Essay on the socio-economic justification of the Master's study

 1. Introduction

1.1

Our country accepted the principles of the Bologna Process by signing the relevant documents in Berlin on September 16, 2003. Thus, it joined the ranks of European countries that have committed themselves to fulfilling the conditions for a complete transition to this type of study by 2010. The Framework Law on Higher Education in Bosnia and Herzegovina, which entered into force on August 7, 2007, provides a legal framework for implementing the reform of higher education according to the Bologna Declaration, i.e. building European Higher Education Area (EHEA). At the University of Zenica, preparations for this job are carried out by organizing expert and info-seminars, sessions of individual University committees and sessions of the University Senate.

Publishing the Program Master's degree study for the academic year 2008/2009. year at the Department of Mathematics and Informatics at the Faculty of Education of the University of Zenica as a special document that also has a function guide, it is expedient to indicate some significant events and facts.

The Faculty of Pedagogy in Zenica is a transformed and expanded form of the Pedagogical Academy, which was created in 1994 as a response to the exceptional need for teaching staff in primary and secondary schools. Teachers of mathematics and informatics were trained at the Pedagogical Academy, and thus the problem of the lack of teachers in primary schools in the area of ZE - DO Canton was solved. As the problem of teaching staff in secondary schools was still present, and the desire of the ZE-DO cantonal government to solve the existing problem, classes for the third and fourth year of the teaching major were established at the Pedagogical Academy, and thus the Pedagogical Academy grew into the Faculty of Pedagogy. At the same time, the two-year course is abolished. The Department of Mathematics and Informatics is one of the departments at the Faculty of Education, where students obtain diplomas with the title of Professor of Mathematics and Informatics.

The curriculum at the Department of Mathematics and Informatics aimed to achieve that students acquire a fundamental theoretical and practical didactic-methodical education, which during the one-year internship after graduation is complemented by the development of practical teaching competencies. By carrying out the study program, the following goals are achieved:

a) training students for independent teaching of mathematics and informatics in educational institutions of all profiles in which the curriculum provides for the teaching of the mentioned subjects,

b) training students for independent further study and training in accordance with the specific needs of their students.

c) Training students to monitor results as well as active participation in professional and scientific research in the field of teaching mathematics and informatics.

1. 2. Coordination with ECTS

As a member of the University of Zenica, the Faculty of Education has voluntarily undertaken the obligation to align its study programs with the European credit transfer system, the so-called European Credit Transfer System (ECTS), by in which 60 ECTS points are usually acquired in one year of study", i.e. 30 ECTS points per semester. In the past three academic years, the Faculty of Pedagogy has devoted itself to this task at the level of the first cycle (undergraduate study), and now it is taking into account the second cycle. cycle (Master's degree study), thereby meeting the establishment of a vertical system of passability through all three cycles, which were determined by the Bologna process (3 + 2 + 3, or 4 + 1 + 3).

On Master's degree study for the academic year 2008/2009. load coefficients (ECTS points) were assigned. On those grounds, according to the principle of gradualness, Master's degree study, at the Faculty of Pedagogy at the Department of Mathematics and Informatics, continues to be harmonized with ECTS. It is a process that begins with a focus on a permanent state in which, among other things, integration is achieved at different levels - faculty, university, national (Bosnia and Herzegovina) and European. The integration process, thanks to ECTS, should first take place within the faculty. One of the signs of such integration within the Faculty of Pedagogy is the possible possibility, which did not exist until now, for graduates of the Faculty of Pedagogy, Department of Mathematics and Informatics to enroll Master's degree study.

In doing so, a new concept will be applied Master's degree  a study based on the so-called triple "point grouping", according to which teaching is organized in two point groups, and in the third point group, teaching and extracurricular scientific activities. The third credit group is about scientific and didactic activities. Scientific activities refer to the preparation of scientific papers for scientific journals (mainly as a co-author), to participation in scientific research projects, and to participation in international and domestic scientific gatherings as well as professional training seminars and evaluated scientific lectures. This concept also contains a description of common teaching subjects (in the case of multiple study courses), compulsory subjects, and optional subjects, with a selection of relevant literature.

 

1. 3. Basic principles and starting points 

Curriculum for Master's degree the study was carried out on the basis of respect for the universal principles of the educational tradition, the experiences of higher education institutions in Bosnia and Herzegovina and in the region, and especially on respect for the basic principles of the Bologna Declaration, which plans the unification of the European higher education area (European Higher Education Area). This applies in particular to:

– affirming the new European study model, comparable criteria and methodologies;

- acceptance of a system based on three educational cycles, undergraduate, graduate and postgraduate;

– introducing the ECTS system as a suitable means of affirming the widest exchange of students;

- affirming the mobility of students, teachers, researchers, administrative staff;

- affirming European and global cooperation in quality assurance;

- affirming and introducing a system of easily recognizable and comparable academic degrees supplements degrees.

