1. The beginnings of mathematics - Paleolithic, Egypt, Mesopotamia, Babylonia. Development of numeration - Egypt, Babylonia, China, Mayans, India, Greek numeration. Babylonian numbering 2. The beginnings of mathematics and informatics in antiquity - important personalities (Thalés, Pythagoras, Sócratés, Platón, Aristotelés, ..., Apoloniós, Ératosthenés, Archimédés, Ptólemaiós, Diophantos) - Beauty in mathematics. Development of technology in antiquity. 3. Development of number theory - Pythagoras (6th century BC) and number theory - perfect numbers, friendly numbers, prime numbers, figurative numbers - Hellenistic mathematics 4. Euclid's basics, Euclid's algorithm, calculation methods, and aids in the Middle Ages. 5. Development of geometry from antiquity to modern times. Geometrical problems in ancient Greece - constructability of planar structures using a ruler and a compass. 6. The golden ratio and its use from antiquity to modern times, the golden number, the Fibonacci sequence, and the golden ratio in architecture and art. 7. Mathematics in the Middle Ages and the Renaissance, until the beginning of the modern age (17th century). Solving quadratic, cubic, and biquadratic equations. The first algorithms. 8. The development of algebra - the beginnings of Boolean algebra and George Boole. Development of linear algebra, vectors, solving systems of equations, G. W. Leibniz, G. Cramer, J. Sylvester, and A. Cayley - the concept of matrices and operations with them 9. The development of mathematical analysis and the use of functions, Isaac Newton and his work. Concept of function and its development. 10. History of probability - from Arabia and the beginnings of permutations and combinations through the beginnings of the calculus of probability, Cardano, Pascal, Fermat, to the modern theory of probability, Kolmogorov. 11. History of statistics: demographic studies, analysis of astronomical and cartographic measurements: Mayer's method of averages, Boscovich's and Lambert's line, and method of least squares. 12. Mathematics and informatics at the end of the 18th century and in the 19th century. Bernard Bolzano and his mathematical results. Development of mathematical analysis in the 19th century. 13. Interesting problems in 19th and 20th-century mathematics: Mandelbrot - dimensions and fractals, the study of chaos, Joseph-Marie Jacquard and punched card looms, August de Morgan and mathematical induction, and more. Hilbert, Godel. Elliptic curves.
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The course aims to acquaint students with the development of mathematics from ancient tools, through medieval mathematics, to the latest concepts. Emphasis is placed on understanding the main ideas of mathematical methods and students' ability to apply the methods.
After completing the course, the student demonstrates knowledge of the history of algebra, geometry, differential and integral calculus, probability, and statistics. On historical tasks, the student learns to apply mathematical methods for explaining, describing, and characterizing various real-life situations requiring mathematical understanding.
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Bečvář, Jindřich. Matematika v proměnách věků. Praha. 2010.
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Bečvář, Jindřich. Matematika ve starověku - Egypt a Mezopotámie. Praha. 2003.
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Bečvářová, Martina. Eukleidovy Základy, jejich vydání a překlady. Praha. 2002.
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Čižmár, Ján. Dejiny matematiky: od najstarších čias po súčasnosť. Bratislava. 2017.
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Chmelíková, Vlasta. Zlatý řez nejen v matematice. Praha. 2011.
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Mačák, Karel. Tři středověké sbírky matematických úloh. Praha. 2001.
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Mačák, Karel. Vývoj teorie pravděpodobnosti v českých zemích do roku 1938. Praha. 2005.
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Saxl Ivan, Ilucová Lucia. Historie grafického zobrazování statistických dat. Robust. 2004.
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