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Lecturer(s)
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Kwiatkowska Alena, Mgr. Ph.D.
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Macháček Ivan, doc. PhDr. CSc.
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Course content
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1. Introduction to philosophy and history of mathematics; particularization of European and non-European knowledge; phenomena and mathematical objects; evidence and calculus 2. Euclid's Elements; Axioms, postulates, basic notions in Elements. 3. Parallelism; infinity, horizon and geometry. The Pythagorean Theorem 4. Rationality and irrationality; the Golden Section. Space, perspective and modern geometry. 5. Solids, body; bodiness; volume; the Platonic solids; 6. Non-Euclidean geometries; topology; evidence in mathematics (and sciences). 7. Hindu and Arabic mathematics; cultural and religious presuppositions. 8. Algorithm; Arabic medieval arithmetics and algebra. 9. European medieval arithmetics and algebra. 10. Renaissance European mathematics; perspective; logarithm; the Cartesian turn. 11. Calculus infinitesimalis. 12. Abel classical and modern algebra; boundaries of mathematics. 13. Existence; modality; temporality; mathematics and logic. Reading texts are different for each academic year.
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Learning activities and teaching methods
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Interactive lecture, Textual studies
- Contact hours
- 26 hours per semester
- Preparation for an examination (30-60)
- 30 hours per semester
- Graduate study programme term essay (40-50)
- 22 hours per semester
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| prerequisite |
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| Knowledge |
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| to list the most important representatives of the field |
| to describe the most significant discoveries in the field and their role in European cultural development |
| Skills |
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| to use modern technologies, especially information databases |
| to process knowledge from a professional text into a comprehensive presentation |
| to analyze and interpret professional text in Czech and English |
| Competences |
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| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| to list key characters and topics from the history and philosophy of mathematics |
| to explain concrete terms and apparatuses related to the history and philosophy of mathematics |
| to describe problems that were solved in the field of history and philosophy of mathematics |
| Skills |
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| to use the terminology of history and philosophy of mathematics with understanding |
| to reproduce the argumentation contained in the given text from the field of history and philosophy of mathematics |
| to interpret and discuss selected period mathematic texts |
| Competences |
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| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Interactive lecture |
| Textual studies |
| Skills |
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| Interactive lecture |
| Textual studies |
| Seminar |
| Competences |
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| Interactive lecture |
| Textual studies |
| Seminar |
| assessment methods |
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| Knowledge |
|---|
| Seminar work |
| Continuous assessment |
| Kolokvium |
| Combined exam |
| Skills |
|---|
| Continuous assessment |
| Kolokvium |
| Seminar work |
| Competences |
|---|
| Continuous assessment |
| Kolokvium |
| Seminar work |
| Combined exam |
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Recommended literature
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Základy. Knihy XI-XII. 1. vyd. Nymburk : OPS, 2011. ISBN 978-80-87269-24-4.
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Abel, Niels Henrik. O algebraických rovnicích. 1. vyd. Kanina : OPS, 2011. ISBN 978-80-87269-23-7.
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Boyer, Carl B. A history of mathematics. 3rd ed. Hoboken : John Wiley & Sons, 2010. ISBN 978-0-470-52548-7.
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Calinger, Ronald S. A contextual history of mathematics : to Euler. Upper Saddle River : Prentice Hall, 1999. ISBN 0-02-318285-7.
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Eukleidés. Základy. Kniha X. 1. vyd. Kanina : OPS, 2012. ISBN 978-80-87269-26-8.
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Eukleidés. Základy. Knihy I-IV. 3., opr. vyd. Plzeň : Západočeská univerzita, 2010. ISBN 978-80-7043-974-6.
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Eukleidés. Základy. Knihy VII-IX. 1. vyd. Nymburk : OPS, 2010. ISBN 978-80-87269-11-4.
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Eukleidés. Základy. Knihy V-VI. 1. vyd. Nymburk : OPS, 2009. ISBN 978-80-87269-05-3.
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Fauvel, John,; Gray, Jeremy. The history of mathematics : A reader. Hampshire : Palgrave Macmillan, 1987. ISBN 0-333-42791-2.
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Hanke, M., Kastnerová, M., Švantner, M., Větrovcová, M. Stopování sémiotiky. Červený Kostelec: Pavel Mervart. ISBN 978-80-7465-142-7.
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Husserl, Edmund. Krize evropských věd a transcendentální fenomenologie : úvod do fenomenologické filozofie. 2. vyd., reprint 1. vyd., Academia 1972. Praha : Academia, 1996. ISBN 80-200-0561-7.
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Kůrka, P.; Matoušek, A. a Velický, B. Spor o matematizaci světa. 2011. ISBN 978-80-7465-012-3.
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Patočka, Jan. Sebrané spisy 1-14. Praha : OIKOYMENH.
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Vopěnka, P., Větrovcová, M., Ostřanský, B. Al-Chvárizmí. Aritmetický a algebraický traktát. Nymburk: OPS, 2009.
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Vopěnka, P., Větrovcová, M. Uvedení do obecné topologie a jejích dějin do roku 1960. Praha: Vyšehrad, 2015.
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Vopěnka, Petr; Novotná, Anna. Vyprávění o kráse novobarokní matematiky : souborné vydání Rozprav o teorii množin. Praha : Práh, 2004. ISBN 80-7252-103-9.
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Vopěnka, Petr. Úhelný kámen evropské vzdělanosti a moci : souborné vydání Rozprav s geometrií. 4. vyd. Praha : Práh, 2011. ISBN 978-80-7252-338-2.
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