Geometry - MX4549
One of the aims of the course is to understand the mathematical concept of
curvature. We will do it, first by studying the geometry of plygonal surfaces,
and then by looking at smooth surfaces in the Euclidean space.
Lecture notes
- version March 27, 2018.
Weekly problems:
Every section of the notes ends with a set of problems. You should try solve
them before the tutorial. Come to the tutorial with questions about the problems
you could not solve. By this I mean that you tried and spent at lest two
hours on the problem and have at least five pages of notes with your
unsuccessful attempts.
Lectures:
Thursday, 10:00-11:00 and 15:00-16:00 (Fraser Noble 156)
Tutorial:
Tuesday, 15:00-16:00 (Fraser Noble 156)
Reading:
The course is partly based on the books 'Metric spaces of non-positive curvature'
by M. Bridson and A. Haefliger and 'A course in differential geometry' by W. Klingenberg.
Reading wikipedia articles about the concepts discussed in the course can be also helpful.
Additional reading, watching and playing:
Invitation to Alexandrov geometry: CAT[0] spaces
by S. Alexander, V. Kapovich and A. Petrunin.
Wireframe, a program for drawing
polygonal surfaces by Danny Calegari.
Dimensions
by Jos Leys, Étienne Ghys and Aurélien Alvarez.
On being Thurstonized
by Benson Farb.
Spaces and Questions
by Misha Gromov.
Puzzles in geometry which I know and love
by Anton Petrunin.
Examples of exam problems.