Course detail

Geometrical Algorithms

FSI-0AVAcad. year: 2007/2008

Basic outline of commutative algebra and algebraic geometry with the emphasis on Groebner basis, Buchbereger algorithm and implicitization. Elliptic curves in cryptography.

Language of instruction

Czech

Number of ECTS credits

2

Mode of study

Not applicable.

Guarantor

doc. RNDr. Miroslav Kureš, Ph.D.

Department

Institute of Mathematics (ÚM)

Learning outcomes of the course unit

The algoritmization of some geometric problems.

Prerequisites

Basics of algebra. The craft of algoritmization.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

Seminar credit: the attendance

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The convergence of mathematician and computer scientist points of view.

Specification of controlled education, way of implementation and compensation for absences

Seminars: will be specified

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme B3901-3 Bachelor's

    branch B3910-00 , 3. year of study, summer semester, elective (voluntary)

Type of course unit

 

Exercise

26 hours, compulsory

Teacher / Lecturer

doc. RNDr. Miroslav Kureš, Ph.D.

Syllabus

1.-2. Rings and fields.
3.-4. Ideals and factorizations.
5.-6. The ordering of monomials and polynomials.
7.-8. Groebner basis.
9.-10. Algebraic varieties.
11. Implicitization.
12.-13. Elliptic curves and the cryptography.