 

1. 4. Principles of program creation 

When developing the program, the following principles were especially highlighted:

- the unity of the model of all studies within the framework of Bosnia and Herzegovina studies, i.e. unique

the duration of all study cycles (3+2+3 or 4+1+3);

– the principle of one semester when designing courses;

- organization of studies in three credit groups, namely: in two

credit groups of organized teaching subjects (compulsory and optional subjects) and third credit groups of curricular and extracurricular scientific activities;

- preparation of a master's thesis of 18 ECTS points.

– principle of optionality or modularity; students are tried to be offered the opportunity to choose some courses and thus take part in the shaping of their studies.

 

2. REASONS FOR INITIATING STUDIES 

2.1. Assessment of the purposefulness of the studies with regard to the needs of the labor market in the public and private sector

The purpose of starting the master's degree is to enable students to deepen the knowledge acquired during the four-year study in mathematics and informatics. Based on the acquired knowledge, skills and abilities, students will be able to be employed primarily in primary and secondary schools as teachers or professors of mathematics and informatics, but they can also be employed in jobs that require in-depth knowledge of mathematics and computing in order to solve problems with mathematical apparatus. and based on knowledge of information and communication technology. Due to the ability of abstract thinking, analytical approach and thoroughness, skills in calculation, experience in programming, knowledge of computer technology and foundations of social psychology, our graduates could find employment in industry, financial institutions, research institutes, administration and elsewhere.

Since computer science is a science in constant development, we have incorporated new content from that field into the proposal. At this level, the student to some extent influences the creation of the study program through the selection of electives. We will periodically change the list of these subjects and thus refresh the program with new content. With our concept, we strive to build a person capable of always acquiring new knowledge from the mathematical, computer and IT field, within the reach of their own capabilities, who is qualified for the responsible transfer of that knowledge to younger generations. A large part of the last year of studies is dedicated to the student's independent work on a topic in mathematics or computer science (free choice of the student) with the supervision and assistance of the teacher. The result is a graduate thesis that can stimulate future professional or scientific interest and/or enrollment in a suitable postgraduate study.

 

2. 2. Connection of studies with modern scientific knowledge and skills based on them

It can be said that the quality of education, especially higher education, represents the very core of contemporary educational trends in Europe, which is also underlined in the conclusions. of Berlin meeting in 2004. Our country will also be obliged to build a self-sustaining system of quality assurance of education at all levels and in all areas, for which it is necessary to provide competent experts and managers. The University of Zenica saw the importance of the quality system in the success of organizations and companies, and took significant steps to improve them. The Faculty of Education, as a member of the University of Zenica, participates in projects to improve the quality of services and the efficiency of internal organization. Most of the professors who will be engaged in the master's study at the Department of Mathematics and Informatics of the Faculty of Pedagogy of the University of Zenica will be distinguished scientists from our country and surroundings, who have acquired their professional and scientific affirmation at domestic and foreign universities, who have been trained in traditional and contemporary literature, who participate in scientific symposia and projects. All this makes a serious assumption for connecting the scientific and educational activity of this faculty with modern scientific knowledge, especially in the field of pedagogy, informatics and mathematics.

 

2. 3. Openness of studies to the mobility of students

The study is aligned according to the standards of the Bologna process. In compiling the program, special attention is paid to the possibility of student mobility with regard to the transfer of ECTS points, changes and continuation of studies. A student acquires the right to enroll in a higher year of study if he has accumulated a sufficient number of ECTS points from the main and compulsory courses and elective courses, seminars, scientific and didactic activities.

 

3. GENERAL PART

3. 1. Realization of the project

The Faculty of Education of the University of Zenica plans to implement a master's degree Mathematics and informatics, in cooperation with the available teaching staff both at the Faculty of Education in Zenica and in Bosnia and Herzegovina.

The curriculum at the Department of Mathematics and Informatics of the Faculty of Education in Zenica largely coincides with the curricula at the Departments of Mathematics and Informatics at other faculties in Bosnia and Herzegovina and the region.

 

3.2. Name of the study program

Mathematics and informatics, teaching major.

  

3.2. Duration and evaluation of studies

The study is organized as a full-time course with a one-year commitment. In order to complete the graduate studies and obtain the master's degree, students must collect a total of 60 ECTS points (30 per semester). In the program Master's degree studies differ: compulsory courses, elective courses and graduate thesis.

Compulsory courses are taken in the first semester of the master's study, and include the following courses:

1. Complex analysis,

2. Cryptography and network security,

3. Methodology of scientific work i

4. Partial differential equations.

In the first semester, students choose one of the two elective courses offered, and in the second semester, students choose two of the six elective courses offered, from the field of Mathematics or from the field of Informatics, depending on the chosen field:

Mathematics:

1. Selected chapters from algebra and geometry

2. Dynamic systems

3. Stochastic processes

4. Functional analysis

Computer science:

1. Multimedia systems

2. Software development

3. Digital image processing and analysis

4. Intelligent systems.

After passing seven (7) exams, the student, in agreement with the subject teacher, chooses a topic for the master's thesis.

