TU Berlin Fakultät II
Institut für Mathematik

Geometry I (WiSe 18)



Geometry Group



Vergangene Semester


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Virtual Math Labs




Geometry I

(Fall 2018)


Lectures Boris Springborn Mon 14-16 MA 141
Wed 10-12 MA 141
Tutorials Hanka Kouřimská Wed 8.30-10 MA 648
Wed 12-14 MA 143
Wed 14-16 MA 744
Thur 8.30-10 MA 744

Information about the second exam

The exam is corrected and the results can be found online in QUISPOS. If for some reason you cannot see your grade, send an email to Hanka :)

The exam overview (Einsicht) will take place on Thursday, 4 Apr 2019, at 15-16 in Room MA 141. Please be on time and bring your student ID with you!

Exam preparation

The following exercises from the homework sheets are a good preparation:

  • Sheet 1, Exercise 4
  • Sheet 2, Exercise 1 and 3
  • Sheet 3, Exercise 2 and 4
  • Sheet 4, Exercise 2 and 3
  • Sheet 5, Exercise 1,2 and 4
  • Sheet 6, Exercise 1 and 3
  • Sheet 7, Exercise 2
  • Sheet 8, Exercise 1, 3 and 4
  • Sheet 9, Exercise 1, 2 and 3
  • Sheet 10, Exercise 1
  • Sheet 11, Exercise 4
  • Sheet 12, Exercise 1, 3 and 4
  • Sheet 13, Exercise 2, 3 and 4

Trial exam (Probeklausur) can be found here: Probeklausur

The solutions to the Probeklausur can be found here: Probeklausur solutions. Please note that there might be mistakes (in particular regarding calculations!)


The solutions of the trial exam are online!
The trial exam is online!
As a compensation of the cancellation of this weeks tutorials Hanka has summed up their contents into a 3-page pdf, available here. The summary contains a few simple questions and should help you with the homework due next week. Happy reading! (and many appologies in advance for the possible typos :))
This is a BMS course and will be held in English. One of the tutorials will be held in German, and the homework sheets can be handed in in German as well.


Lecture Notes

Here is a growing set of lecture notes. Updated versions will be posted at irregular intervals.

Schein - The homework certificate

  • In order to obtain the homework certificate you must collect at least 60% of the points from the homework sheets.
  • You are to hand in the homework sheets in groups of three on Wednesday before the lecture. Your hand-ins have to be STAPLED TOGETHER and contain names and matriculation numbers of all members of the group. We strongly reccommend you to hand in the homework in readable writing, since unreadable writing will not be corrected ;)
  • Your work should be ordered in ascending order of the exercises!
  • The hand-in date will be specified on each homework sheet. You can also hand the homework in earlier in Hanka's office.
  • You can use any language you like writing up the homework sheets, provided that Hanka understands it :)


This course was examined by a 90 minute written exam (Klausur) on Monday, 25 Feb 2019, at 14:00 in Room MA 001.

The second examination date (Nachklausur) is Monday, 1 Apr 2019, at 15:00 in Room MA 001.


  • Springborn, old (but partially updated) lecture notes from the 2007 version of this course at TU Berlin
  • Euclid, Elements: online with java or Greek beside English text
  • Prasolov & Tikhomirov, Geometry, TMM 200, Amer. Math. Soc.
  • Hitchin, lecture notes on Projective Geometry: Chapters 1&2,   3,   4,   5
  • Fuchs & Tabachnikov, Mathematical Omnibus
  • Klein, Vorlesungen über höhere Geometrie, GMW 22, Springer
  • Blaschke, Projektive Geometrie, Birkhäuser
  • Berger, Geometry I & II, Springer
  • Audin, Geometry, Springer
  • Coxeter, Non-Euclidean Geometry, Math. Assoc. Amer.
  • Cannon, Floyd, Kenyon & Parry, Hyperbolic Geometry, from Flavors of Geometry, MSRI
  • Martin, The Foundations of Geometry and the Non-Euclidean Plane, UTM, Springer
  • Henderson, Experiencing Geometry, Prentice Hall

Consultation hours

Boris Springborn see homepage MA 871
Hanka Kouřimská by appointment MA 863

Hana Kourimska . 28.05.2019.