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Geometry I (Winter 2014/2015)


This is a course of the Berlin Mathematical School
held in English.
Contents
Noneuclidean geometry: spherical, hyperbolic, projective,
Möbius,
Lie, and Plücker line geometry.
News
 [13.11.2014]
 In exercise 2 b) on
sheet 4 you should solve for the coordinates of a rightangled triangle
with angles and edge lengths taken from exercise 2 a).
 [31.10.2014]
 There was a factor of 2 missing in one of the identities
given as hints for ex 2.3, see updated
version.
 [30.10.2014]
 Here
are some hints for the second exercise sheet.
 [28.08.2014]
 The first lecture will be October 13th.
The tutorials start in the second week (i.e. Wednesday,
Oct 22nd).
Exercise sheets
 Sheet
1, due Oct 27
 Sheet
2, due Nov 03
 Sheet
3, due Nov 10
 Sheet
4, due Nov 17
 Sheet
5, due Nov 24
 Sheet
6, due Dec 01
 Sheet
7, due Dec 08
 Sheet
8, due Dec 15
 Sheet
9, due Jan 05
 Sheet
10, due Jan 12
 Sheet
11, due Jan 19
 Sheet
12, due Jan 26
 Sheet
13, due Feb 2
 Sheet
14, due Feb 9
Homework policy

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
Monday.
Late homework is accepted only with a medical excuse.
Examinations
There will be oral exams at the end of the semester.
Literature
For this course, there will be a book collection ("Semesterapparat") in
the Mathematics
Library on the first floor.
 Lecture
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.
Grundlehren der
Mathematischen Wissenschaften, 22. SpringerVerlag, Berlin, 1968.
 Wilhelm Blaschke. Projektive Geometrie.
Birkhäuser, Basel, 1954.
 Dmitry Fuchs & Serge Tabachnikov.
Mathematical
Omnibus: Thirty Lectures on Classic Mathematics. American
Mathematical Society, Providence, RI, 2007.
Preprint.
 Marcel Berger. Geometry. I & II.
SpringerVerlag, Berlin, 1987.
 Michèle Audin. Geometry.
SpringerVerlag, Berlin, 2003.
 H. S. M. Coxeter. NonEuclidean 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 59115. 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 1138.
(This list is not ordered according to any relevant criteria.)
Office hours