 

3. 2. Conditions for study enrollment

Master's degree Mathematics and informatics candidates who have completed an undergraduate (four-year) course in Mathematics and Informatics at the Faculty of Education at the Departments of Mathematics and Informatics or at the Faculty of Science and Mathematics at the Department of Mathematics, as well as candidates who have completed a related undergraduate course with additional exams from subjects of the undergraduate study, which will be determined by the Teaching and Research Council of the Faculty, and collect the required number of ECTS points from the main and compulsory subjects.

Knowledge of at least one foreign language (English, German, French, Russian) is mandatory for all candidates. Preference is given to candidates already involved in certain streams of pedagogic-didactic and scientific work with proven inclinations and demonstrated interest in pedagogic work and scientific research, and with published professional and scientific works.

In scientific-research work, the orientation of the Master's study is the contemporary tendencies of scientific research in mathematics and informatics.

Foreign citizens apply for the competition under the conditions stipulated in the Rules of the University of Zenica and the Rules of the Faculty.

The teaching-scientific council of the Faculty announces the competition on the notice board of the Faculty and in a daily newspaper. The Master's Study Council (hereinafter referred to as the Council) appoints a three-member competition committee that proposes candidates for admission to the Master's study. In case of application of a larger number of candidates than foreseen by the competition, priority is given to candidates with better references from the previous study cycle. Candidates are selected by the Study Council.

Master's degree students from other faculties who want to make the transition to the master's degree Mathematics and informatics  at the Faculty of Pedagogy, they can only do so with the special approval of the Council of Studies and with the specific conditions prescribed by it, which are not provided for in the general acts on master's studies.

 

3. 3. Objective andcompetences that are acquired upon completion of the master's degree

The aim of the Master's study Mathematics and informatics is to expand, supplement, deepen and additionally modernize and systematize the knowledge acquired in undergraduate studies, and ensure vertical academic mobility for students who have completed the first cycle of studies at the Department of Mathematics and Informatics.

Study tasks are carried out in compulsory and optional subjects and/or modules so that each one from its scientific aspect contributes to the deepening of knowledge in mathematics and informatics, and students acquire the ability to mathematically model problems and solve them using mathematical tools, acquire knowledge about modern software packages, software languages, and knowledge of the application of the latest computer and information technology in various occupations, they are also trained to continue their studies in mathematics or informatics. A successfully completed master's degree allows the student to continue his doctoral studies (third degree studies) at the Faculty of Science and Mathematics in Sarajevo.

This study qualifies students for independent research work and publication of scientific papers, it qualifies them especially for scientific research in the field of upbringing and education, for work on scientific and professional projects that deal with topics from the methodology of teaching mathematics and informatics in primary and secondary schools.

 

3. 4. Professional or academic title or degree obtained upon completion of studies

Upon completion of the master's degree, the student acquires a professional title

Master of Mathematics and Informatics,

 from the area:

            a) mathematics,

or from the area of:  

            b) informatics.

 

PLAN STRUCTURE OF THE MASTER'S STUDY IN THE DEPARTMENT OF MATHEMATICS AND INFORMATICS

 

ECTS CREDITS

Code	SEMESTER I	P	V	S	K	Pr	Preparation	S
P	U
PFM 001	Complex analysis	1.5	1.5	1	–	–	1,5	1,5	7
PMF 003	Cryptography and network security	1	1	1	–	–	1.5	1.5	6
PFM 002	Partial differential equations	2	1	1	–	–	1,5	1,5	7
PFM 004	Methodology of scientific work	1	1	1	–	–	–	1	4
PFM 005	Elective mathematics or informatics subject	1.5	1.5	1	–	–	1	1	6
TOTAL								30

P - lectures, V - exercises, S - seminar work, projects, etc., K - consultations, Pr - practice, P - written exam, U - oral exam, S – in total

 

ECTS CREDITS

Code	SEMESTER II	P	V	S	K	Pr	Preparation	S
P	U
PFM 006	First elective	2	2	–	–	–	1	1	6
PFM 007	Second elective	2	2	–	–	–	1	1	6
PFM 008	Graduate work			–	4	–	10	4	18
TOTAL								30

P - lectures, V - exercises, S - seminar work, projects, .., K - consultations, Pr - practice, P - written exam, U - oral exam, S – in total

 

