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Geometry I - NMUM203

Title:	Geometrie I
Guaranteed by:	Department of Mathematics Education (32-KDM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016 to 2020
Semester:	winter
E-Credits:	5
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	Mgr. Zdeněk Halas, DiS., Ph.D. doc. RNDr. Jarmila Robová, CSc.
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 :	NMUM808, NUMP010
Interchangeability :	NMUM808, NUMP010
Is incompatible with:	NMUM808, NUMP010
Is interchangeable with:	NMUM808, NUMP010

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Annotation -

Last update: Mgr. Zdeněk Halas, DiS., Ph.D. (08.09.2013)

Analytical geometry of affine and Euclidean spaces and their subspaces. Sets of points defined by distance. This subject provides the high-school analytical geometry with theoretical base using linear algebra.

Literature -

Last update: Mgr. Zdeněk Halas, DiS., Ph.D. (08.09.2013)

Sekanina, M. a kol. Geometrie I. SPN, Praha, 1986.

Lávička, M. Geometrie I. Pomocný učební text. Plzeň, 2008. Dostupné z < http://home.zcu.cz/~lavicka/subjects/G1/texty/G1_texty.pdf>.

Jennings, G. A. Modern Geometry with Applications. Springer, 1996.

Bennett, M. K. Affine and Projective Geometry. John Wiley et sons, 1995.

Syllabus -

Last update: Mgr. Zdeněk Halas, DiS., Ph.D. (08.09.2013)

Affine space

Affine space, subspace.

Coordinates and their transformation.

Linear combination of points. Definition of basic geometrical figures in plane, segment of line and its center, triangle, center of gravity.

Parametric equations of subspace.

(n-1)-dimensional subspace and its equation.

Subspace as intersection of (n-1)-dimensional subspaces.

Euclidean space

Vector spaces with scalar product, geometrical interpretation of scalar product.

Outer and vector product, geometrical interpretation. Axioms of measure.

Euclidean space and subspace, equation of (n-1)-dimensional subspace.

Cartesian coordinates.

Orthogonal subspaces.

Distance from a point to a subspace, distance of two subspaces.

Angle and its measure, angle of a line and a subspace.

Set of points satisfying a given property

Set of points defined by distance; axis of a segment of line, angle, belt.

Circle of Apollonios; power of a circle with respect to the point, chordal of two circles, chordal center of three circles.

General equation of a conic section, classification, singular and regular conic sections. Equations of regular conic sections and their properties. Conic sections as sections of a cone.