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Course, academic year 2022/2023
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History of mathematical thinking - OPNM3M011A
Title: History of mathematical thinking
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2021
Semester: winter
E-Credits: 4
Examination process: winter s.:
Hours per week, examination: winter s.:1/1, C [HT]
Extent per academic year: 0 [hours]
Capacity: 30 / 30 (unknown)
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: English
Teaching methods: full-time
Note: course can be enrolled in outside the study plan
enabled for web enrollment
priority enrollment if the course is part of the study plan
Guarantor: prof. RNDr. Ladislav Kvasz, DSc., Dr.
Teacher(s): prof. RNDr. Ladislav Kvasz, DSc., Dr.
Is interchangeable with: OKNM3M011A
Annotation -
Last update: prof. RNDr. Naďa Vondrová, Ph.D. (02.02.2022)
Introduction to the study of the history of mathematics. 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.
Descriptors - Czech
Last update: prof. RNDr. Naďa Vondrová, Ph.D. (10.09.2021)
Celková časová zátěž studenta 106,0
Přidělené kredity 4
Zakončení Z
Přímá výuka  
Přednášky prezenční studium: 1
Cvičení prezenční studium: 1
 Cvičení kombinované studium: 10
Příprava na výuku  
Doba očekávané přípravy na 1 hodinu přednášky 30 minut
Doba očekávané přípravy na 1 cvičení 60 minut
Samostudium literatury (za semestr) 30 hodin
Práce se studijními materiály (za semestr) 10 hodin
Plnění průběžných úkolů (za semestr) 10 hodin
Plnění předmětu  
Seminární práce 0 hodin
Příprava na zápočet 0 hodin
Příprava na zkoušku a zkouška 14 hodin
Literature - Czech
Last update: STEHLIKO (30.09.2019)

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

Requirements to the exam
Last update: prof. RNDr. Ladislav Kvasz, DSc., Dr. (03.02.2022)

Every student has to choose some of the historical texts discussed in the course

and write an essay having from 4 to 8 pages that contains:

1. an exposition of the main aim, concepts and methods of the historical text

2. a discussion of the concepts and methods from the viewpoint of contemporary mathematics

3. a discussion of the potential of the content of the historical text for use in classroom

(interesting problems, motivating examples, illustration of the uses of mathematics learned in the classroom)

Last update: prof. RNDr. Ladislav Kvasz, DSc., Dr. (01.11.2021)

In the course the languages of the following fundamental mathematical theories:

elementary arithmetic,                     synthetic geometry,

algebra,                                          analytic geometry

differential and integral calculus,       fractal geometry,

predicate logic,                                set theory

will be analyzed from the point of view of six basic linguistic parameters:

logical power,                              

expressive power,

methodological power,

integrative power

explanatory power, and

metaphorical power.

Learning resources - Czech
Last update: STEHLIKO (17.09.2019)

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