | |||||||||

1 | М4-33 | Geometric Practicum | ТМ | EB | 2 | 2 | 5 | ||

2 | М4-28 | Modern Teaching Aids | ТМ | EB | 2 | 2 | 5 | ||

GROUP C (elective on fourth year) | |||||||||

1 | М4-29 | Fixed Point Theory | SP | EB | 2 | 2 | 5 | ||

2 | М4-30 | Operator Theory | SP | EB | 2 | 2 | 5 | ||

GROUP D (elective on fourth year) | |||||||||

1 | М4-31 | Number Theory | SP | EB | 2 | 2 | 5 | ||

2 | М4-32 | Graph Theory | SP | EB | 2 | 2 | 5 |

- 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