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Relations and their applications
Čulíková, Markéta ; Novotná, Jarmila (advisor) ; Zamboj, Michal (referee)
The thesis deals with relations and their applications. The first chapter summarizes the introductory theoretical knowledge that is necessary for understanding the topic relations: an element, set, ordered pairs, Cartesian Product. The important definitions are introduced for all of these concepts and the related information is summarized within this chapter. The second chapter defines the concept of relations and operations on them. It includes various types of graphical representations of relations and their advantages and disadvantages. The concept of relation on a set and the properties of this relation alongside with some special types of relations derived from them are introduced in this chapter. The concepts of function are also defined in this part of the thesis. The third chapter indicates the relations that appear in real life - in relationships and games, in curriculum and puzzles. The properties of those relations are determined and the knowledge of relations and their properties is used to facilitate the solution of logical problems. It also supports gaining deeper understanding of those problems. The thesis includes two groups of tasks. The first one covers elementary tasks related to the topic of sets, ordered pairs, Cartesian Product and relations. The second part is concerned with...
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Environment of Family-tree in primary school mathematics
Bartošová, Zuzana ; Jirotková, Darina (advisor) ; Hejný, Milan (referee)
The Rodokmen (Family tree) environment is one of the many envirnments listed in Fraus publishing house textbooks based on the RVP pro ZV (The Framework Educatinal Programme for Basic Education). The environment offers a tool for building of the mathematical schema of terms and their inter-realations as well as the development of the logical thought. In the theorethicl part of this Diploma thesis the relationship of the Rodokmen environment to the RVP pro ZV is being explained, basic mathematical and geneaologic terminology is stated. In this part of the thesis I also explain the relations in the set cocncept, clasify the family relationships and adress the methodology of the age example solving. In the practical part of the thesis I - by the way of experiment - determine how and in what context students understand the stated mathematical terms, the way they apply the understanding in order to solv the relation and age exams or problems, where the numeric operations take place.
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Binary relations and mappings in teaching of mathematics
Muzikářová, Zdena ; Robová, Jarmila (advisor) ; Hromadová, Jana (referee)
The diploma thesis presents a collection of solved problems in binary relations. Students are familiarized with various applications of binary relations on high school mathematics and geometry. The work focuses on graphical representation of binary relations and their use in solving equations, inequalities and their sys- tems. It is a teaching text designated for a mathematics seminar at high school. In addition to exercises, it also includes an introduction of new concepts which are supplemented by relevant definitions and illustrative examples. 1
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Reasoning in Description Logics
Malenko, Jaromír ; Kučera, Antonín (advisor) ; Lukasová, Alena (referee) ; Křemen, Petr (referee)
Title: Reasoning in Description Logics Author: Mgr. Jaromír Malenko Department: Department of Theoretical Computer Science and Mathematical Logic, Faculty of Mathematics and Physics, Charles University in Prague Supervisor: Prof. RNDr. Petr Štěpánek, DrSc.; Department of Theoretical Computer Science and Mathematical Logic, Faculty of Mathematics and Physics, Charles University in Prague Keywords: Description logic, Reasoner, Cartesian product, Non-monotonic reasoning Abstract: We deal with several aspects of reasoning in Description Logics. First, since description logic (DL) is a subset of First Order Logic (FOL), we use a FOL reasoner to reason in DL. We implemented dl2fol, a DL reasoner that takes an ontology (a DL theory with rules), translates it into a FOL theory, passes this set of formulae to an underling FOL reasoner, and interprets the result in terms of given ontology. This is an effective method for reasoning with newly introduced language constructors. However, we observed longer running times and that satisfiability of some DL concepts wasn't proved due to FOL undecidability. Second, we extend two DLs by introducing new language construct: cartesian product (CP) of concepts and roles. This allows for expressing relationships, that are not expressible by other means in weaker DLs. We...
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Environment of Family-tree in primary school mathematics
Bartošová, Zuzana ; Jirotková, Darina (advisor) ; Hejný, Milan (referee)
The Rodokmen (Family tree) environment is one of the many envirnments listed in Fraus publishing house textbooks based on the RVP pro ZV (The Framework Educatinal Programme for Basic Education). The environment offers a tool for building of the mathematical schema of terms and their inter-realations as well as the development of the logical thought. In the theorethicl part of this Diploma thesis the relationship of the Rodokmen environment to the RVP pro ZV is being explained, basic mathematical and geneaologic terminology is stated. In this part of the thesis I also explain the relations in the set cocncept, clasify the family relationships and adress the methodology of the age example solving. In the practical part of the thesis I - by the way of experiment - determine how and in what context students understand the stated mathematical terms, the way they apply the understanding in order to solv the relation and age exams or problems, where the numeric operations take place.
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