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.
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)
Syllabus
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:
