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Course specification
Course title Fuzzy Metric Spaces
Acronym MS1FMP
Study programme Electrical Engineering and Computing
Module Applied Mathematics
Type of study master academic studies
Lecturer (for classes) prof. dr Siniša Ješić
Lecturer/Associate (for practice) doc. dr Nataša Ćirović
Lecturer/Associate (for OTC)
ESPB 6 Status elective
Condition Knowledge of classical mathematical analysis, notion of metric spaces and function theory
The goal Introducing students with spaces with non-deterministic distances, fuzzy metric and probabilistic Menger spaces, properties of mappings defined on these spaces, nonlinear conditions and applications in nonlinear fields of science.
The outcome Students are capable to form iterative methods as optimal for solving various types of equations that come out of actual problems in physics, electrical engineering and other sciences and have non-deterministic (parametric) definitions.
Contents
Contents of lectures Definition of fuzzy metrics. Completeness and compactness of sets in fuzzy metric spaces. Continuity and uniform continuity of functions. Fixed points of mappings and iterative methods as consequences. Optimization problems.
Contents of exercises Implementation of iterative methods using mathematical software.
Literature
1S. Ješić, Teorija funkcija na fazi metričkim prostorima, skripta, Beograd 2006., S. Jesic. Theory of functions on fuzzy metric spaces, script, Belgrade 2006.
2Chaos, Solitons and Fractals, naučni časopis sa SCI liste, praćenje aktuelnih naučnih članaka., Chaos, Solitons and Fractals, scientific journal on SCI list, following current scientific articles.
Number of hours per week during the semester / trimester / year
Lectures Exercises OTC Study and Research Other classes
3 1
Methods of teaching Combination of traditional presentation on blackboard, slides, communication of students through internet and individual work with students while working on home work and explanation of current topics. Discussion about home work during semester, colloquium at the end of semester.
Knowledge score (maximum points 100)
Pre obligations Points Final exam Points
Activities during lectures 0 Test paper 50
Practical lessons 0 Oral examination 20
Projects 0
Colloquia 30
Seminars 0