Modern Geometry
Course code
MLM6224.DT
old course code
MLM6224
Course title in Estonian
Kaasaegne geomeetria
Course title in English
Modern Geometry
ECTS credits
4.0
approximate amount of contact lessons
52
Teaching semester
autumn
Assessment form
Examination
lecturer of 2019/2020  Autumn semester
Mart Abel (eesti keel)
lecturer of 2019/2020  Spring semester
lecturer not assigned
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.
Independent work
Work with the lecture materials and literature.
Learning outcomes in the course
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.
Assessment methods
Written test. The mark is evaluated by the score of maximum of 100 credits. These 100 credits are given as maximum 50 credits for the test during the semester and as maximum 50 credits for the test after the end of the lectures. The mark is positive if the student gathers at least 51 credits during the tests.
Teacher
prof Mart Abel
Prerequisite course 1
Study literature
K. Ariva, Lobatševski geomeetria, Valgus 1992;
M. Väljas, Analüütiline geomeetria, TTÜ kirjastus, 2012;
R. Kolde, M. Väljas, Teisenduste rühmad geomeetrias Valgus 1991.
Replacement literature
G. A. Jennings. Modern geometry with applications, Springer, 1994
David A Thomas. Modern geometry, Grooks/Cole 2002.
H. S. M. Coxeter. Non-euclidean geometry, The Mathematical Association of America, 2002.
H. S. M. Coxeter. Introduction to Geometry, Wiley, 1989.