SUBJECT
Title
Basic geometry (reading course)
Type of instruction
lecture
Level
master
Faculty
Part of degree program
Credits
5
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
- Non-euclidean geometries: Classical non-euclidean geometries and their models. Projective spaces. Transformation groups.
- Vector analysis: Differentiation, vector calculus in dimension 3. Classical integral theorems. Space curves, curvature and torsion.
- Basic topology: The notion of topological and metric spaces. Sequences and convergence. Compactness and connectedness. Fundamental group.
Readings
- M. Berger: Geometry I–II (Translated from the French by M. Cole and S. Levy). Universitext, Springer-Verlag, Berlin, 1987.
- P.C. Matthews: Vector Calculus (Springer Undergraduate Mathematics Series). Springer, Berlin, 2000.
- W. Klingenberg: A Course in Differential Geometry (Graduate Texts in Mathematics). Springer-Verlag, 1978.
- M. A. Armstrong: Basic Topology (Undergraduate Texts in Mathematics), Springer-Verlag, New York, 1983.