SubjectsSubjects(version: 945)
Course, academic year 2023/2024
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Introduction to Geometry of Space - NMUM205
Title: Základy prostorové geometrie
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: winter
E-Credits: 2
Hours per week, examination: winter s.:1/1, colloquium [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Jarmila Robová, CSc.
RNDr. Vlasta Moravcová, Ph.D.
Class: M Bc. MZV
M Bc. MZV > Povinné
M Bc. MZV > 2. ročník
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
Incompatibility : NMTM205, NMUM819
Pre-requisite : NMUM106
Interchangeability : NDGE004, NMTM205, NMUM819
Is incompatible with: NMTM205
Is interchangeable with: NMTM205, NUMZ013
Annotation -
Last update: doc. RNDr. Jarmila Robová, CSc. (12.09.2013)
The course focuses on the properties of geometric figures and transformations in three-dimensional space. This course deepens and expands the curriculum of secondary school stereometry. There is used the synthetic approach in deriving and justifying relations and in problem solving.
Course completion requirements -
Last update: doc. RNDr. Jarmila Robová, CSc. (28.10.2019)

The course is finalized by a colloquium.

Requirements for receiving the credit:

1. Active attendance (including using drawing aids) - three absences are allowed.

2. Successful completion of the written part and oral part of the colloquium. The written part is preceded by the oral part; failure in the first part means to fail the colloquium. The written part includes two short theoretical questions and three examples in the scope of the syllabus. Requirements for the oral part correspond to the syllabus.

Literature -
Last update: T_KDM (29.04.2013)
  • Kadleček, J. Geometrie v rovině a v prostoru pro střední školy. Prometheus, Praha, 1996.
  • Kuřina, F. 10 pohledů na geometrii. MÚ Akademie věd ČR, Praha, 1996.
  • Eukleidovy Základy (Elementa). Přeložil František Servít, JČM, Praha, 1907. Dostupné z
  • Adamar, Ž. Elementarnaja geometrija. Časť pervaja. Planimetrija. 3. vyd., UČPEDGIZ, Moskva, 1948.
  • Adamar, Ž. Elementarnaja geometrija. Časť vtoraja. Stereometrija. 2. vyd., UČPEDGIZ, Moskva, 1951.
  • Geometrie pro devátý až jedenáctý postupný ročník, SPN, Praha, 1954.
  • Hejný, M. Aj geometria naučila človeka myslieť. 2. upr. vyd. SPN, Bratislava, 1990.
  • Hruša, K. a kol. Přehled elementární matematiky. 4., nezměn. vyd., SNTL, Praha, 1964.
  • Klein, F. Elementary Mathematics from an Advanced Standpoint. Geometry. Dover Publications, 2004.
  • Pomykalová, E. Matematika pro gymnázia - stereometrie. Prometheus, Praha, 2009.

Syllabus -
Last update: doc. RNDr. Jarmila Robová, CSc. (01.10.2018)

• Basic properties of geometric figures in three-dimensional space.

• Fundamental theorems of stereometry and their proofs.

• Positional and metric properties of spatial figures.

• Solids and their properties, particularly polyhedra, Euler's theorem.

• Geometric transformations in three-dimensional space (isometries, similarities).

• Geometric constructions in three-dimensional space.

 
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