PROGRAM STRUCTURE MASTER'S STUDIES IN THE DEPARTMENT OF MATHEMATICS AND INFORMATICS

Subject name	Complex analysis
Code
Level	Advanced-Compulsory subject (3+2)
Year	V.	Semester	I
ECTS (with appropriate explanation)	7 ECTS points (Seminar work 2 ECTS points, self-study and exam 5 points)
Competences to be acquired	In this course, students are introduced to basic concepts and results from the theory of complex functions of complex variables with an emphasis on the theory of analytic functions. Students must develop the ability to understand the results presented in lectures as well as to set and solve tasks and problems that can be set in connection with these results. Students acquire techniques for solving tasks in exercises.
Content	The space of complex numbers C and convergence of series and series in C. Complex functions of a complex variable. Concept of analytic function and basic properties. Basic analytical functions and their properties. Integral of a complex function. Closed curve index. Cauchy's theorem and Cauchy's integral formula. Morera's theorem. Series and series of complex functions and series of powers. Taylor's order. Theorem on the uniqueness of the analytic function. Liouville's theorem. Isolated singularities and their classification. Meromorphic functions. Residue theorem and applications. Gamma and Beta function. Principle of argument. Rouché's theorem. The inverse function of the analytic function. Conformal mappings. Mobius transformations and their properties.
Recommended reading	H. Kraljević, S. Kurepa, Mathematical analysis 4/I: Functions of a complex variable, Technical book, Zagreb, 1986.
Supplementary literature	S. Kurepa, Mathematical analysis III, Technical book, Zagreb, 1975.Š. Hungary, Mathematical analysis 4, (script), Zagreb, 2001.W. Rudin, Real and complex analysis, McGraw-Hill, New York, 1970. MA Lavrentjev, BV Shabat, Metody teorii funktions kompleksnogo peremennogo, Science, Moscow, 1973.
Forms of teaching	Lectures on the topics listed in the Contents. The exercises consist of solving tasks and problems selected according to the topics from the lectures.
Method of testing knowledge and taking exams	The final exam consists of a written and an oral part and is taken at the end of the class. Previously, the student should complete and defend a seminar paper. The written and oral parts of the exam are evaluated equally in the final grade.
Language of instruction and tracking options in other languages	Bosnian

Subject name	Stochastic processes
Code
Level	Advanced mathematics course (2+2)-Elective
Year	V.	Semester	II
ECTS (with appropriate explanation)	6 ETCS points (Seminar work 3 ECTS points and exam 3 ECTS points)
Competences to be acquired	Students are introduced to the concepts of Markov chains with continuous time, renewal theory and Brownian motion and are equipped to apply the acquired knowledge in practice.
Prerequisites for enrollment	Probability and Statistics
Content	Markov chains with continuous time. Definition and construction. Markov property. Backward equation, generating matrix. Poisson process. Reversibility and transience. Analysis of random walks. Stationary and marginal distribution. Convergence to the marginal distribution. Ergodic theorem. Laplace transform method. Time reversal. An introduction to continuous-time Markov chains. Application of Markov chains: electrical networks. Application of Markov chains in biology. Markov decision processes. MCMC (Markov chain Monte Carlo).Theory renewal. Analytical background. Counting renewals. Recovery equation. Limit renewal theorems. Poisson process as renewal process.Introduction in Brown's movement. Definition and relation to random walk. Basic properties of Brownian motion. Markov property and strong Markov property. Stopping times of Brownian motion and relation to martingales
Recommended reading	SI Resnick, Adventures in Stochastic Processes, Birkhäuser, 1992.D. Stirzaker, Stochastic Processes and Models, Oxford University Press, 2005.P. Bremaud, Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues, Springer Verlag, 1999.JR Norris, Markov Chains, Cambridge University Press, 1997.
Supplementary literature	J. Medhi: Stochastic Processes, J. Wiley, 1982. PZ Peebles: Probability, Random Variables and Random Signal Principles, McGraw-Hill, 1987.
Forms of teaching	Prescribed topics are covered in the lectures, and corresponding tasks are solved in the exercises.
Method of testing knowledge and taking exams	Written + Oral exam
Method of monitoring the quality and performance of each subject and/or module	Statistics of exam results and student evaluation through an anonymous survey at the end of the course.

Subject name	Functional analysis
Code
Kind	Elective – Lectures and auditory exercises (2+2+1)
Level	Advanced mathematics course
Year	V.	Semester	II
ECTS (with appropriate explanation)	6 ECTS points (Assignment or seminar work 2 ECTS points and exams 4 ECTS points)
Competences to be acquired	In addition to mastering the basics of functional analysis, students will master the techniques of functional analysis, as well as the application of basic results to other areas.
Prerequisites for enrollment
Content	Topological and metric spaces. Fixed point theorems. Examples. Normed spaces, Banach spaces. Examples. Linear operators. Hahn-Banach theorem. The Open Mapping Theorem. The closed graph theorem. Banach-Steinhus theorem. Examples. Reflexivity. Examples. Adjunct operator. Fully continuous operators. Invariant subspaces. Fredholm theorems. Application. Hilbert space. Basic features. Examples. Orthogonality. Theorem on the element with the smallest norm. Riesz's representation theorem. Examples. Different types of operators. Traits. Application
Recommended reading	Bela Bollobas, Linear Analysis, An Introductory course, Cambridge University Press, 1990.
Supplementary literature
Forms of teaching	Prescribed topics are covered in the lectures, and corresponding tasks are solved in the exercises.
Method of testing knowledge and taking exams	Written and oral exam
Language of instruction and tracking options in other languages	Bosnian
Method of monitoring the quality and performance of each subject and/or module	Achieved results on the written and oral exam

