13D081SIMB - Selected Topics in Symbolic Algebra

Course specification
Course title Selected Topics in Symbolic Algebra
Acronym 13D081SIMB
Study programme Electrical Engineering and Computing
Module Applied Mathematics
Type of study doctoral studies
Lecturer (for classes)
Lecturer/Associate (for practice)
    Lecturer/Associate (for OTC)
      ESPB 9.0 Status elective
      Condition Mathematics 1 (OO1MM1), Mathematics 2 (OO1MM2)
      The goal Introducing students with basic and advanced 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 bases of polynomial and differential-polynomial ideals.
      Contents of lectures The theory of differential fields and differential Grebner basis. Solvability systems of algebraic-differential equations. Software realizations of differential Groebner’s bases in modern CAS packages.
      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.
      1. J.F. Ritt: Differential algebra, Amer. Math. Soc. Publication 1950.
      2. K. Geddes, S. Czapor, G. Labahn: Algorithms for Computer Algebra, Kluwer, Boston, MA, 1992.
      3. R. Karp: Great Algorithms, CS Cousre 294-5, spring 2006, Berkeley (
      4. 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.
      5. Christian Aistleitner: Relations between Gröbner bases, differential Gröbner bases, and differential characteristic sets, Master in Computermathematik, Institut für Symbolisches Rechnen, Linz, Dezember 2010
      Number of hours per week during the semester/trimester/year
      Lectures Exercises OTC Study and Research Other classes
      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 50 Test paper 50
      Practical lessons 0 Oral examination 0
      Colloquia 0
      Seminars 0