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Geometry I (Winter 2014/2015)
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This is a course of the Berlin Mathematical School
held in English.
Contents
Non-euclidean 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 right-angled 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. Springer-Verlag, 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.
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.
(This list is not ordered according to any relevant criteria.)
Office hours
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