Week 1
From Euclid to Klein: Conceptual introduction
I start by discussing the five "Postulates" that Euclid gives in volume
XIII of "The Elements" to specify his view of geometry. I explain how
groups of motions are intrinsic to that picture and hence make a natural
appearance in geometry. This observation is the essential ingredient in
Klein's "Erlangener Programm", which gives a less restrictive and more
modern idea of geometry, as we shall see.
This is a conceptual introduction
which will allow me to explain the main outline of the course.
Helpful literature:
-
M. Reid, Geometry and Topology, chapters of forthcoming
textbook by M. Reid and B. Szendröi, available from General Office:
Sections 6.1-6.3 and introduction to 4.
- H.S.M. Coxeter,
Introduction
to Geometry, John Wiley & Sons:
Sections 1.1-1.2 and 10, and look up "Klein" in the index.
- D. Mumford, C. Series, D. Wright,
Indra's Pearls: The Vision of Felix Klein,
Cambridge University Press:
Introduction and (parts of) Chapter 1.
Note:
Only topics covered in the lectures and exercises
will be asked in the exam.
The list of helpful literature is meant as an aid, also to raise further
interest, but not as an obligation.