Geometry I

Winter Semester 2007/08

This is a course of the Berlin Mathematical School held in English.

The tutorials will be conducted in two groups. You should choose one.

News

Please pick up your Übungschein at Frau Gillmeister's office, room MA 320.

Contents

Exercise sheets

Lecuture notes

Downloads and Links

• Spherical Triangle Demo
• Stereographic Projection Demo
• Triangle Group Demo shows Euclidean, hyperbolic, and spherical geometry of the plane.
• The hyperbolic geometry song
• Theorem of Desargues Demo (Java applet)

Homework policy

To get a certificate for the tutorial, you need to satisfactorily complete 50% of the homework assignments.

In case of heavy correction load, the assistant may choose to correct only a subset of the assigned problems. The 50% requirement refers to the total of the corrected problems.

The homeworks are due weekly at the beginning of the Tuesday lecture (12:15). No homework will be accepted after the deadline has passed.

Homeworks may be turned in directly to the assistant at the lecture, or left with the Sekretariat in MA 3-2 (Room 320).

If you are tempted to copy homework from a classmate, please ask yourself, "What am I learning when I do this?".

Literature

• V. V. Prasolov & V. M. Tikhomirov. Geometry. Translations of Mathematical Monographs, 200. American Mathematical Society, Providence, RI, 2001.
• Nigel Hitchin's lecture notes on Projective Geometry.
• Felix Klein. Vorlesungen über höhere Geometrie. Grundlehren der Mathematischen Wissenschaften, 22. Springer-Verlag, Berlin, 1968.
• Wilhelm Blaschke. Projektive Geometrie. Birkhäuser, Basel, 1954.
• Marcel Berger. Geometry. I & II. Springer-Verlag, Berlin, 1987.
• Michèle Audin. Geometry. Springer-Verlag, Berlin, 2003.
• H. S. M. Coxeter. Non-Euclidean Geometry. Mathematical Association of America, Washington, DC, 1998.
• J. W. Cannon, W. J. Floyd, R. Kenyon, R. Parry. Hyperbolic Geometry. In: S. Levy (editor). Flavors of Geometry. Mathematical Sciences Research Institute Publications 31. Cambridge University Press, Cambridge, 1997. Pages 59-115. Download PDF from the MSRI.
• D. V. Alekseevskij, E. B. Vinberg, A. S. Solodovnikov. Geometry of spaces of constant curvature. In: E. B. Vinberg (editor). Geometry II. Encyclopedia of Mathematical Sciences 29. Springer, Berlin, 1993. Pages 1-138.

Office Hours