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13M081ESN - Elements of Symbolic-Numeric Computation in Mathematics

Course specification
Course title Elements of Symbolic-Numeric Computation in Mathematics
Acronym 13M081ESN
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 Introducing students with basic concepts of symbolic-numeric computation related to the system of polynomial equations and pseudo-inverse matrices with application in electrical engineering and computer science.
    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. Groebner basis and Buchberger’s algorithm. Applications of Groebner’s bases on the solvability of system, computer graphics and robotics. Numerical aspects of determination of roots of systems of polynomial equations. Theory of pseudo-inverses matrices. Symbolic and numeric forms of 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. D.A. Cox, J.B. Little, D. O'Shea: Ideals, Varieties, and Algorithms - An Introduction to Computational Algebraic Geometry and Commutative Algebra, Springer 3rd ed. 2007. (Original title)
    2. R. Karp: Great Algorithms, CS Cousre 294-5, spring 2006, Berkeley (Original title)
    3. K. Geddes, S. Czapor, G. Labahn: Algorithms for Computer Algebra, Kluwer, Boston, MA, 1992. (Original title)
    4. G.V. Milovanović, P.S. Stanimirović: Simbolic implementation of nonlinear optimization, PMF Niš 2002.
    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 0 Test paper 50
    Practical lessons 0 Oral examination 0
    Projects 0
    Colloquia 0
    Seminars 50