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

Contents

Euclidean and non-euclidean geometry: projective, hyperbolic, Möbius, and maybe Lie geometry. The continuation is Geometry II: Discrete Differential Geometry.

Exercise sheets

The exercise sheets can be found here.

Homework policy

To get a certificate of participation, you need to satisfactorily complete 60% of the homework assignments.

The exercises are to be solved in groups of two people.

The homeworks are due weekly at the beginning of the lecture on Thursday. No homework will be accepted after the deadline has passed.

Lecture notes / Blog

The idea is to interactively create lecture notes using wordpress. Each homework group of students is responsible to write up a lecture once during the semester and publish it as a post in our blog.

To be registered as a user for the blog, please write an email to Emanuel (huhnen[at]math.tu-berlin.de) that contains your desired username (minimum 4 characters, only lower case letters and numbers) and the email address you want to use for the blog. An account will be created for you and you will receive an invitation email to join the blog.

Exam / Grading

At the end of the semester, oral exams will be offered.

Literature

• Lecture notes by Boris Springborn
• V. V. Prasolov & V. M. Tikhomirov. Geometry. Translations of Mathematical Monographs, 200. American Mathematical Society, Providence, RI, 2001.
• Lecture notes on Projective Geometry by Nigel Hitchin.
• 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.

Office Hours