Subject name	Cryptography and network security
Code
Kind	Compulsory (2+2+1)
Level	Advanced mathematics course
Year	V.	Semester	I
ECTS (with appropriate explanation)	6 ECTS points (Attendance of lectures and exercises 2 ECTS points; making a seminar paper 1 ECTS point, self-study and exams 3 ECTS points)
Teacher	v. prof. Dr. Bernadin Ibrahimpašić and Assoc. Dr. Almir Huskanović
Competences to be acquired	The student gets acquainted with the basic methods for encrypting messages, and with the mathematical background on which the security of those codes is based.
Content	Classical cryptography. Basic terms. Substitution codes. Vigenere's code. Playfair's code. Hill's code. Transposition codes. Encryption devices (Enigma).Modern symmetric block cryptosystems. History of DES. Description of the DES algorithm. Cryptanalysis of DES. Some more modern block cryptosystems. Advanced Encryption Standard.Public key cryptosystems. The idea of a public key. RSA cryptosystem. Cryptanalysis of the RSA cryptosystem. Other public key cryptosystems.Simplicity tests and factorization methods. Pseudoprimes. Solovay-Strassen and Miller-Rabin test. Factorization. Factor bases. Square sieve method.Network security. Hash functions. Digital signatures. Email security. Internet Protocol Security.
Recommended reading	DR Stinson, Cryptography. Theory and Practice, CRC Press, 2002.W. Stallings, Cryptography and Network Security. Principles and Practice, Prentice Hall, 1999.
Supplementary literature	N. Koblitz, A Course in Number Theory and Cryptography, Springer Verlag, 1994.J. Daemen, V. Rijmen, The Design of Rijndael. AES – The Advanced Encryption Standard, Springer Verlag, 2002.D. Kahn, The Codebreakers. The Story of Secret Writing, Scribner, 1996. (Croatian translation: Ciphers against spies, Center for Information and Publicity, Zagreb, 1979)J. Menezes, PC Oorschot, SA Vanstone, Handbook of Applied Cryptography, CRC Press, 1996.A. Salomaa, Public-Key Cryptography, Springer Verlag, 1996.
Forms of teaching	Guiding the student through the necessary activities through seminar and consultation forms of teaching.
Method of testing knowledge and taking exams	The final part of the exam is taken in written or oral form. The final grade is formed on the basis of success in the preparation of the seminar, and the grade of the answers in the final part of the exam.
Language of instruction and tracking options in other languages	Bosnian
Method of monitoring the quality and performance of each subject and/or module	Exam results.

 

Subject name	Partial differential equations
Code
Kind	Mandatory
Level	Advanced math course
Year	V.	Semester	I
ECTS (with appropriateexplanation)	7 ECTS points (Seminar paper 2 points, self-study and exam 5 points)
Teacher	Asst. Ph.D. Dževad BurgićDoc. Dr. Esmir Pilav
Competences to be acquired	The student gains insight into the basic properties of partial differential equations and techniques that have proven useful in their analysis. He masters the mathematical models of numerous physical and other phenomena from the domain of this subject.
Prerequisites for enrollment	Good knowledge of differential and integral calculus, especially multi-variable. Modules: Linear Algebra, Ordinary Differential Equations and Analysis I and II
Content	A boundary value problem for an ordinary differential equation. Laplace equation, separation method, Fourier series. Wave equation, characteristics, Fourier method. Conduction equation. Classification of partial differential equations of the 2nd order. Hyperbolic system.
Recommended reading	1) I. Aganović, K. Veselić, Linear differential equations, Element,2) JD Logan, Applied Mathematics, John Wiley & Sons, New York, 1997.3) VS Vladimirov, Equations of Mathematical Physics, Mir Publishers, Moscow, 1984.4) VS Vladimirov, A Collection of Problems on Equations of MathematicalPhysics, Mir Publishers, Moscow, 1986.
Supplementary literature	1) WA Strauss, Partial Differential Equations, an Introduction, J. Wiley and Sons, New York, 1992.2) AV Bitsadze, Equations of Mathematical Physics, Mir Publishers, Moscow, 1980.3) AV Bitsadze and DF Kalinichenko, A Collection of Problems on Equations ofMathematical Physics, Mir Publishers, Moscow, 1980.
Forms of teaching	Frontal lectures combined with auditory exercises.
Method of testing knowledge and taking exams	Written and oral exam.
Language of instruction and tracking options in other languages	Bosnian

