The study programme Applied Mathematics (MAP) is a study program of undergraduate academic studies that is based and relies on years of tradition and experience in the education of mathematicians in the field of mathematics and applied mathematics at the Faculty of Sciences in Novi Sad.
Title and Goals of the Study Programme
Type of Studies and Outcome of the Education Process
The study programme is a three-year undergraduate level programme with a total of 180 ECTS. In order to obtain a BSc degree in APPLIED MATHEMATICS each student is expected to pass all the compulsory courses within the study program and collect at least 180 ECTS. The final total number of collected ECTS points may vary from student to student depending on their choice of elective courses with a maximal value of 201 ECTS points. The syllabus, as well as forms and methods of teaching enable students to acquire fundamental knowledge in mathematics and applications of mathematical proficiency in practice. Students who master the programme in APPLIED MATHEMATICS acquire the ability of logical thinking, formulating hypotheses and drawing conclusions in a formal or formalized way.
Professional, Academic, or Scientific Title
Upon 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 by 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.
Structure of the Study Programme/strong>
The study programme consists of a group of compulsory courses, three optional modules and elective courses. The compulsory courses group consists of 16 courses organized into six semesters. At the final year of studies students have an obligatory Professional Practice and they write and defend a Bachelor Thesis. Students who enrol in this programme choose between one of the three optional modules: Data Analytics and Statistics, Mathematics of Finance, or Techno-mathematics. The elective courses group consists of 15 courses.
Time Allotted for the Realization of Particular Study Forms
The studies are conducted through teaching classes 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 at least 180 ECTS points.
Credit Values of Particular Courses
Each course has a scoring value consistent with the load required to complete the individual course.
Realization of Teaching
The entire teaching process conducted at the study program will take place using modern IT technologies, contemporary software packages and computer equipment.
Diploma Work
ЗThe final work, Bachelor Thesis, has a scoring value consistent with the load required for its preparation (research), production and defense. The Bachelor Thesis is registered in the study programme at two positions: 1) Bachelor Thesis – Research that has a credit point value of 2 ECTS and 2) Bachelor Thesis – Production and Defense that has a point value of 3 ECTS.
Prerequisites for Particular Courses
Each course description contents enlists the prerequisites for the enrolment of the particular course..
Way of Choosing Courses from Other Study Programmes
It is possible to choose courses from other study programmes depending on the syllabus of the courses elected. The group of free elective courses enlists several courses from other study programmes. Moreover, a student can choose courses from another module, as well as courses from other undergraduate (bachelor) study programmes provided that the cumulative sum of their credit points does not exceed 20 ECTS.
Transferring from Another Study Programme
It is possible to transfer from other related programmes to this study programme and vice versa using the credit transfer system for the same or similar courses.
Undergraduate academic studies of APPLIED MATHEMATICS have a dual purpose. Since mathematics studies are organized according to a 3 + 2 system, these three-year studies represent the first stage in university education of mathematicians experts in the field of applied mathematics. In the second stage, through two-year studies, a student acquires the title of Master in Mathematics in one of two master study programmes of applied mathematics: Applied Mathematics or Applied Mathematics – Data Science. In this sense, these undergraduate (bachelor) studies represent a solid basis for the continuation and successful mastery of the related master academic studies, based on the selection of topics and areas of theoretical mathematics, applied mathematics and related disciplines (depending on modules these are engineering and technical disciplines, economic and financial disciplines or disciplines related to statistics and data analytics).
In addition to this purpose within the 3 + 2 study system, these studies possess also an independent role. They train students for occupations in various areas of economy, especially industry and financial institutions. Based upon the choice between the three elective modules a student is being prepared for jobs that require knowledge from the basics of applied mathematics, informatics, data analytics and statistical methods, ability of analytical thinking and logical judgment. These studies provide an acquisition of skills for basic aspects of mathematical modeling and the ability to solve practical problems.
The objectives of the study programme include education of mathematicians in the field of applied mathematics, which is a profession that enables the graduates to work in research and development centres, modern industry, chambers of commerce, IT centers, institutions for data analytics and statistical analytics, or financial institutions and public administration, as well as in all other places where there is a need for multidisciplinary work.
Through a group of mathematical courses, students are introduced to classical mathematical theories in a modern way, as well as current trends in mathematics. In addition to adopted theoretical and practical knowledge, such education enables students to become capable of abstraction and logical reasoning. 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 participants and principal investigators of several national and international research projects.
Through the elective module of Data Analytics and Statistics, students master basic notions and skills in the fields of machine learning, optimization and statistics. Through the related courses, students are trained to analyze data, as well as to communicate with various experts in the field of data analytics and statistics.
