SubjectsSubjects(version: 849)
Course, academic year 2019/2020
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Analytic Geometry I - OB2310203
Title in English: Analytická geometrie I
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2018
Semester: summer
E-Credits: 3
Examination process: summer s.:
Hours per week, examination: summer s.:1/2 C+Ex [hours/week]
Capacity: unknown / unknown (999)
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Is provided by: OPBM2M112A
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: doc. RNDr. Darina Jirotková, Ph.D.
doc. RNDr. Naďa Vondrová, Ph.D.
Class: Matematika 1. cyklus - povinné
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
Pre-requisite : OB2310012
Interchangeability : OB2310N016, OB2310016
Is pre-requisite for: OB2310268, OB2310204
Is interchangeable with: OB2310N016
Annotation -
Last update: JANCARIK/PEDF.CUNI.CZ (19.05.2010)
The subject focuses on analytic geometry in spaces E2, E3 and E4 and the method of generalising knowledge from E2, through E3 to E4. Conics are studied in E2 only.
Aim of the course -
Last update: JANCARIK/PEDF.CUNI.CZ (19.05.2010)

The goal is for students to consolidate and deepen their knowledge of analytic geometry from the secondary school and to understand more deeply the connection of the structures of geometry, algebra and arithmetic.

Literature -
Last update: JANCARIK/PEDF.CUNI.CZ (19.05.2010)

§ Coxeter, H.S.M. Introduction to Geometry. John Wiley & Sons, USA 1989.

§ Gatial, J., Hejný, M. Od pravouhlých súradníc k vektorom. SPN, Bratislava 1980.

§ Stehlíková, N., Hejný, M., Jirotková, D. Úvod do analytické geometrie. PedF UK, Praha 2006.

§ Sekanina, M. a kol. Geometrie 1. SPN, Praha, 1986.

§ Vančura, Z. Analytická geometrie v geometrii. I, II, III. SNTL, Praha 1957.

§ Hlaváček, A. Sbírka řešených příkladů z vyšší matematiky.

§ Kuřina, F. Deset pohledů na geometrii

§ Vejvoda, F., Talafous, F. Sbírka úloh z matematiky

Teaching methods -
Last update: JANCARIK/PEDF.CUNI.CZ (19.05.2010)

Lectures and seminars.

Requirements to the exam - Czech
Last update: ZHOUF/PEDF.CUNI.CZ (02.03.2012)

Požadavky k zápočtu
Aktivní účast na semináři
Napsání testu - studenti mohou používat všechny pomůcky (vyjma komunikace s ostatními) - jsou 3 pokusy (kdo má zapsán kurz podruhe, tak 4 pokusy), za test je 100% úspěšný je ten, kdo ziská aspoň jednou 50%, nebo aspoň dvakrát 40%, nebo v součtu tří pokusů aspoň 100%

Zkouška za předmět AG2 v následujícím semestru bude zahrnovat látku za AG1 i AG2.

Syllabus -
Last update: JANCARIK/PEDF.CUNI.CZ (19.05.2010)

Main topics:

§ Geometry of grid paper and its generalisation into E2 as a context suitable for experimenting and independent discovery of geometrical rules.

§ Linear dependency of vectors, basis, coordinate systems, orthonormal and ortogonal coordinate systems in E2, E3 and E4.

§ Description and investigation of shapes in E2 and E3 in an analytic way.

§ Geometry of space of the fourth dimension as a context suitable for abstraction, some hypersolids, generalisation of shapes from E2 and E3.

§ Analytic geometry of conics.

 
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