Subject name	Multimedia systems
Code
Kind	Optional
Level	Advanced
Year	V.	Semester	II
ECTS (with appropriate explanation)	6 ECTS points (Seminar paper 2 points, self-study and exam 4 points)
Teacher	c. Prof. Dr. Samra Mujačić and Assoc. Dr. Haris Šupić
Competences to be acquired	Students will adopt the principles of planning and development of multimedia systems, the principles of software engineering for multimedia systems, and become familiar with algorithms and data structures used for the development of multimedia systems.
Content	Introduction to multimedia systems. Description, understanding and illustration of basic principles of multimedia systems. Presentation of multimedia data: sound, video, text, image and animation. Multimedia data compression standards. Overview of the most important standards: JPEG, MPEG-2, MPEG-4, MPEG-7. Specifics of using multimedia on the Internet. Specifics of using multimedia in mobile telephony. Project management for the construction of multimedia systems. Implementation and distribution of multimedia systems. Rules for the design of multimedia applications and their integration into one product. Software engineering for multimedia systems. Data structures and algorithms used in the development of multimedia systems. Application of multimedia systems in education and business presentations. Multimedia databases. Intelligent multimedia systems. Multimedia television, marketing, video conferencing and virtual reality. Current scientific research in the field of multimedia systems.
Recommended reading	Chapman & Chapman, Digital Multimedia, Wiley. Steinmetz, Nahrstedt, Multimedia: Computing, Communications, and Applications, Prentice Hall, 2002 Tannenbaum, RS, Theoretical Foundations of Multimedia. Computer Science Press, New York, 2000. Furth, B., Handbook of Multimedia Computing. CRC Press, Boca Raton, 1998.
Forms of teaching	Through lectures, students will become familiar with the theory, tasks and application examples within thematic units. Lectures consist of a theoretical part, presentational descriptive examples, genesis and solving certain tasks. Additional examples and test tasks are discussed and solved during laboratory exercises. Carrying out laboratory exercises and creating assignments will enable students to continuously work and test their knowledge.
Method of testing knowledge and taking exams	Review of the seminar paper and its defense
Language of instruction and tracking options in other languages	Bosnian

Subject name	Software development
Code
Kind	Chosen subject
Level	Advanced
Year	V.	Semester	I
ECTS (with appropriate explanation)	6 ECTS points
Teacher	c. prof. Ph.D. Nedžad Dukić and v. prof. Dr. Nermin Sarajlić
Competences to be acquired	The student acquires knowledge about the elements of software design, risk analysis, software development process, requirements specifications of simple software systems, object-oriented software construction, software testing, graphic user interface design.
Content	Java for C++ Developers: JVM Introduction, Primitive Types, Classes, Interfaces, Packages, Exception Handling, Generic Classes. Software testing, unit testing. UML notation: diagrams of classes, sequences, objects, packages, components, activities. Classic and agile software development methodologies. Samples of software design: singleton, template, adapter, factory, composite, visitor, decorator. Code refactoring.
Recommended reading	1. C. Larman, Applying UML and Patterns: An Introduction to Object-Oriented Analysis and Design and Iterative Development, 3 ed., Addison Wesley, 20042. M. Fowler, UML Distilled: A Brief Guide to the Standard Object Modeling Language, 3 ed, Addison Wesley, 20033. E. Gamma, R. Helm, R. Johnson, and J. Vlissides, Design Patterns: Elements of Reusable Object-Oriented Software, Addison Wesley, 1997.
Supplementary literature
Forms of teaching	Lectures and exercises (audit and laboratory).
Method of testing knowledge and taking exams	Written, oral exam and assignments.
Language of instruction and tracking options in other languages	Bosnian
Method of monitoring the quality and performance of each subject and/or module	Conversations with students, before and after the activity.

 

