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

The study programme title is Applied Mathematics (MB). The aim of the study programme is to educate master level graduates in Applied Mathematics as competent professionals in commerce, industry, financial and economic institutions.

The curriculum is prepared according to the requirements of ECMI Educational Programme

(http://www.ecmi-indmath.org/) and is waiting for final ECMI accreditation.

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

The study programme is a two-year master level programme with total of 120 ECTS. The syllabus, as well as forms and methods of teaching enable students to acquire fundamental knowledge in advance mathematics, applications of mathematical knowledge in real world problems, and skills of mathematical modelling for problems coming from industry in general. By mastering the programme, a student will acquire the ability of logical thinking, formulating and solving mathematical models and applying advanced mathematical knowledge in other disciplines. Besides mathematical subjects, a student is required to have knowledge in a chosen minor discipline (physics and technology or economics and finances). The ability to communicate with engineers or economists is one of the requirements of the programme together with computer science skills.

**Admission Conditions**

Admission of the candidates is based on open competition announced by the University of Novi Sad and implemented at the Faculty of Sciences. To be eligible to enrol in the programme, a candidate should hold a bachelor degree in mathematics and should pass an entrance exam in mathematics. The ranking is formed according to grades from the bachelor level, entrance exam result and the duration of previous studies. A candidate with bachelor degree from some other area is eligible to enrol in the programme after passing the exam consisting of four mathematical subjects that are publicly announced in the competition call.

**The Structure of the Study Programme**

The study programme consists of a group of compulsory courses, two optional modules, free elective courses and master thesis. The compulsory courses are grouped in 3 semesters. A student has to choose one of the modules: Mathematics of Finance, or Technomathematics. The elective courses comprise 26 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 master studies is two years (four semesters), during which a student needs to collect 120 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**

The final work, master thesis, is a final exam for obtaining the title Master in Mathematics – Applied Mathematics. It is a work done by a student with some help from the thesis adviser/mentor and represents a nontrivial application of the mathematical knowledge acquired during the studies on a problem that is relevant in finance, economics or technology in broad sense. The thesis could also be a substantial expansion of theoretical knowledge relevant for the study programme. The master thesis has a credit value of 30 ECTS.

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

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

**Transferring from Another Study Programme**

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

The purpose of the study programme is to educate professionals with the title of Master in Mathematics – Applied Mathematics. Two possible modules, Mathematics of Finance and Technomathematics allow a student to choose his/her minor field of interest and thus complete his/her mathematical knowledge with relevant understanding and skills in the minor field. On the one hand, the graduates are equipped with advanced mathematical knowledge in different areas of applied and numerical mathematics, statistics, computer science while, on the other hand, they posses certain knowledge in technology or economics and finance. The programme trains future professionals for analytical and logical thinking, and provides them with the ability of creative solving of complex mathematical models and forming mathematical models in challenging real world issues coming from the relevant minor fields of study. The final aim of the programme is to train professionals who will creatively and optimally apply the vast mathematical knowledge in practical problems coming from different areas, and thus will be engaged in industry.

The goals of the study programme is to provide the graduates with knowledge in the most important areas of applied mathematics and, according to one of the elective modules, relevant knowledge in technological or economics-financial topics. These courses are designed in a way that allows a student to pursue career in industry and financial institutions.

The five obligatory courses consist of topics and contents that are the most relevant to mathematical modelling and solving of mathematical models. The knowledge acquired through these courses is upgraded and complemented with the topics in one of the two modules – Mathematics of Finance, or Technomathematics, and therefore a student is directed towards one of these two areas.

The module of Mathematics of Finance consists of 3 courses, provides the knowledge necessary to work in financial institutions, public institutions as well as in insurance industry.

The four courses in the module of Technomathematics are designed to provide advanced knowledge in physics and selected engineering courses.

Knowledge in the field of computer science enables adequate application of modern software necessary for industrial development and the use of modern software tools in financial analysis. The graduates are competent and well-trained professionals who are in great demand in the market economy.

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

Students enrolled in this programme will have the ability of logical thinking, the ability of abstraction necessary to transform a real life problem into a mathematical model, will posses high-level knowledge of mathematics, as well as understanding of concepts and language in technology or economics and finance – according to the selected module, will be able to communicate with engineers or economists and therefore will be able to participate in teamwork and fundamentally contribute to the industrial development. The knowledge in computer science will equip students with the ability of using the modern software tools. Finally, the ability of acquiring new knowledge and developing new mathematical models according to real industrial needs will be the main asset of a graduate in Master Academic Studies in Applied Mathematics.

**Learning outcomes**

A successful graduate of this programme will possess high-level knowledge in the most important field of applied mathematics. He or she will be able to apply that knowledge for solving real world problems coming from the needs of industry and society. The application of knowledge will include the ability of developing new mathematical models as well as the ability of solving the models according to the needs of industry. Finally, the ability to work as a part of a multidisciplinary team of professionals will be achieved through couple of courses that are taught in a specific manner to strengthen communication and presentation skills.

Five obligatory courses with total of 34 ECTS are distributed as follows: 3 courses are in the first semester; the second and the third semester contains one obligatory course each, while the fourth semester is dedicated to the master thesis project with 30 ECTS. After the enrolment in the study programme, a student has to choose one of the modules: Mathematics of Finance or Technomathematics. The module of Mathematics of Finance consists of 3 courses with 20 ECTS, while Technomathematics consists of 4 courses with 20 ECTS. The rest of ECTS is selected from the list of 26 courses (with total of 133 ECTS), taking at least 34 ECTS. The list of elective courses is divided into two parts, A and B, and a master student in Applied Mathematics has to choose at least 5 courses from list A.

