Foundations of Geometry
Course code
MLM6254.DT
old course code
Course title in Estonian
Geomeetria alused
Course title in English
Foundations of Geometry
ECTS credits
4.0
Assessment form
assessment
lecturer of 2025/2026 Spring semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
lecturer of 2026/2027 Autumn semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
Course aims
To introduce axiomatic approach to Geometry, Basic notions and Theorems. To offer an overview of different geometries (Euclidean Geometry, Hyperbolic Geometry, Elliptic Geometry, Projective Geometry). To develop the knowledge about geometry and axiomatics. To show the connections 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:
- states main notions and result of euclidean geometry and understand the relations between them;
- states main notions and result of projective geometry and understand the relations between them;
- states main notions and result of hyperbolic geometry and understand the relations between them;
- states main notions and result of spherical geometry and understand the relations between them;
- makes difference between the axiomatic principles of different geometries;
- proves some theorems about the subject.
- states main notions and result of euclidean geometry and understand the relations between them;
- states main notions and result of projective geometry and understand the relations between them;
- states main notions and result of hyperbolic geometry and understand the relations between them;
- states main notions and result of spherical geometry and understand the relations between them;
- makes difference between the axiomatic principles of different geometries;
- proves some theorems about the subject.
Teacher
Mart Abel
Prerequisite course 1
Study programmes containing that course