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Mathematics in Ancient India
Sýkorová, Irena ; Bečvář, Jindřich (advisor) ; Veselý, Jiří (referee) ; Hykšová, Magdalena (referee)
The thesis is devoted to ancient Indian mathematics; it describes the mathe- matical knowledge, computational techniques and methods for solving various ari- thmetic, algebraic and geometric problems that the Indians knew and used. The thesis follows the development of Indian mathematics from the oldest knowledge contained in ancient Vedic texts to the knowledge originated from the classic me- dieval arithmetic and algebraic works. This is the first comprehensive text written in Czech which contains the translation of original problems and analysis of their solutions in the current mathematical formulation and symbolism. The sources are mainly English translations of ancient Sanskrit texts and their commentaries.
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Geometry of Linear Model
Línek, Vítězslav ; Hykšová, Magdalena (advisor)
The advantage of the geometric approach to linear model and its applications is known to many authors. In spite of that, it still remains to be rather unpopular in teaching statistics around the world and is almost missing in the Czech Republic. In this work, we use geometry of multidimensional vector spaces to derive some well-known properties of the linear model and to explain some of the most familiar statistical methods to show usefulness of this approach, also known as "free-coordinate". Besides, historical background including selected results of R. A. Fisher is briefly discussed; it follows that the geometry approach to linear model is justifiable from the historical point of view, too. Powered by TCPDF (www.tcpdf.org)
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Geometry of Linear Model
Línek, Vítězslav ; Hykšová, Magdalena (advisor) ; Nagy, Ivan (referee) ; Hlubinka, Daniel (referee)
The advantage of the geometric approach to linear model and its applications is known to many authors. In spite of that, it still remains to be rather unpopular in teaching statistics around the world and is almost missing in the Czech Republic. In this work, we use geometry of multidimensional vector spaces to derive some well-known properties of the linear model and to explain some of the most familiar statistical methods to show usefulness of this approach, also known as "free-coordinate". Besides, historical background including selected results of R. A. Fisher is briefly discussed; it follows that the geometry approach to linear model is justifiable from the historical point of view, too. Powered by TCPDF (www.tcpdf.org)
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Mathematics in Ancient India
Sýkorová, Irena ; Bečvář, Jindřich (advisor) ; Veselý, Jiří (referee) ; Hykšová, Magdalena (referee)
The thesis is devoted to ancient Indian mathematics; it describes the mathe- matical knowledge, computational techniques and methods for solving various ari- thmetic, algebraic and geometric problems that the Indians knew and used. The thesis follows the development of Indian mathematics from the oldest knowledge contained in ancient Vedic texts to the knowledge originated from the classic me- dieval arithmetic and algebraic works. This is the first comprehensive text written in Czech which contains the translation of original problems and analysis of their solutions in the current mathematical formulation and symbolism. The sources are mainly English translations of ancient Sanskrit texts and their commentaries.
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Game Theory for Gifted Secondary School Students
Skálová, Alena ; Hykšová, Magdalena (advisor) ; Staněk, Jakub (referee)
The thesis contains a textbook for gifted secondary school students. Its aim is to give to these students (or to their teachers) a Czech-written text covering fundamental principles in the field of game theory. In the first part we introduce the combinatorial games and some elementary methods of their solution. The second part is devoted to the game of Nim, to the Sprague-Grundy function and to the sums of the combinatorial games. It also contains a necessary introduction to the binary numeral system. In the third part we present the concept of matrix and bimatrix games. There is a lot of exercises and examples in the textbook. At the end we bring solutions to the most of them, providing the active reader with the opportunity of checking their own solutions.
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Life and Work of Wilhelm Matzka
Chocholová, Michaela ; Bečvářová, Martina (advisor) ; Hora, Jaroslav (referee) ; Hykšová, Magdalena (referee)
Wilhelm Matzka (1798-1891) was a German mathematician as well as an important person of the University of Prague and an eminent representative of the mathematical community in the Czech countries in the middle of the 19th century. This thesis is original and reminds of his life as well as of his scientific, pedagogical and organizational activities. The center of this work is formed by the analysis and the evaluation of Matzka's mathematical work, its classification in the development of mathematics and its education. There are mentioned his studies and monographs on mathematical applications like physics, chronology, astronomy and geodesy as well, which give the thesis a sig- nificant interdisciplinary character. This thesis presents also lot of historical connections and provides a view of the situation in the German, Czech and European world of mathematics in the 19th century.
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Skolem paradox in set theory
Liepoldová, Tereza ; Honzík, Radek (advisor) ; Hykšová, Magdalena (referee)
This works aims to map the development of the Löwenheim-Skolems the- orem from Ernst Schröder to Thoralf Skolem using original mathematical notation. It describes its consequence in the form of the Skolem paradox and its influence on set theory and associated issues concerning orders of logic. 1
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Geometry of Linear Model
Línek, Vítězslav ; Hykšová, Magdalena (advisor)
The advantage of the geometric approach to linear model and its applications is known to many authors. In spite of that, it still remains to be rather unpopular in teaching statistics around the world and is almost missing in the Czech Republic. In this work, we use geometry of multidimensional vector spaces to derive some well-known properties of the linear model and to explain some of the most familiar statistical methods to show usefulness of this approach, also known as "free-coordinate". Besides, historical background including selected results of R. A. Fisher is briefly discussed; it follows that the geometry approach to linear model is justifiable from the historical point of view, too. Powered by TCPDF (www.tcpdf.org)
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