Lecturer(s)


Seibert Jaroslav, doc. RNDr. CSc.

Seinerová Kateřina, Ing.

Course content

Cartesian product of two sets. Relation and its characteristics. Graphics processing. Algebraic structures with one operation. Characteristics of operations. Magma (or grupoid), semigroup, group. Abelian group. Algebraic structures with two operations (circle and solid). Examples of algebraic structures. Permutations. Eclipsing motions. Groups in certain situations in the practice.

Learning activities and teaching methods

Methods of individual activities, Projection, Skills training

Learning outcomes

The course acquaints the students with basic terms and applications of the group theory. The aim of the course is to strengthen reasoning of the students, their ability in the analysis of mathematical problems as well as the ability in structuring the concrete situations.
The course intenzifies ligical thinking ant forming of the competence of mathematical analysis of a given problem. An indispensable part is also the competence of partition of a given situation into particular components.

Prerequisites

Basic knowledge of mathematical logic, linear algebra and mathematical analysis (in extent of the first year of university study)

Assessment methods and criteria

Written examination, Discussion, Systematic monitoring
The assignment is granted upon passing the final written test.

Recommended literature


CHAJDA, I. Úvod do algebry (grupoidy a grupy). Olomouc, 2005.

MAC LANE,S., BIRKHOFF, G. Algebra. Alfa, 1974.

MAREŠ, J. Algebra (Úvod do obecné algebry). ČVUT Praha, 1999.
