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

Name of the study programme is Mathematics (M3). The aim of the study programme, depending on the module selected is education of theoretical mathematicians, and mathematicians who are trained in application of mathematics in commerce, industry, financial and economic institutions.

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

Study of Mathematics belongs to a group of three-year undergraduate studies. Total number of ECTS is 180. The syllabus, as well as the forms and methods of teaching, enable students to acquire basic mathematical knowledge and to apply it in practice. Students who master this programme acquire the ability of logical thinking, formulating hypotheses and drawing conclusions in a formal or formalized way.

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

After completing three years of studies and earning 180 ECTS points, a student receives the professional title of Bachelor in Mathematics.

**Admission Conditions**

Admission of the candidates is based on the competition announced by the University of Novi Sad, and implemented at the Faculty of Sciences. To be eligible to enrol in the first year of the study, a candidate should have completed the four-year high school education and should pass an entrance exam in mathematics. Based on the criteria of the competition, a final ranking is made.

**The Structure of the Study Programme**

The study programme consists of a group of compulsory courses, three optional modules and free elective courses. The group consists of 16 compulsory courses organized into six semesters. Students who enrol in this programme choose one of the three optional modules (Theoretical Mathematics, Mathematics of Finance, or Technomathematics). Each module consists of 4 obligatory courses. There are 19 elective courses.

**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 undergraduate studies is three years (six semesters), during which a student needs to collect 180 ECTS.

**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**

Final work (graduation thesis) is not foreseen.

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

It is possible to choose courses from other study programs depending on the syllabus of the courses elected.

**Transferring from Another Study Programme**

Study programme of Bachelor Academic Studies in Mathematics has a dual purpose. Since the study of mathematics is organized as a 3+2 system, the three-year study is the first stage in university education of an expert mathematician. In the second stage, through two-year studies, a student acquires the title of Master in Mathematics. In this sense, the bachelor studies make the basis for the continuation of the related master academic study programme. In addition to this purpose within the 3+2 system, these studies have an independent role, particularly the modules of Financial Mathematics and Technomathematics. These modules train students for jobs in various areas of economy, especially in industry and financial institutions. These are the two optional modules that provide competency in applied mathematics. The choice of the two modules related to applied mathematics prepares students for jobs that require knowledge of the basics of applied mathematics, computer science and statistical methods, as well as the ability of analytical thinking and logical reasoning. The students would acquire skills and basic aspects of mathematical modelling and the ability to solve practical problems.

The objectives of the study programme include education of mathematicians, which is a profession that enables the graduates to work in research and development centres, modern industry, chambers of commerce, or the financial institutions and public administration, and in all places where there is a need for multidisciplinary work. Through a group of mathematical courses students get acquainted with the classical mathematical theories, as well as with current trends in mathematics. In addition to the knowledge acquired, 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 with considerable reputation in the scientific world and who are the participants and holders of several national and international research projects. Through the theoretical mathematics elective module, the students master the basics of theoretical mathematics. Through the module of Financial Mathematics, the students master the basic concepts and principles of economics, finance and accounting. Through the related courses, students are trained to communicate with economists and managers. Through the elective module of Technomathematics students master the concepts and principles of physics and selected engineering courses. The group of applied mathematics courses enables students to creatively work on mathematical models in modern technology, economics, and finance. Mathematical models allow deeper understanding of modern technology and economic laws. Knowledge in the field of information technology that is obtained during the study enable adequate application of modern software necessary for industrial development and the use of modern software tools in financial analysis. Graduate students become competent and well trained professionals who are in high demand in the market economy.

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

A Bachelor in Mathematics who completes this degree program would be able to address all aspects of the basic mathematical problems and tasks that involve handling of real and complex functions, topological, algebraic and combinatorial structures, geometric configurations, probability spaces, and the (exact) solution of basic types of differential equations and basic numerical problems. In addition, students would be able to systematically and clearly reinterpret the most important theoretical concepts in these areas and to apply them in simple modelling situations in practice. Finally, students would be able to perform the basic operations on the computer, and the software implementation of the basic forms of the problems considered. Depending on the choice of modules, students would gain the basic concepts and principles of the selected disciplines: physics and engineering or economics, finance and accounting. In addition, students of applied mathematics modules acquire the competence to communicate with engineers and, in addition, the ability to design and review mathematical models of modern technologies, economics and finance.

**Learning outcomes**

Upon graduation, a successful student would possess knowledge on the system of mathematical disciplines and the relationships among them, and he/she would deeply understand the basic concepts and results of the mentioned mathematical disciplines. This knowledge would allow him/her to successfully handle complex and sophisticated mathematical contents and applications of the acquired knowledge. Students of modules Technomathematics and Financial Mathematics, after successfully completing these bachelor studies, would gain basic knowledge of the major disciplines of applied mathematics. The knowledge gained would be a prerequisite for successful mastering of specific areas of applied mathematics on master academic studies (if a student continues his/her studies on master level). In addition, students would be able to apply their knowledge in practice, making the basic mathematical models. They would be able to recognize, select and use suitable mathematical models and solve practical problems in industry and economics.