Through the elective module of Mathematics of Finance, 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 Techno-mathematics students master the concepts and principles of physics and selected engineering disciplines. Through the related courses, students are trained to communicate with physicists and engineers.
The group of applied mathematics courses enables students to creatively work on mathematical models in modern technology, economics, and finance. Mathematical models allow a deeper understanding of modern technology, economic laws, statistical laws and data analytics principles. Familiarity in the field of computer science and information technologies obtained during the studies enable an adequate application of modern software platforms 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 and whose knowledge and expertise never becomes obsolete. There is also the possibility of further education and acquisition of a master title in applied mathematics.
General and course-specific competencies of students
Upon mastering the study programme APPLIED MATHEMATICS, students acquire the following general competencies:
- ability of a logical thinking, formulating hypotheses and drawing conclusions in a formal or formalized manner;
- knowledge of the fundamental classical mathematical theories and contemporary trends in mathematics;
- ability to solve mathematical problems and use their acquired knowledge in applications;
- basic knowledge in informatics and programming implementation of simpler problems;
- ability to formulate and analyze mathematical models in modern technologies, economy and finance.
Upon mastering the study programme APPLIED MATHEMATICS, students acquire the following course-specific competencies:
- thorough knowledge of the fundamental notions and principles of their selected discipline: physics and engineering; or economy, finance and accounting; or data analytics, machine learning and statistics;
- ability to solve specific simpler problems from real life practice related to the appropriate course module;
- capacity to communicate with engineers;
- capacity to communicate with experts from financial institutions;
- capacity to communicate with experts in various fields related to data analytics and statistics;
- ability to use information technologies in gaining expertise and solving problems.
Learning outcomes
A successful graduate of this programme will possess insight into concepts and acquire basic knowledge about the most important disciplines of applied mathematics. The corpus of acquired knowledge represents a prerequisite for successfully mastering some more specific areas of applied mathematics on master academic studies (if a student continues his/her studies on master level). In addition, the student will be able to apply his/her acquired knowledge in practice, using the techniques he/she has mastered, making some basic mathematical models. They will be able to recognize, select and use suitable mathematical tools and form simpler mathematical models to solve practical problems from industry, economy, finance and information technology industries that involve data analysis and statistics.
The APPLIED MATHEMATICS study programme offers students the latest scientific and professional knowledge in the field of applied mathematics. The study programme is consistent, among others, with accredited programmes of bachelor studies in applied mathematics at the following universities: Copenhagen, Denmark; Lund, Sweden; Eindhoven, Netherlands; Warwick, England and MIT, USA.
The Department of Mathematics and Informatics of the Faculty of Sciences in Novi Sad is a member of the ECMI (European Consortium for Industrial Mathematics) association whose website https://ecmiindmath.org states that our faculty is one of those offering a master study programme in Applied mathematics. This proves that this programme is recognized to be among the leading study programmes in applied mathematics in Europe.
Sixteen joint compulsory courses with a total of 90 ECTS (50%) including the mandatory Professional Practice and Bachelor Thesis, the latter being divided into two parts (Bachelor Thesis – Research and Bachelor Thesis – Production and Defense) are distributed as follows: in the first, second and third semesters 3 joint compulsory courses are foreseen, while in the fourth semester 2 courses are foreseen. The fifth semester, in addition to 2 joint compulsory courses includes a mandatory 90-hour professional practice scoring 3 ECTS points. In the sixth semester, the student conducts research related to his/her bachelor thesis, writes and defends the thesis (Bachelor Thesis – Research and Bachelor Thesis – Production and Defense) both together scoring 5 ECTS. The ECTS for the bachelor thesis are included in the total ECTS points of the study programme.
A student selects one of three elective modules when enrolling into the study programme. These modules are: Data Analytics and Statistics, Mathematics of Finance, and Techno-mathematics. Therefore, in addition to joint compulsory courses, the student has compulsory courses also within the selected module:
- The Data Analytics and Statistics module contains 10 courses, totalling 50 ECTS.
- The Mathematics of Finance module contains 8 courses, totalling 48 ECTS.
- The Techno-mathematics module contains 9 courses, totalling 48 ECTS.
The remaining amount of points, depending on the selected module, is collected by a selection of elective courses. The list of joint elective courses consists of a total of 15 courses (8 from the winter semester and 7 in the summer semester), totalling 76 ECTS. Each elective course has a predefined set of semesters (study years) at which it is available. In addition to the joint elective courses, a student can also select courses from other modules. Moreover, a student can select courses from other study programmes of the same level (bachelor study programmes) that do not exceed 20 ECTS totals. Students who have enrolled the Techno-mathematics module or Mathematics of Finance module must choose courses worth at least 42 ECTS from the list of elective courses, while students who have enrolled the Data Analytics and Statistics module must choose elective courses totalling at least 40 ECTS.
