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
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