The master thesis is a project done by the student and supervised by a professor acting as a thesis advisor. The work has to be a nontrivial application of advanced mathematical knowledge to a problem that is relevant for industry or society in broad sense. The actual input from industry is desirable. The thesis can be theoretical assuming that the topic is well beyond the scope of mathematical courses taken during the studies. The topic of the thesis is approved by the Scientific and Education Council of the Department of Mathematics and Informatics. The thesis is written and submitted to the Evaluation Board formed by the Scientific and Educational Council. Before the public defence, the thesis is subject to the approval of the Evaluation Board and the Council.

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

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

No. | Title | L | E | |||

FIRST YEAR | ||||||

1 | МА-01 | Partial Differential equations | I | 4 | 2 | 7 |

2 | МБ-01 | Numerical Analysis 2 | I | 4 | 2 | 7 |

3 | МБ-02 | Stochastic Analysis | I | 4 | 2 | 7 |

4 | МБ-03 | Numerical methods of linear algebra 2 | II | 4 | 2 | 7 |

Active teaching per semester | W:12 S:4 | W:6 S:2 | ||||

Total ECTS | 28 | |||||

SECOND YEAR | ||||||

1 | МБ-04 | Modelling Seminar 1 | III | 1 | 5 | 6 |

2 | МБ-05 | Master Thesis | IV | - | 30 | |

Student research work | 26 | |||||

Active teaching per semester | W:1 S:0 | W:5 S:0 | ||||

Total ECTS | 36 | |||||

Elective module: Financial Mathematics | Elective module: Financial Mathematics | Elective module: Financial Mathematics | Elective module: Financial Mathematics | Elective module: Financial Mathematics | Elective module: Financial Mathematics | Elective module: Financial Mathematics |

1 | МБ-06 | Financial Mathematics 2 | I | 4 | 2 | 7 |

2 | МБ-07 | Маthematical Models in Economics | II | 4 | 2 | 7 |

3 | МБ-08 | Еconometrics | III | 3 | 2 | 6 |

Active teaching per semester | W:7 S:4 | W:4 S:2 | ||||

Total ECTS | 20 | |||||

Elective module: Techno-mathematics | Elective module: Techno-mathematics | Elective module: Techno-mathematics | Elective module: Techno-mathematics | Elective module: Techno-mathematics | Elective module: Techno-mathematics | Elective module: Techno-mathematics |

1 | МБ-09 | Information and Coding Theory | I | 3 | 3 | 7 |

2 | МБ-25 | Contemporary Theoretical Physics | I | 4 | 3 | 5 |

3 | МБ-10 | Equations of Mathematical Physics | IV | 3 | 1 | 5 |

4 | МБ-11 | Modelling Seminar 2 | IV | 1 | 2 | 3 |

Active teaching per semester | W:7 S:4 | W:6 S:3 | ||||

Total ECTS | 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

**Elective courses in the Study Program**

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

L | E | |||||

ELECTIVE COURSES А | Elective courses А | Elective courses А | Elective courses А | Elective courses А | Elective courses А | Elective courses А |

1 | МБ-12 | Selected Topics in Applied Algebra | W | 3 | 1 | 5 |

2 | МА-14 | Fixed Point Theory | W | 2 | 2 | 5 |

3 | МБ-13 | Time Series | W | 2 | 2 | 5 |

4 | МБ-14 | Operations Research | W | 4 | 2 | 7 |

5 | МБ-15 | Numerical Optimization | W | 4 | 2 | 7 |

6 | МБ-16 | Advanced Programming for mathematicians | W | 3 | 3 | 7 |

7 | МБ-17 | Information Systems | W | 2 | 3 | 6 |

8 | МБ-18 | Seminar in informatics | W | 1 | 3 | 4 |

9 | МБ-19 | Financial Economics 2 | W | 3 | 1 | 5 |

10 | ФДОИ40И12 | Gravity Theory | W | 3 | 2 | 6 |

11 | МБ-20 | Statistical Modelling | S | 2 | 2 | 5 |

12 | MA-19 | Differential Geometry | S | 3 | 1 | 5 |

13 | МБ-21 | Decision Theory | S | 2 | 2 | 5 |

14 | МБ-22 | Actuarial Mathematics | S | 3 | 3 | 7 |

15 | МБ-23 | Analysis of financial statements | S | 2 | 2 | 5 |

16 | МБ-24 | Insurance Theory | S | 2 | 2 | 5 |

17 | МА-20 | Numerical solving of PDEs | S | 3 | 1 | 5 |

18 | ФДОИ18И12 | Relativity Theory | S | 3 | 2 | 6 |

19 | ФДОК12О12 | Contemporary Experimental Physics 2 | S | 3 | 4 | 7 |

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

ELECTIVE COURSES B | ||||||

1 | МП-01 | Teaching of mathematics 1 | W | 2 | 2 | 5 |

2 | МП-02 | Evolutionary and educational psychology | W | 3 | 1 | 5 |

3 | МП-03 | Pedagogy | S | 3 | 0 | 5 |

4 | МП-05 | Teaching of mathematics 2 | S | 2 | 2 | 5 |

5 | МП-06 | School practise | S | 0 | 6 | 6 |

Total ECTS | Total ECTS | 26 |

- 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