Subject name	Methodology of scientific work
Code
Kind	mandatory
Level	Advanced
Year	V.	Semester	I
ECTS (with appropriate explanation)	4 ECTS points (Seminar paper 2 points and exam 2 points)
Teacher	Prof. Dr. Željko Škuljević and Prof. Dr. Faruk Kozić
Competences to be acquired	Through this subject, students are introduced to the methods used in the creation of scientific work, which represents the basis for future work on scientific research projects and doctoral dissertations. Therefore, the student should be able to: recognize the essence and importance of science; accept the morals and ethics of a scientific worker; formulates, plans and leads a research project; choose and evaluate an adequate research method; demonstrates experience in procedures and methods for structuring, collecting and processing information; make a presentation of your scientific work.
Content	Introduction, Structure of science - assumptions; Structure of science - concepts and hypotheses; Structure of science - laws and theories; Structure of science - subject and methods; Structure of science - norms, task; The structure of science - the meaning of science; Conceptualization of research; About scientific research work; The origin of scientific work; Collection of material and literature; Data organization, text writing, citations; Stylistic features and grammatical correctness; Scientific research. Abstraction, deduction and concretization. Creation of a scientific research project. Using scientific sources. Characteristics of scientific language. Scientific explanation, prediction and understanding. Scientific facts, scientific laws and scientific theories. Evaluating and comparing scientific theories. Experiential testing of theories and hypotheses. Methodology in the structure of metascience. Traditional and new research paradigm.
Recommended reading	Šamić, Midhat: How scientific work is created, Sarajevo 1980. Termiz, Dževad: Methodology of social sciences, TKD Šahinpašić, Sarajevo, 2003. Dubić, S.: Introduction to scientific work, Sarajevo 1970.
Supplementary literature	Zaječaranović, G.: Osnovi metodologije nauka, Belgrade, 1977.
Forms of teaching	Lecture and exercises
Method of testing knowledge and taking exams	Practical work - seminar and oral.
Language of instruction and tracking options in other languages	Bosnian
Method of monitoring the quality and performance of each subject and/or module	Conversations with students, before and after the activity.

 

Subject name	Digital image processing and analysis
Code
Kind	Chosen subject
Level	Advanced
Year	V.	Semester	II
ECTS (with appropriate explanation)	6 ECTS points (Seminar paper 2 points and oral part of the exam 4 points)
Competences to be acquired	The student becomes familiar with basic algorithms and instruments for analyzing digital media. Based on the acquired knowledge, the student will be able to create algorithms based on image processing techniques, image activation, which can be applied in video surveillance, biometrics, medical image analysis and other environments.
Content	Digitized image and its characteristics. Data structures for image processing and analysis. Discrete linear image transformations (DFT, Discrete cosine transform, Karhunen-Leve transform, Har transform, Wavelet transform). Geometric image transformations. Improving digital image quality. Linear filters. Design of linear filters in spatial and frequency domain. Non-linear filters. Edge and corner detectors. Image restoration. Degradation models. Inverse and pseudo inverse filter. Wiener filter. Image compression. Image segmentation, image segmentation based on threshold, segmentation based on edges and regions. Analysis of binary images. Mathematical morphology. Descriptors and shape representation. Recognition of objects (patterns), statistical shape recognition, neural networks, syntactic shape recognition, optimization techniques in recognition. Color image analysis.
Recommended reading	1. AKJain, Fundamentals of Digital Image Processing, Prentice Hall, Englewood Cliffs, 1989.2. M. Sonka, V. Hlavac, R. Boyle, Image Processing, Analysis and Machine Vision, Brooks Cole, 1998.3. R. Gonzalez, Richard Woods, Digital Image Processing, Addison Wesley Publishing, 2002.4. MATLAB - MathWorks, relevant ToolBoxes
Supplementary literature
Forms of teaching	Lecture and exercises.
Method of testing knowledge and taking exams	Written, oral exam and assignments.
Language of instruction and tracking options in other languages	Bosnian
Method of monitoring the quality and performance of each subject and/or module	Conversations with students, before and after the activity.

Subject name	Intelligent systems
Code
Kind	Chosen subject
Level	Advanced
Year	V.	Semester	II
ECTS (with appropriate explanation)	6 ECTS points (Seminar paper 2 points and oral part of the exam 4 points)
Competences to be acquired	Upon completion of the course, the student has basic knowledge of artificial-intelligent systems. It is able to determine what can be done with the VI approach. It is able to determine the problems for the solution of which VI approaches are applied. Knows the characteristics of the considered VI methods. It can propose a way to solve problems, and for some problems it can choose and implement the appropriate VI method. It is prepared for specialized subjects in the field of artificial intelligence (AI) and computer intelligence.
Content	Intelligence and the concept of machine intelligence. Presenting the problem. Methods of internal representation. Alternative search methods when solving problems. Data organization and reasoning. Learning. Expert systems. Phase sets and logic. Artificial neural networks. Applications of machine intelligence. Computer and machine vision. Intelligent robotic systems.
Recommended reading	1.S. Haykin, Neural Networks, Prentice-Hall, 1994 2.B. Kosko, Neural Networks and Fuzzy Systems, Prentice Hall, 1992 3. MR Genesereth, Logical Foundations of Artificial Intelligence, Morgan Kaufmann, Los Altos, CA, 1987 4. L. Bielawski, R. Lewland, Intelligent Systems Design, J. Wiley&Sons, 1991. 5.SKFu, RCGonzales, CSGLee, Robotics, Control, Sensing, Vision and Intelligence, McGraw Hill, New York, 1987.
Supplementary literature
Forms of teaching	Lecture and exercises (laboratory)
Method of testing knowledge and taking exams	Written, oral exam and assignments.
Language of instruction and tracking options in other languages	Bosnian
Method of monitoring the quality and performance of each subject and/or module	Conversations with students, before and after the activity.

