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Introduction to the study of the history of mathematics. The first historical mathematical texts. Egypt - notation of numbers, arithmetic operations, some computational problems, geometry: areas of planar figures. Mesopotamia - cuneiform symbols of numbers, approximate methods of arithmetic calculations, tabulation of arithmetic operations, quadratic equations. Mathematics in Ancient Greece. Pythagorean teachings of even and odd. Irrationalities and Eudox's theory of quantities. Classical geometric problems (trisection of the angle, quadrature of a circle and doubling of a cube). The axiomatic system of Euclids Elements. Proof of Pythagorean Theorem. Criticism of the axiom about parallel lines. Zenon's aporia. Eudox's exhaustive method. Archimedes quadrature of the parabola segment. Mathematics of China, India, their character and influence on Arabic written mathematical texts. European familiarization with the results of oriental mathematics. The first independent results of European mathematics.
Last update: Kvasz Ladislav, prof. RNDr., DSc., Dr. (10.09.2024)
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Studující bude mít základní představu o historii matematiky a především o tom, jak se matematika v historii měnila a jak se měnily její pojmy. Last update: Kvasz Ladislav, prof. RNDr., DSc., Dr. (17.09.2024)
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Last update: Kvasz Ladislav, prof. RNDr., DSc., Dr. (10.09.2024)
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Ladislav Kvasz (2008): Patterns of Change. Birkhauser, Basel. Ivor Grattan-Guiness (ed.) (1994): Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, Routledge, London Last update: Kvasz Ladislav, prof. RNDr., DSc., Dr. (10.09.2024)
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Every student has to choose some of the historical texts discussed in the course and write an essay having from 4 to 8 pages that contains: 1. an exposition of the main aim, concepts and methods of the historical text 2. a discussion of the concepts and methods from the viewpoint of contemporary mathematics 3. a discussion of the potential of the historical text for use in classroom (interesting problems, motivating examples, illustration of the uses of mathematics learned in the classroom) Last update: Kvasz Ladislav, prof. RNDr., DSc., Dr. (10.09.2024)
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In the course the languages of the following fundamental mathematical theories: elementary arithmetic, synthetic geometry, algebra, analytic geometry differential and integral calculus, fractal geometry, predicate logic, set theory will be analyzed from the point of view of six basic linguistic parameters: logical power, expressive power, methodological power, integrative power explanatory power, and metaphorical power. Last update: Kvasz Ladislav, prof. RNDr., DSc., Dr. (10.09.2024)
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https://dl1.cuni.cz/course/view.php?id=7866 Last update: Kvasz Ladislav, prof. RNDr., DSc., Dr. (10.09.2024)
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Studující vysvětlí motivaci a kontext vzniku vybraných matematických pojmů a tvrzení. Studující s porozuměním a pomocí konkrétních příkladů bude schopen vysvětlit, jak matematici postupovali v minulosti. Last update: Kvasz Ladislav, prof. RNDr., DSc., Dr. (17.09.2024)
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