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MS1SA - Symbolic Algebra

Course specification
Course title Symbolic Algebra
Acronym MS1SA
Study programme Electrical Engineering and Computing
Module Applied Mathematics
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 algebra 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.
    Contents
    Contents of lectures Computer algebra systems and solving systems of polynomial equations. Rings, ideals and fields. Polynomial ring of one and more variables. Monomial ideals and orders. Algorithm of division. Groebner basis and Buchberg’s algorithm. Minimal and reduced Groebner basis. Applications of Groebner’s bases on the solvability of system, computer graphics and robotics.
    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. R. Karp: Great Algorithms, CS Cousre 294-5, spring 2006, Berkeley (http://www.cs.berkeley.edu/~karp/greatalgo/) (Original title)
    2. 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)
    3. K. Geddes, S. Czapor, G. Labahn: Algorithms for Computer Algebra, Kluwer, Boston, MA, 1992. (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 0 Test paper 50
    Practical lessons 0 Oral examination 0
    Projects 50
    Colloquia 0
    Seminars 0