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Problems of solving systems of polynomial equations in mathematics teaching
KÖNIGSMARKOVÁ, Soňa
The aim of this thesis is to map the current state of teaching and student problem solving strategies for polynomial equations. A substantial part of the work is devoted to the use of these systems of equations in solving problems of the loci of a given property at different types of schools. On this basis, where warranted, suggestions are made for enriching teaching in this area with methods reflecting current trends in the use of systems of computer algebra. Considering the above objectives, the author focuses on the current state of teaching systems of polynomial equations in terms of the methods of solution used at primary schools, secondary schools and faculties preparing teachers of mathematics. The author does not neglect the solution of more complex problems, especially problems of the loci of a given property, by future mathematics teachers. The potential of computer algebra systems for improving the current state is also mentioned. The thesis is divided into 9 chapters, with the first four chapters justifying the topicality of the topic. The historical development of the solution of problems on systems of equations and especially the current state of the subject from the point of view of the position of the curriculum and the occurrence of relevant problems in textbooks, entrance and final exams and in the Mathematical Olympiad are presented. Considering the topic of the thesis, examples of solving problems by elementary methods and methods based on the theory of Gröbner bases and the use of computer technology are given. The fifth chapter defines the objectives of the thesis. The next three chapters are devoted to the actual research at secondary and higher education institutions, which deals with the solution of systems of polynomial equations and the solution of problems of loci of a given property in terms of the choice of solution methods and the occurrence of errors in their use.The final chapter summarizes the research results and gives some recommendations for secondary school teaching and for the preparation of future mathematics teachers. Appendices contain an original and research-based draft of teaching material on methods of solving systems of polynomial equations and solving problems on sets of points given characteristics for gifted secondary school students and university teaching students.
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Cluster analysis in mathematical software
Starý, Josef ; Karpíšek, Zdeněk (referee) ; Žák, Libor (advisor)
This bachelor thesis is focused on methods of cluster analysis in mathematical software. The goal is to describe basic methods of cluster analysis, to describe their implementation in mathematical software, to use the methods for clustering of prepared data and to compare the functionality of chosen software.
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Cluster analysis in mathematical software
Starý, Josef ; Karpíšek, Zdeněk (referee) ; Žák, Libor (advisor)
This bachelor thesis is focused on methods of cluster analysis in mathematical software. The goal is to describe basic methods of cluster analysis, to describe their implementation in mathematical software, to use the methods for clustering of prepared data and to compare the functionality of chosen software.
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Multimedia support of mathematics teaching
SOCHOROVÁ, Iva
This master's thesis Multimedia support of teaching mathematics aims at supporting teachers in introducing innovations in teaching and support in their own teaching materials. It is dedicated to supporting the pupil in self-education. It also serves as an overview of selected resources to support the use of technology and software in teaching. This master's thesis includes examples of the use of mathematical programs in mathematics classes, and a proposal to engage pupils in teaching, by implementing the "Teach Your Fellow" project, which aims to create learning videos for pupils.
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