MU:MU03261 Computer Algebra - Course Information

MU03261 Computer Algebra

Mathematical Institute in Opava
Summer 2018

Extent and Intensity

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

Guaranteed by

Course Enrolment Limitations

The course is offered to students of any study field.

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.