The purpose of this course is to introduce the basic notions of linear algebra and to prove rigorously the main results of the subject.
After dealing with the basic theory of curves and surfaces in the plane and the Euclidean space,
we will study selected chapters: minimal surfaces, surfaces with constant mean curvature,
caustics, hyperbolic geometry.
Riemannian Geometry is one of the (or possibly the) most central subject in differential geometry and in contemporary geometry in general. The subject is very rich and this course is a basic introduction to the subject.
The subject deals with differential geometry and its relation to global analysis, partial differential equations, geometric measure theory and variational principles to name a few.
The goal of this course is to introduce the student to the basic notion of analysis on metric (measure) spaces, quasiconformal mappings, potential theory on metric spaces, etc. The subjects covered will vary each year.