Modern Geometry

Course code

MLM6253.DT

old course code

Course title in Estonian

Kaasaegne geomeetria

Course title in English

Modern Geometry

ECTS credits

4.0

Assessment form

assessment

lecturer of 2024/2025 Autumn semester

Mart Abel (language of instruction:Estonian)

lecturer of 2024/2025 Spring semester

Not opened for teaching. Click the study programme link below to see the nominal division schedule.

Course aims

To introduce notions and theorems from modern geometry and their applications. To deepen the knowledge of students about the geometry. To demonstrate the connenctions between geometry and other branches of mathematics.

Brief description of the course

Axiomatic structure of mathematics. Euclidean geometry based on the axiomatics of Hilbert. Absolute geometry. Affine geometry. Projective geometry: perspective, projective plane, projective space, Theorem of Desargues, ratio of division of the segment, cross ratio, homogenuous linear coordinates and duality.

Lobachevsky geometry: angle of parallelism, direction of parallelism, equidistant, horocycle, horosphere.

Spherical geometry, problems of navigation, maps, applications of stereographic projection, elliptic geometry, spherical trigonometry, hyperbolic trigonometry.

Geometry based on the axiomatics of Weyl: euclidean space, pseudo-euclidean space, hyperbolic space.

Erlanger Programme of Klein.

Topology and its connections with geometry.

Lobachevsky geometry: angle of parallelism, direction of parallelism, equidistant, horocycle, horosphere.

Spherical geometry, problems of navigation, maps, applications of stereographic projection, elliptic geometry, spherical trigonometry, hyperbolic trigonometry.

Geometry based on the axiomatics of Weyl: euclidean space, pseudo-euclidean space, hyperbolic space.

Erlanger Programme of Klein.

Topology and its connections with geometry.

Learning outcomes in the course

Upon completing the course the student:

- knows the basic notions and main results of euclidean geometry;

- knows the basic notions and main results of projective geometry;

- knows the basic notions and main results of hyperbolic geometry;

- knows the basic notions and main results of spherical geometry;

- knows different axiomatic approaches to the geometry;

- is able to prove some theorems about the subject.

- knows the basic notions and main results of euclidean geometry;

- knows the basic notions and main results of projective geometry;

- knows the basic notions and main results of hyperbolic geometry;

- knows the basic notions and main results of spherical geometry;

- knows different axiomatic approaches to the geometry;

- is able to prove some theorems about the subject.

Teacher

Mart Abel

Prerequisite course 1

Study programmes containing that course

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Mathematics, Mathematical Economics and Data Analysis (MLMB/22.DT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/21.DT)

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