Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Selected Chapters 1 in Mathematics (17.DZ01M)

Native organizations units: Department of Fundamentals Sciences

Type of studies	Title
Doctoral Academic Studies	Occupational Safety Engineering (Godina: 1, Winter)
Doctoral Academic Studies	Mechanical Engineering (Godina: 1, Winter)
Doctoral Academic Studies	Power, Electronic and Telecommunication Engineering (Godina: 1, Winter)
Doctoral Academic Studies	Graphic Engineering and Design (Godina: 1, Winter)
Doctoral Academic Studies	Civil Engineering (Godina: 1, Winter)
Doctoral Academic Studies	Mathematics in Engineering (Godina: 1, Winter)
Doctoral Academic Studies	Engineering Animation (Godina: 1, Winter)
Doctoral Academic Studies	Disaster Risk Management and Fire Safety (Godina: 1, Winter)
Doctoral Academic Studies	Information Systems Engineering (Godina: 1, Winter)
Doctoral Academic Studies	Traffic Engineering (Godina: 1, Winter)
Doctoral Academic Studies	Biomedical Engineering (Godina: 1, Winter)
Doctoral Academic Studies	Industrial Engineering / Engineering Management (Godina: 1, Winter)
Doctoral Academic Studies	Environmental Engineering (Godina: 1, Winter)
Doctoral Academic Studies	Mechatronics (Godina: 1, Winter)
Doctoral Academic Studies	Computing and Control Engineering (Godina: 1, Winter)
Doctoral Academic Studies	Geodesy and Geoinformatics (Godina: 1, Winter)

General information:

Category	Scientific-professional
Scientific or art field	Teorijska i primenjena matematika
Interdisciplinary	Yes
ECTS	5

Educational goal:

To acquire knowledge which can be used in professional subjects and practical work, develop and solve mathematical models for engineering courses using the knowledge gained through selected chapters in mathematics.

Educational outcome:

Student is competent for using acquired knowledge in further education within professional courses, as well as for making, analysing and solving mathematical models. He is able to solve tasks from the above fields and to follows courses in which algebra,mathematical analysis, business and financial mathematics are applied. Acquired knowledge is used for solving mathematical models in professional courses.

Course content:

Student can choose in consultation with programme supervisor, one of the suggested modules: 1. Numerical Mathematics 1; 2. Optimization 1; 3. Pattern Recognition 1; 4. Partial Differential Equations 1; 5. Nonlinear Equations 1; 6. Computational geometry 1; 7. Elements of Functional Analysis 1; 8. Combinatorics 1; 9. Graph Theory 1; 10.Operational Research- Linear Programming 1; 11. Probability 1; 12. Statistics 1; 13. Stochastic Processes 1; 14. Vector analysis 1; 15. Complex Analysis 1; 16. Linear Algebra 1; 17. Differential and Difference Equations 1; 18. Euclidean and Non-Euclidean Geometry 1; 19. Fractional Calculus,Differential Equations 1; 20. Operational Research-Quiuing theory 1; 21. Logic in Computing 1; 22. Discrete Mathematics 1; 23. Higher order Logic 1; 24. Theory of Mobile Processes 1; 25. Numerical Methods of Linear Algebra 1; 26. Fuzzy Sets 1; 27. Economic and Financial Mathematics 1; 28. Groups and Algebras Li 1; 29. Formal Languages and Automata Theory 1; 30. Process Algebras 1; 31. History of Mathematics. Part of the course is in the form of independent research and study in the field of mathematics. Study and research work is based on primary scientific sources, organization and conduction of experiments and statistical data analysis, numerical simulations, and possible paper in the field of mathematics.

Teaching methods:

Lectures. (The student can choose in consultation with supervisor, one or more modules depending on module scope). Consultations. Lectures are organized in combined form. The presentation of the theoretical part is followed by the corresponding examples which contribute to better understanding of the theoretical part. In addition to lectures there are regular consultations. Through research and study work the student will, on the bases of scientific journals and other relevant literature that has been studied independently, develop further understanding of the material covered in lectures. Working with the course teacher the student develops the ability to independently work on a scientific paper.

