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Course, academic year 2019/2020
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Seminar on History of Mathematics - OKB2310V02
Title in English: Proseminář z dějin matematiky
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2012
Semester: summer
E-Credits: 3
Examination process: summer s.:
Hours per week, examination: summer s.:0/0 C [hours/semester]
Extent per academic year: 8 [hours]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
State of the course: not taught
Language: Czech
Teaching methods: combined
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.
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Annotation -
Last update: JANCARIK/PEDF.CUNI.CZ (04.06.2010)
The aim of the seminar is to outline the main changes of the notion of space in the development of geometry from Euclid to the birth of algebraic topology at the dawn of the twentieth century. It attempts to offer a broader perspective on the various areas of classical geometry which the students are been taught in their courses during their study of mathematics. Special seminars are devoted to Euclid's Elements (both their axiomatic construction as well as their implicit presuppositions), to the discovery of space in the Renaissance, to the birth of projective geometry in the 17th century, to the geometry of the projective plane (its non-orientability, one sidedness, as well as the duality of points and straight lines) and to projective coordinates. Then follow seminars devoted to non-Euclidean geometry, to Beltrami model and its metric, to Klein's Erlanger program, and to the classification of geometries. The final third series of seminars is devoted to fundamental notions of algebraic topology in Riemann and Poincare (homotopy, homology, and the fundamental group). The exposition is based on classical texts and it is rather informal and intuitive.
Aim of the course -
Last update: JANCARIK/PEDF.CUNI.CZ (04.06.2010)

The aim of the seminar is to outline the main changes of the notion of space in the development of geometry from Euclid to the birth of algebraic topology at the dawn of the twentieth century. It attempts to offer a broader perspective on the various areas of classical geometry which the students are been taught in their courses during their study of mathematics.

Literature -
Last update: JANCARIK/PEDF.CUNI.CZ (04.06.2010)

Roberto Bonola (1912): Non-Euclidean Geometry, Dover, New York 1955

Jeremy Gray (1979): Ideas of Space, Euclidean, Non-Euclidean, and Relativistic, Clarendon Press, Oxford

A. P. Norden (1956): Ob osnovanijach geometrii, Sbornik klassičeskich rabot. 1956 GITTL, Moskva

Boris Abramovič Rozenfeľd (1976): Istorija neebklidovoj geometrii, Moskva 1976

Petr Vopěnka (1989): Rozpravy s geometrií, Panorama, Praha

Petr Vopěnka (1995): Rozpravy s geometrií, Otevření neeuklidovských geometrických světů, Vesmír, Praha

Teaching methods -
Last update: JANCARIK/PEDF.CUNI.CZ (04.06.2010)

On the seminar the teacher will first shortly characterize the particular topic, its importance and relations to other topics and then the students will in the form of presentations discuss the topic's mathematical, historical and educational aspects.

Syllabus -
Last update: JANCARIK/PEDF.CUNI.CZ (04.06.2010)
  • Euclid's Elements (their axiomatic structure and implicit presuppositions),
  • the discovery of space in Renaissance painting,
  • the birth of projective geometry in the 17th century,
  • the geometry of the projective plane,
  • the geometry of Lobachevski,
  • Beltrami's model and its metric,
  • Klein's Erlanger program and the classification of geometries,
  • basic notions of algebraic topology.
 
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