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19M081ETO - Elements of optimization theory and symbolic computations

Course specification
Course title Elements of optimization theory and symbolic computations
Acronym 19M081ETO
Study programme Electrical Engineering and Computing
Module
Type of study master academic studies
Lecturer (for classes)
Lecturer/Associate (for practice)
Lecturer/Associate (for OTC)
    ESPB 6.0 Status elective
    Condition Mathematics 1 (OO1MM1), Mathematics 2 (OO1MM2)
    The goal Students are able to apply algorithms of symbolic algebra based on Groebner basis of polynomial ideals and theory of pseudo-inverse matrices.
    The outcome Students are able to apply algorithms of symbolic algebra based on Groebner basis of polynomial ideals and theory of pseudo-inverse matrices.
    Contents
    Contents of lectures General problem of symbolic-numeric computation in mathematics. Computer algebra systems and solving systems of polynomial equations.Groebner basis and Applications on the solvability of system, computer graphics and robotics.  Selected methods of the optimization: Discrete least squares method. Linear programming. Theory of pseudo-inverses matrices. Moore-Penrose inverse with applications.
    Contents of exercises Through examples, tasks and problems student learns how to apply theorems and basic concepts that are learnt through theoretical contents. Especially students are prepared how to solve problems that are occurring in computer science and technique.
    Literature
    1. G.V. Milovanović, P.S. Stanimirović: Simbolička implementacija nelinearne optimizacije, PMF Niš 2002. (Original title)
    2. R. Karp: Great Algorithms, CS Cousre 294-5, spring 2006, Berkeley (Original title)
    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, free mathematical software (SAGE, SymPy) communication with students through internet and individual work with students while working on home work tasks, and explanation of current topics.
    Knowledge score (maximum points 100)
    Pre obligations Points Final exam Points
    Activites during lectures Test paper
    Practical lessons Oral examination 50
    Projects
    Colloquia
    Seminars 50