Literature:

Authors	Title	Year	Publisher	Language
Shamos, M. I., Preparata, F. P.	Computational Geometry: An Introduction	1985	Springer-Verlag, New York-Berlin-Heidelberg-Tokyo	English
D. Sangiorgi	The pi-calculus, a Theory of Mobile Processes	2001	Cambridge University Press	English
Alexander Mood	Introduction to the theory of statistics	2005	McGraw Hill	English
Saaty, T. L	Modern Nonlinear Equations	1981	Dover Publications, Inc., New York	English
Pap E.	Parcijalne diferencijalne jednačine	1986	Univerzitet u Novom Sadu, Institut za matematiku, Građevinska knjiga, Beograd	Serbian language
Ralević, N., Kovačević, I.	Zbirka rešenih zadataka iz Funkcionalne analize	2004	Fakultet tehničkih nauka, Novi Sad	Serbian language
Bishop, C. M.	Pattern Recognition and Machine Learning	2006	Springer-Verlag, New York	English
J. Lambek and P. J. Scott	Introduction to Higher Order Categorical Logic	1986	Cambridge University Press	English
Prvanović, M.	Osnovi geometrije	1980	Građevinska knjiga, Beograd	Serbian language
G.Winskel	The Formal Semantics of Programming Languages	1993	MIT Press	English
Z. Ognjanovic	Teorijsko racunarstvo	2008	Matematicki institut SANU	Serbian language
Janičić, P.	Matematička logika u računarstvu	2008	Matematički fakultet, Beograd	Serbian language
M. Sipser	Introduction to the Theory of Computation	2006	Thomson Course Technology	English
Berman, A., Plemmons, R.J.	Nonnegative Matrices in the Mathematical Sciences	1994	Classics in Applied Mathematics 9, SIAM, Philadelphia	English
Jorge Nocedal, Stephen J. Wright	Numerical Optimization	2006	Springer	English
Zeidler E.	Nonlinear Functional Analysis and Aplications	1985	Springer-Verlag, New York-Berlin-Heidelberg-Tokyo	English
Petrić, J., Zlobec, S.	Nelinearno programiranje	1989	Naučna knjiga, Beograd	Serbian language
D. Miller, Gopalan Nadathur	Programming with Higher-order Logic	2012	Cambridge University Press	English
Franco P. Preparata, Michael Ian Shamos	Computational Geometry an Introduction	1985	Springer	English
Stojaković, M.	Slučajni procesi	1999	Fakultet tehničkih nauka, Novi Sad	Serbian language
Ralević, N., Medić, S.	Matematika I. Deo 2	2002	Fakultet tehničkih nauka, Novi Sad	Serbian language
Jevremović, V., Mališić, J.	Statističke metode u metorologiji i inženjerstvu	2002	Savezni hidrometorološki zavod, Beograd	Serbian language
Dauxois, M. Peyrard	Physics of Solitons	2006	Cambridge University Press, Cambridge, New York	English
Teofanov, Lj., Ralević N.	Odabrana poglavlјa iz numeričke matematike	2019	Fakultet tehničkih nauka, Novi Sad	Serbian language
Hung T. Nguyen	An Introduction to Random Sets	2006	Chapman and Hall/CRC	English
Kovačević, I., Ralević, N.	Funkcionalna analiza	2004	Fakultet tehničkih nauka, Novi Sad	Serbian language
Papoulis, A.	Probability, Random Variables And Stoshastic Processes	1984	McGraw Hill, Tokyo	English
Heinz-Otto Peitgen, H. Juergens, D. Saupe	Chaos and Fractals	2004	Springer Verlag, New York	English

Knowledge evaluation:

Course activity	Pre-examination	Obligations	Number of points
Theoretical part of the exam	No	Yes	50.00
Project	Yes	Yes	50.00

Lecturers:

prof. dr Gilezan Silvia

Full Professor

Study research work

prof. dr Kostić Marko

Full Professor

Lectures

doc. dr Ovcin Zoran

Assistant Professor

Lectures

doc. dr Milićević Srđan

Assistant Professor

Lectures

prof. dr Teofanov Ljiljana

Full Professor

Lectures

prof. dr Medić Slavica

Full Professor

Lectures

vanr. prof. dr Ivetić Jelena

Associate Professor

Study research work

prof. dr Ralević Nebojša

Full Professor

Lectures

prof. dr Kostić Marko

Full Professor

Study research work

prof. dr Lukić Tibor

Full Professor

Study research work

prof. dr Grbić Tatjana

Full Professor

Lectures

vanr. prof. dr Nedović Maja

Associate Professor

Lectures

prof. dr Mihailović Biljana

Full Professor

Lectures

vanr. prof. dr Nedović Maja

Associate Professor

Study research work

prof. dr Čomić Lidija

Full Professor

Lectures

prof. dr Doroslovački Ksenija

Full Professor

Study research work

vanr. prof. dr Tomić Filip

Associate Professor

Lectures

prof. dr Pantović Jovanka

Full Professor

Study research work

prof. dr Pantović Jovanka

Full Professor

Lectures