Subject name	Dynamic systems
Code
Level	Advanced- Elective
Year	V.	Semester	II
ECTS (reasoning)	6 ECTS points (Seminar and/or assignments 2 ECTS points and the oral part of the exam 4 ECTS points)
Competences to be acquired	Students should get to know and master discrete dynamical systems and differential equations in a general sense. After introducing students to solving methods, stability theory and nonlinear theory, the goal is to introduce students to specific applications of different equations in various fields of science and technology, especially the principle of competitiveness.
Content	Introduction and linear theory: Motivation and examples of differential equations. Linear differential equations and systems. Methods of solving linear differential equations and systems. Definitions of stability.Nonlinear theory: Methods of solving some nonlinear differential equations. Riccati's differential equation. Stability. Periodic solutions. Linearized stability. Schur-Cohn stability conditions. Stable and unstable manifolds. Global attractiveness. Bifurcations and bifurcation diagrams. Lyapunov exponents and numbers. Chaos in the case of differential equations of the first order. Chaos in the case of differential equations of higher order. Invariants and Lyapunov functions.Application: Applications in engineering – signal analysis. Applications in modeling biological and economic systems. Competitive and cooperative systems of the second order. The principle of competitive coexistence. The principle of competitive exclusivity.
Recommended reading	1. MRS Kulenović and G. Ladas, Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures, Chapman and Hall/CRC, Boca Raton, London, 2001.2. MRS Kulenović and O. Merino, Discrete Dynamical systems and Difference Equations with Mathematica, Chapman and Hall/CRC, Boca Raton, London, 2002.3. M. Nurkanović,  Differential equations - Theory and applications, University textbook, Denfas, Tuzla, 2008.4. S. Elaydi, An Introduction to Difference Equations, Springer, New York / Berlin / Barcelona / London, 1999.
Supplementary literature	1. A. Keley and A. Peterson, Difference Equations: An Introduction with Applications (2nd Edition) Harcourt/Academic Press, London, 2000.2. J. Burgic, Global bifurcations and non-hyperbolic dynamics of monotonic dynamical systems, doctoral dissertation, Tuzla, 2008.3. E. Pilav, Global Dynamics of Monotonic and Antimonotonic Discrete Dynamical Systems in Level, doctoral dissertation, Sarajevo, 2011.
Forms of teaching	Lecture and exercises.
Method of testing knowledge and taking exams	Written, oral exam and assignments.
Language of instruction	Bosnian
Subject name	Selected chapters in algebra and geometry
Code
Level	Advanced mathematics course - Elective
Year	V.	Semester	II
ECTS (with explanation)	6 ECTS points
Goal	Getting to know and mastering the theory of equations (through the Galois theory), and the concept of inversion and its application in solving various problems, especially constructive ones (only with the help of a compass or only with the help of a ruler), as well as the basic concepts of differential geometry on manifolds.
Competences to be acquired	Students acquire and expand their knowledge in the fields of Algebra and Geometry.
Content	Algebra: Solvability of groups. Algebraic equations: Field; Field extensions; Final extensions; Algebraic extensions; Normal extensions; Separable extensions. Galois group of fields: Galois group of algebraic equations; Galois resolvent; Solving a quadratic equation; Solving an algebraic equation of the third degree; Solving a quadratic equation; Equation of the fifth degree; Solvability of algebraic equations using radicals.Geometry: Introductory considerations and the meaning of constructive tasks. Three famous Greek constructive tasks. Primary and basic structural tasks in the plane. Definition and properties of inversion. Geometric definition of inversion and inversion theorems. Relation of inversion and homothety. Application of inversion to solving constructive tasks. Applying inversion to problem solving. Constructions only with a compass and constructions only with a ruler. Elements of Riemannian geometry (manifolds, connections, covariant derivative, Lie groups).
Recommended reading	Literature: H. Jamak: Algebra, Sesame, Sarajevo, 2004. V. Perić: Algebra II, Svjetlost, Sarajevo, 1989. DS Malik, JN Mordeson, MKSen: Fundamentals of Abstract Algebra, McGraw-Hill, Boston, 1997. M. Malenica, L. Smajlović: "Power of a point in relation to a circle; Inversion and application”, University book, Bemust, Sarajevo, 2007. M. Malenica:On basic constructive tasks in plane and space”, Svjetlost, Sarajevo, 1988. M. Spivak, “A Comprehensive Introduction to Differential Geometry”, Publish or Parish, 1979 Berkeley. DJ Struik, "Lecturers on Classical Differential Geometry", Dover, New York 1988.
Supplementary literature
Method of testing knowledge and taking exams	Written + oral
Language of instruction and tracking options in other languages	Bosnian