History of mathematical thinking - OENMM2119Z

• Title: History of mathematical thinking
• Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
• Faculty: Faculty of Education
• Actual: from 2022
• Semester: winter
• E-Credits: 5
• Examination process: winter s.:
• Hours per week, examination: winter s.:0/0, MC [HS]
• Extent per academic year: 15 [hours]
• Capacity: unknown / unknown (20)
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: yes / 10
• Key competences: 4EU+ Flagship 2
• State of the course: taught
• Language: English
• Teaching methods: distance
• Teaching methods: distance
• Note: enabled for web enrollment; priority enrollment if the course is part of the study plan
• Guarantor: prof. RNDr. Ladislav Kvasz, DSc., Dr.

Annotation

Last update: prof. RNDr. Naďa Vondrová, Ph.D. (11.07.2021)

Introduction to the study of the history of mathematics which is an inspiration for today's teaching of mathematics.

Descriptors

Last update: prof. RNDr. Naďa Vondrová, Ph.D. (02.09.2022)

The lessons will be organised as follows (the link to the online teaching will be sent to the participants):

14.10.2022 14:45-17:15

11.11.2022 11:40-13:10

2.12.2022 11:40-14:10

6.1.2023 11:40-13:10

Literature

Last update: Kateřina Esserová, DiS. (07.07.2021)

Ivor Grattan-Guiness (ed.) (1994): Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, Routledge, London
John Fauvel and Jeremy Gray (1987): The History of Mathematics - A Reader, Macmillan,  London
Jean Dieudonné (1987): Mathematics - The Music of Reason, Springer, Berlin
Morris Kline (1972): Mathematical Thought from Ancient to Modern Times, Oxford UP, New York
Dirk J. Struik (1969): A Source Book in Mathematics, 1200-1800, Harvard UP, Cambridge MA
Carl Benjamin Boyer (1968): A History of Mathematics, John Wiley, New York

Syllabus

Last update: prof. RNDr. Naďa Vondrová, Ph.D. (09.07.2021)

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.

Entry requirements

Last update: prof. RNDr. Naďa Vondrová, Ph.D. (11.07.2021)

Keen interest in mathematics and the knowledge of at least secondary school mathematics.

Course completion requirements

Last update: prof. RNDr. Naďa Vondrová, Ph.D. (11.07.2021)

An essay on the topic assigned by the lecturer.

Learning resources

Last update: prof. RNDr. Naďa Vondrová, Ph.D. (11.07.2021)

https://dl1.cuni.cz/course/view.php?id=7866

Online teaching in MS Teams.