**The curriculum scheme – Obligatory courses**

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

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

FIRST YEAR | Број часова | ||||

1 | М3-01 | Elementary Mathematics 1 | I | 2+2 | 5 |

2 | М3-02 | Introduction to Analysis | I | 4+3 | 8 |

3 | М3-03 | Algebra 1 | I | 3+3 | 8 |

4 | М3-04 | Programming 1 | I | 3+3 | 8 |

5 | М3-05 | Analysis 1 | II | 3+3 | 8 |

6 | М3-06 | Algebra 2 | II | 3+3 | 8 |

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

Total ECTS | 45 | ||||

SECOND YEAR | |||||

1 | М3-07 | Analysis 2 | III | 4+3 | 8 |

2 | М3-08 | Linear Algebra | III | 4+3 | 8 |

3 | М3-09 | Foundations of Geometry 1 | III | 4+4 | 8 |

4 | М3-10 | Combinatorics | IV | 3+2 | 6 |

Active teaching hours per year– total | 27 | ||||

Total ECTS | 30 | ||||

THIRD YEAR | |||||

1 | М3-11 | Ordinary Differential Equations | V | 3+3 | 7 |

2 | М3-12 | Probability | V | 3+3 | 7 |

3 | М3-13 | Numerical Analysis 1 | V | 3+4 | 8 |

4 | М3-14 | Metric and normed spaces | VI | 3+3 | 7 |

5 | М3-15 | Statistics | VI | 3+3 | 7 |

6 | М3-16 | History of Mathematics | VI | 3+1 | 5 |

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

Total ECTS | 41 |

- 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**

**Elective modules**

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

Active teaching hours | |||||

ELECTIVE MODULE: THEORETICAL MATHEMATICS | Elective module: Theoretical Mathematics | Elective module: Theoretical Mathematics | Elective module: Theoretical Mathematics | Elective module: Theoretical Mathematics | Elective module: Theoretical Mathematics |

1 | М3-17 | Analytic Geometry | II | 2+2 | 5 |

2 | М3-18 | Complex Analysis | IV | 3+3 | 7 |

3 | М3-19 | Foundations of Geometry 2 | IV | 2+2 | 5 |

4 | М3-20 | Group Theory | VI | 3+3 | 7 |

Active teaching hours– total | 20 | ||||

Total ECTS | Total ECTS | Total ECTS | Total ECTS | Total ECTS | 24 |

ELECTIVE MODULE: MATHEMATICS OF FINANCE | |||||

1 | М3-21 | Mathematical Principles of Economics | I | 4+0 | 5 |

2 | М3-22 | Financial Mathematics 1 | II | 3+4 | 8 |

3 | М3-23 | Finance 1 | III | 3+3 | 7 |

4 | М3-24 | Numerical Methods of Linear Algebra 1 | IV | 3+4 | 8 |

Active teaching hours– total | 24 | ||||

Total ECTS | 28 | ||||

ELECTIVE MODULE: TECHNOMATHEMATICS | |||||

1 | ФДОК1О12 | Mechanics | III | 3+3 | 8 |

2 | М3-24 | Numerical Methods of Linear Algebra 1 | IV | 3+4 | 8 |

3 | М3-25 | Thermodynamics | IV | 3+3 | 7 |

4 | М3-26 | Theoretical Mechanics | VI | 2+2 | 5 |

Active teaching hours– total | 23 | ||||

Total ECTS | 28 |

- 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 modules**

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

1 | М-01 | Boolean algebra and optimization | winter | 2+3 | 6 |

2 | М-02 | English language 1 | winter | 2+0 | 4 |

3 | М-03 | Optimization | winter | 2+3 | 6 |

4 | М-04 | Projective Geometry | winter | 2+2 | 5 |

5 | М-05 | Accounting | winter | 3+2 | 6 |

6 | М-06 | Fourier analysis | winter | 2+2 | 5 |

7 | М-07 | Databases 1 | winter | 2+3 | 6 |

8 | ФДОК5О12 | Electromagnetism | winter | 3+4 | 7 |

9 | ФДОИ2И12 | Fluid Mechanics | winter | 3+2 | 6 |

10 | М-08 | Elementary Mathematics 2 | summer | 2+2 | 5 |

11 | М-09 | English Language 2 | summer | 2+0 | 4 |

12 | М-10 | Combinatorial Geometry | summer | 2+2 | 5 |

13 | М-11 | Modelling of Dynamical Systems | summer | 2+2 | 5 |

14 | М-12 | Business informatics | summer | 2+4 | 7 |

15 | М-13 | Programming 2 | summer | 3+3 | 7 |

16 | М-14 | Audit | summer | 3+3 | 7 |

17 | М-15 | Sociology | summer | 2+0 | 4 |

18 | М-16 | Theory of Automata | summer | 2+2 | 5 |

19 | ФДОК8О12 | Foundations of Electronics | summer | 3+3 | 7 |

Total ECTS | 107 |

- 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