Videos, and Games
Geometry I (Winter 2014/2015)
This is a course of the Berlin Mathematical School
held in English.
Non-euclidean geometry: spherical, hyperbolic, projective,
Lie, and Plücker line geometry.
- In exercise 2 b) on
sheet 4 you should solve for the coordinates of a right-angled triangle
with angles and edge lengths taken from exercise 2 a).
- There was a factor of 2 missing in one of the identities
given as hints for ex 2.3, see updated
are some hints for the second exercise sheet.
- The first lecture will be October 13th.
The tutorials start in the second week (i.e. Wednesday,
1, due Oct 27
2, due Nov 03
3, due Nov 10
4, due Nov 17
5, due Nov 24
6, due Dec 01
7, due Dec 08
8, due Dec 15
9, due Jan 05
10, due Jan 12
11, due Jan 19
12, due Jan 26
13, due Feb 2
14, due Feb 9
To get a certificate for the tutorial, you need to satisfactorily
complete 50% of the homework assignments.
The exercises are to be solved in groups of two people.
The homework is due weekly at the beginning of the first lecture on
Late homework is accepted only with a medical excuse.
There will be oral exams at the end of the semester.
For this course, there will be a book collection ("Semesterapparat") in
Library on the first floor.
(This list is not ordered according to any relevant criteria.)
notes by Boris Springborn
- 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.
Mathematischen Wissenschaften, 22. Springer-Verlag, Berlin, 1968.
- Wilhelm Blaschke. Projektive Geometrie.
Birkhäuser, Basel, 1954.
- Dmitry Fuchs & Serge Tabachnikov.
Omnibus: Thirty Lectures on Classic Mathematics. American
Mathematical Society, Providence, RI, 2007.
- 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
S. Levy (editor). Flavors of Geometry. Mathematical
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
constant curvature. In: E. B. Vinberg (editor). Geometry
II. Encyclopedia of Mathematical Sciences 29. Springer,
1993. Pages 1-138.