Course objectives:
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Introduction to the historical evolution of mathematics and to famous mathematical persons. Periodization of the development of mathematics . Prehistory development of mathematics and indirect sources. Specific conditions for the development of mathematics in Greece and hellenic areas, centers of scientific work. Causes and consequences of the decline of ancient mathematics, transmission of results to the Orient, mathematics of islamic countries. Mathematics in Europe and learning ancient and oriental mathematics. Foundations of mathematical analysis in the 17th century, mathematical analysis of the 18th century. Trends of mathematics in the 18th, 19th, eventually 20th centuries.
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Requirements on student
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The exam is combined. The written part consists of a project on a chosen topic of maths history. The
topic is chosen by a student in agreement with the teacher. The oral form of the exam involves the
analysis of this topic and in case of need, other additional questions are given
in the scope of the course contents.
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Content
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1. Main periods of maths evolution. The first period of maths evolution (the stage of
elementary mathematical concepts).
Prehistorical first steps in counting, the way to the beginning of geometry.
2. Egyptian and Mesopotamian mathematics, Chinese and Indian mathematics at the age
before Christ.
3. The second period of maths evolution (the stage of constant quantities in mathematics).
The oldest period of Greek (antique) mathematics.
4. Greek (antique) mathematics till the beginning of our era.
5. Antique and oriental mathematics in the first millenium.
6. Mathematics in the medieval Europe (6-th - 15-th century).
7. Mathematics in the 16-th century.
8. The third period of maths evolution (the stage of varying quantities in mathematics).
Mathematics in 17-th century.
9. Mathematics in 18-th century.
10. The fourth period of maths evolution (the stage of modern mathematics).
Mathematics in 19-th century.
11. Mathematics in 20-th century.
12. Famous Czech mathematicians.
13. Conclusion - summing up and recapitulation of delivered lectures.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Basic:
Struik, D.J. Dějiny matematiky.. Praha : Orbis, 1963. ISBN 1-123-63.
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Basic:
Polá, Josef. Didaktika matematiky III. část: Historie matematiky pro ucitele. 2016. ISBN 978-80-7489-338-4.
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Basic:
Stillwell, John. Mathematics and its history. 2nd ed. New York : Springer, 2002. ISBN 0-387-95336-1.
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Extending:
Mareš, M. Příběhy matematiky.. Příbram : Pistorius-Olšanská, 2008. ISBN 978-80-87053-16-4.
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Extending:
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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Recommended:
Stillwell, John. The four pillars of geometry. New York : Springer, 2005. ISBN 0-387-25530-3.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Contact hours
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26
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Preparation for an examination (30-60)
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30
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Presentation preparation (report) (1-10)
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10
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Total
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66
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
orientovat se v poznatcích základních matematických teorií |
uvědomit si základní historické souvislosti a zařadit významné události do historického kontextu |
vyjmenovat několik známých matematiků |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
aplikovat osvojené postupy na vybrané matematické úlohy |
přiřadit některé matematické výsledky ke konkrétním osobnostem |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
rozumět vývoji matematiky ve starověku, středověku a novověku |
popsat přínos nejvýznamnějších matematických osobností k vývoji matematiky |
orientovat se v návaznostech a souvislostech jednotlivých matematických disciplín s ohledem na jejich historický vývoj |
rozumět vývoji matematických metod s přihlédnutím k řešení vybraných problémů |
rozpoznat a formulovat předpoklady i důsledky matematických myšlenek konkrétní historické doby a zhodnotit jejich význam pro dějiny evropské kultury |
Skills - skills resulting from the course: |
popsat hlavní směry historického vývoje matematiky |
demonstrovat na vybraných problémech různé přístupy k řešení konkrétních matematických problémů |
dokumentovat na konkrétních případech vliv matematického poznání na vývoj evropské civilizace |
provádět důkazy vybraných důležitých vět aparátem matematiky určitého historického období |
provést rozbor historického matematického textu |
Competences - competences resulting from the course: |
N/A |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Skills - skills achieved by taking this course are verified by the following means: |
Combined exam |
Competences - competence achieved by taking this course are verified by the following means: |
Combined exam |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture supplemented with a discussion |
Textual studies |
Self-study of literature |
Skills - the following training methods are used to achieve the required skills: |
Lecture supplemented with a discussion |
Textual studies |
Self-study of literature |
Competences - the following training methods are used to achieve the required competences: |
Lecture supplemented with a discussion |
Textual studies |
Self-study of literature |
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