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Lecturer(s)
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Ferizi Petr, prof. RNDr. Ph.D.
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Course content
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1. Introduction and basic overview 2. Periodization of the development of mathematics. History of number systems 3. The Pythagorean Theorem. Geometry in ancient Greece 4. Greek number theory. Infinity in Ancient Greece 5. History of solving algebraic equations 6. The coordinate method and the birth of analytic geometry 7. Origin and development of infinitesimal calculus 8. Complex (and hypercomplex) numbers. The beginnings of complex analysis 9. Non-Euclidean geometry 10. Beginnings of group theory. Sets and logic 11. Beginnings of differential geometry. Origin of topology 12. Additional topics, presentation of semester projects 13. Conclusion and summary
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Learning activities and teaching methods
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Lecture supplemented with a discussion
- Graduate study programme term essay (40-50)
- 10 hours per semester
- Contact hours
- 26 hours per semester
- Preparation for an examination (30-60)
- 25 hours per semester
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| prerequisite |
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| Knowledge |
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| to be familiar with the basic concepts and methods of university-level mathematics (in particular algebra, geometry, and basic analysis) |
| to understand standard mathematical terminology and notation used in academic texts |
| to have a basic overview of the main areas of mathematics and their interrelations |
| Skills |
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| to work with academic texts (read with understanding, identify key information, and take concise notes) |
| to find and use basic study and reference resources (textbooks, encyclopedias, library catalogues) |
| to write a clear short summary or a reasoned argument on an academic topic |
| Competences |
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| N/A |
| N/A |
| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| to navigate the chronology of the history of mathematics from antiquity to the modern era and its main thematic areas |
| to explain the development of key mathematical concepts (e.g., numeral systems, algebra, geometry, calculus, set theory) in their historical context |
| to distinguish major sources and approaches in the history of mathematics (primary sources vs. secondary literature) and describe their role |
| to identify selected key figures and milestones and briefly characterize their contributions |
| Skills |
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| to analyze a historically oriented scholarly text and articulate its main theses and reasoning |
| to connect a historical account with a modern mathematical formulation using a concrete example |
| to prepare a short written paper or presentation on a selected topic in the history of mathematics using relevant sources |
| to discuss, clearly and factually, historical motivations and the impact of mathematical discoveries on contemporary mathematics and teaching. |
| Competences |
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| N/A |
| N/A |
| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Lecture supplemented with a discussion |
| Textual studies |
| Self-study of literature |
| Skills |
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| Lecture supplemented with a discussion |
| Textual studies |
| Self-study of literature |
| Competences |
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| Lecture supplemented with a discussion |
| Textual studies |
| Self-study of literature |
| assessment methods |
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| Knowledge |
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| Combined exam |
| Skills |
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| Combined exam |
| Competences |
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| Combined exam |
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Recommended literature
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Mareš, M. Příběhy matematiky.. Příbram: Pistorius-Olšanská, 2008. ISBN 978-80-87053-16-4.
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Polák, Josef. Didaktika matematiky III. část: Historie matematiky pro ucitele. 2016. ISBN 978-80-7489-338-4.
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Potůček, Jiří. Vývoj vyučování matematice na českých středních školách v období 1900 - 1945. 1. díl, Vznik a vývoj jednotlivých typů škol a jejich.
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Stillwell, John. Mathematics and its history (third edition). New York, 2010. ISBN 978-1-4419-6052.
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Stillwell, John. Mathematics and its history. 2nd ed. New York: Springer, 2002. ISBN 0-387-95336-1.
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Stillwell, John. The four pillars of geometry. New York: Springer, 2005. ISBN 0-387-25530-3.
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Struik, D.J. Dějiny matematiky.. Praha: Orbis, 1963. ISBN 1-123-63.
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