Lecturer(s)


Boháčová Hana, Mgr. Ph.D.

Course content

The cartesian product of sets. Relations and their properties. Graphical processing of the exercises. Algebraic structures with one operation. Properties of the algebraic operations. Grupoid, semigroup, group. The Abel groups. Algebraic structures with two operations (ring, field). Examples of algebraic structures. Permutation. Groups in practical situations.

Learning activities and teaching methods

Methods of individual activities, Projection, Skills training

Learning outcomes

The aim of this course is to inform the students about the foundations of the group theory. It should a superstructure which gives an overview in mathematical branches and provides to find the connections and analogies.
Students should be able to do a logical analysis of problems and a partition of a given situation into particular components.

Prerequisites

The basic knowledge of mathematical logic, linear algebra and mathematical analysis (in range ussual for the first university year).

Assessment methods and criteria

Written examination, Discussion, Systematic monitoring
Assignment  passing a final written test.

Recommended literature


Birkhoff, G.  Mac Lane, S. Algebra. Chelsea, 1999. ISBN 0821816462.

Eidelman, Yuli. Functional analysis : an introduction. Providence: American Mathematical Society, 2004. ISBN 0821836463.
