Euclidean spaces

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Code:	45744
ECTS:	5.0
Lecturers in charge:	izv. prof. dr. sc. Zrinka Franušić
Lecturers:	izv. prof. dr. sc. Zrinka Franušić - Exercises Mateo Tomašević , mag. math. - Exercises
English level: 1,0,0	All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.

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1. komponenta

Lecture type Total

Lectures 30

Exercises 30

* Load is given in academic hour (1 academic hour = 45 minutes)

Description:

COURSE AIMS AND OBJECTIVES: Give an axiomatic approach to the notions of affine and euclidean spaces as generalizations of standard three-dimensional space. Introduce all fundamental notions and prove corresponding theorems.

COURSE DESCRIPTION AND SYLLABUS:
1. Definitions of affine and euclidean spaces. Examples. Elementary properties.
2. Planes in affine space (affine subspaces). Parallelism of the planes.
3. Intersection of the planes. Sum of the planes.
4. Coordinate system in an affine space.
5. Equations of a plane, hyperplane and straight line.
6. Convex sets. Halfspaces.
7. Parallelotope. Simplex.
8. Affine transformations. Affine group of an affine space.
9. Analytic representation of an affine transformation.
10. Euclidean space. Cartesian (rectangular) coordinates.
11. Distance. Angle.
12. Volume.
13. Analytic geometry of an euclidean space.
14. Isometry. Isometric operators.
15. Subgroups of the group of isometries.

Literature:

1. semester

Geometrija i topologija - Regular study - Mathematics Education

2. semester Not active

Geometrija i topologija - Regular study - Mathematics Education

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Link to the course web page: https://web.math.pmf.unizg.hr/nastava/eukl/

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Euclidean spaces

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