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Lecturer(s)
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Seibert Jaroslav, doc. RNDr. CSc.
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Seinerová Kateřina, Ing.
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Course content
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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.
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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 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 intensifies the logical thinking ant forming of the competence of mathematical analysis of the problem. An indispensable part is also the competence of partition of the given situation into particular components.
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Prerequisites
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Basic knowledge of mathematical logic, linear algebra and mathematical analysis (in extent of the first university year).
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Assessment methods and criteria
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Written examination, Discussion, Systematic monitoring
Assignment - passing the final written test.
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Recommended literature
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Chajda I. Úvod do algebry (grupoidy a grupy). Olomouc, 2005.
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Kuroš A.G. Kapitoly z obecné algebry. Akademia, 1968.
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Mareš J. Algebra (Úvod do obecné algebry). ČVUT Praha, 1999.
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