MU:MU03261 Computer Algebra - Course Information

MU03261 Computer Algebra

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: zk (examination).

Guaranteed by

doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Geometry (programme MU, M1101)
• Geometry (programme MU, N1101)
• Mathematical Analysis (programme MU, M1101)
• Mathematical Analysis (programme MU, N1101)
• Secondary School Teacher Traning in Physics and Mathematics (programme FPF, M1701 Fyz)
• Secondary School Teacher Training in Mathematics (programme FPF, M7504)
• Upper Secondary School Teacher Training in Mathematics (programme MU, N1101)
• Secondary school teacher training in general subjects with specialization in Mathematics (programme FPF, M7504)

Course objectives

The course covers basic concepts, methods, and applications of computer algebra. Emphasis is laid on practical application.

Syllabus

• Systems of computer algebra, data structures, symbolic manipulations.
  Rational arithmetics, polynomial arithmetics, greatest common divisor, extended Euclidean algorithm, computation in algebraic extensions.
  Gaussian elimination, computation of determinants and resultants.
  Systems of algebraic equations, polynomial ideals, algebraic varieties, triangular systems, Gröbner bases.
  Symbolic differentiation, symbolic integration, symbolické solution of systems of differential equations.

Literature

recommended literature
• J. von zur Gathen, J. Gerhard. Modern computer algebra. Cambridge University Press, New York, 1999. info
• A. M. Cohen, H. Cuypers a H. Sterk. Some Tapas of Computer Algebra. Springer, Berlin, 1999. info
• B. Buchberger, G.E. Collins, R. Loos a R. Albrecht. Computer algebra. Symbolic and Algebraic Computation. Springer, Wien, 1983. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.

Teacher's information

Individual or small-group project-based learning.
The examination consists of an oral defense of the elaborated project.

• Enrolment Statistics (Summer 2011, recent)
  
• Permalink: https://is.slu.cz/course/sumu/summer2011/MU03261