Depending on the selection of elective courses, the amount of gained credit points may vary from 180 ECTS up to 201 ECTS. Since the elective courses have a range of points from 4 ECTS to 7 ECTS, during the 6 semesters of the study programme the number of gained points may vary by 21 ECTS. This reflects the intention to provide students a great extent of choice and possibility to create their own programme in accordance with their personal preferences, ambitions and capabilities.
Distribution of joint compulsory courses per semester and academic years of studies
| Course Code | Course Title | Semester | Active classes | Other classes | ECTS | |||
| L | E | SRW | ||||||
| FIRST YEAR | ||||||||
| 1 | M101 | Elementary Mathematics | 1 | 2 | 4 | 0 | 0 | 7 |
| 2 | P101 | Introduction to Analysis | 1 | 2 | 3 | 0 | 0 | 6 |
| 3 | P102 | Discrete Mathematics 1 | 1 | 2 | 3 | 0 | 0 | 5 |
| 4 | P201 | Differential and Integral Calculus | 2 | 3 | 3 | 0 | 0 | 7 |
| 5 | P202 | Discrete Mathematics 2 | 2 | 3 | 3 | 0 | 0 | 7 |
| 6 | M107 | Programming 1 | 2 | 3 | 3 | 0 | 0 | 7 |
| Total classes (lectures + exercises + SIR + other classes) and ECTS per year: | 34 | 39 | ||||||
| SECOND YEAR | ||||||||
| 1 | P301 | Multidimensional Analysis | 3 | 3 | 3 | 0 | 0 | 6 |
| 2 | P302 | Linear Algebra | 3 | 3 | 3 | 0 | 0 | 7 |
| 3 | P303 | Databases and Business Informatics | 3 | 2 | 3 | 0 | 0 | 6 |
| 4 | P401 | Probability | 4 | 2 | 3 | 0 | 0 | 6 |
| 5 | P402 | Numerical Analysis 1 | 4 | 2 | 3 | 0 | 0 | 6 |
| Total classes (lectures + exercises + SIR + other classes) and ECTS per year: | 27 | 31 | ||||||
| THIRD YEAR | ||||||||
| 1 | P501 | Programming 2 | 5 | 2 | 3 | 0 | 0 | 6 |
| 2 | P502 | Statistics | 5 | 2 | 3 | 0 | 0 | 6 |
| 3 | PSTR | Professional Practice | 5 | 0 | 0 | 0 | 6 | 3 |
| 4 | P600 | Bachelor Thesis – Research | 6 | 0 | 0 | 2 | 0 | 2 |
| 5 | P601 | Bachelor Thesis - Production and Defense | 6 | 0 | 0 | 0 | 3 | 3 |
| Total hours (lectures + exercises + SRW + other classes) and ECTS per year: | 12 | 20 |
- Active teaching classes: L-lectures, E-exercises, SRW- study research work
Distribution of compulsory courses on module Data Analytics and Statistics per semester and academic years of studies
| Course Code | Course Title | Semester | Active classes | ECTS | ||
| L | E | |||||
| FIRST YEAR | ||||||
| 1 | P103 | Basic Principles of Data Analytics | 1 | 3 | 0 | 4 |
| Total classes (lectures + exercises) and ESPB on the year: | 3 | 4 | ||||
| SECOND YEAR | ||||||
| 1 | P304 | Software Packages for Data Analytics | 3 | 1 | 4 | 6 |
| 2 | M143 | Modeling of Dynamical Systems | 4 | 2 | 2 | 5 |
| Total classes (lectures + exercises) and ECTS per year: | 9 | 11 | ||||
| THIRD YEAR | ||||||
| 1 | P505 | Sampling and Experimental Design | 5 | 2 | 1 | 4 |
| 2 | P506 | Introduction to Machine Learning | 5 | 2 | 2 | 5 |
| 3 | P504 | Numerical Methods and Optimization | 5 | 2 | 2 | 5 |
| 4 | P602 | Regression Analysis | 6 | 2 | 2 | 5 |
| 5 | P603 | Data Protection | 6 | 2 | 2 | 5 |
| 6 | P604 | Data Analytics Project | 6 | 2 | 2 | 5 |
| 7 | P605 | Artificial Intelligence and Neural Networks | 6 | 2 | 3 | 6 |
| Total classes (lectures + exercises) and ECTS per year: | 27 | 35 |
- Active classes: L-lectures, E-exercises
Distribution of compulsory courses on module Mathematics of Finance per semester and academic years of studies
