Instructor: Dr. Gyula Lakos
Text: E. G. Rees, Notes on Geometry + handouts
Prerequisite: Beyond calculus, linear algebra and high school
geometry some familiarity with groups is indispensable. The small amount
of topology necessary to understand the course will be introduced, but some experience with some elementary concepts of topology (e.g. metric
spaces, homeomorphisms, identification spaces) is useful.
This course gives an outline of Euclidean and non-Euclidean geometry with a special emphasis on the role of groups of transformations. One of the main goals is to show how linear algebra, group theory and topology can be combined in order to understand fundamental similarities and differences between various types of
Euclidean spaces and Euclidean isometries.
Classification of Euclidean isometries in dimensions 2 and 3.
Finite groups of isometries and Platonic solids.
Quaternions and spherical geometry.
Projective spaces and projectivities.
Conics, quadratic forms and polarities.
Hyperbolic geometry, projective and conformal models.
Classification of hyperbolic plane isometries.
Some formulas of non-Euclidean trigonometry.