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Lecturer(s)
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Boháčová Hana, Mgr. Ph.D.
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Course content
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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, semi-group, group. The Abel groups. Algebraic structures with two operations (ring, field). Examples of algebraic structures. Permutation. Groups in practical situations.
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Learning activities and teaching methods
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Methods of individual activities, Projection, Skills training
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Learning outcomes
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The aim of this course is to inform the students about the foundations of the group theory. It should a super-structure 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.
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Prerequisites
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The basic knowledge of mathematical logic, linear algebra and mathematical analysis (in range ussual for the first university year).
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Assessment methods and criteria
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Written examination, Discussion, Systematic monitoring
Assignment - passing a final written test.
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Recommended literature
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Birkhoff, G. - Mac Lane, S. Algebra. Chelsea, 1999. ISBN 0-8218-1646-2.
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Eidelman, Yuli. Functional analysis : an introduction. Providence: American Mathematical Society, 2004. ISBN 0-8218-3646-3.
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