| Course Code | Course Title | Semester | Active classes | ECTS | ||
| L | E | |||||
| FIRST YEAR | ||||||
| 1 | M133 | Mathematical Foundations of Economics | 2 | 4 | 0 | 5 |
| Total classes (lectures + exercises) and ESPB on the year: | 4 | 5 | ||||
| SECOND YEAR | ||||||
| 1 | M137 | Finance 1 | 3 | 3 | 3 | 7 |
| 2 | M149 | Financial Mathematics 1 | 4 | 3 | 4 | 8 |
| 3 | P403 | Multidimensional Integral Calculus and Applications | 4 | 2 | 2 | 5 |
| Total classes (lectures + exercises) and ESPB on the year: | 17 | 20 | ||||
| THIRD YEAR | ||||||
| 1 | P504 | Numerical Methods and Optimization | 5 | 2 | 2 | 5 |
| 2 | P503 | Metric and Normed Spaces | 5 | 3 | 2 | 6 |
| 3 | M118 | Ordinary Differential Equations | 6 | 3 | 3 | 7 |
| 4 | P602 | Regression Analysis | 6 | 2 | 2 | 5 |
| Total classes (lectures + exercises) and ECTS per year: | 19 | 23 |
- Active classes: L-lectures, E-exercises
Distribution of compulsory courses on module Techno-mathematics per semester and academic years of studies
| Course Code | Course Title | Semester | Active classes | ECTS | ||
| L | E | |||||
| FIRST YEAR | ||||||
| 1 | M104 | Analytic Geometry | 1 | 2 | 2 | 5 |
| Total classes (lectures + exercises) and ECTS per year: | 4 | 5 | ||||
| SECOND YEAR | ||||||
| 1 | M139 | Mechanics | 3 | 3 | 3 | 7 |
| 2 | P403 | Multidimensional Integral Calculus and Applications | 4 | 2 | 2 | 5 |
| 3 | P404 | Seminar Work in Modeling | 4 | 2 | 0 | 3 |
| Total classes (lectures + exercises) and ECTS per year: | 12 | 15 | ||||
| THIRD YEAR | ||||||
| 1 | M114 | Complex Analysis | 5 | 2 | 2 | 5 |
| 2 | P503 | Metric and Normed Spaces | 5 | 3 | 2 | 6 |
| 3 | M118 | Ordinary Differential Equations | 6 | 3 | 3 | 7 |
| 4 | M121 | Physics 1 | 6 | 2 | 2 | 5 |
| 5 | M148 | Theoretical Mechanics | 6 | 2 | 2 | 5 |
| Total classes (lectures + exercises) and ECTS per year: | 23 | 28 |
- Active classes: L-lectures, E-exercises
Common elective courses:
| Course Code | Course Title | Semester | Active classes | ECTS | ||
| L | E | |||||
| WINTER SEMESTER | ||||||
| 1 | M132 | English Language 1 | 1, 3, 5 | 3 | 0 | 4 |
| 2 | M135 | Mathematical Mosaic | 1, 3, 5 | 1 | 3 | 5 |
| 6 | M131 | Boolean Algebras and Optimization | 3, 5 | 3 | 2 | 6 |
| 4 | M136 | Accounting | 3, 5 | 3 | 2 | 6 |
| 5 | M138 | Fourier Analysis | 3, 5 | 2 | 2 | 5 |
| 6 | M150 | General Physics | 3, 5 | 2 | 2 | 5 |
| 7 | P111 | Networks: Models and Analysis | 5 | 2 | 2 | 5 |
| 8 | P112 | Internet of Things | 5 | 2 | 2 | 5 |
| SUMMER SEMESTER | ||||||
| 1 | M141 | English Language 2 | 2, 4, 6 | 3 | 0 | 4 |
| 2 | M146 | Sociology | 2, 4, 6 | 2 | 1 | 4 |
| 3 | M145 | Audit | 4, 6 | 3 | 3 | 7 |
| 4 | P113 | Algebraic Structures and Applications | 4, 6 | 2 | 2 | 5 |
| 5 | P115 | Automata and Algorithms | 4, 6 | 2 | 2 | 5 |
| 6 | P114 | Data Visualization | 6 | 2 | 2 | 5 |
| 7 | P116 | Applied Statistics Project | 6 | 2 | 2 | 5 |
- Active classes: L-lectures, E-exercises
NOTE: The list of common elective courses includes courses available to students of all three modules. In addition to the common elective courses, a student can choose courses from the other two modules. Moreover, a student can choose courses from other study programs at bachelor level, so that the cumulative sum of their ECTS points does not exceed 20, and the Council of the Department grants an approval.