Note: The file above is a Problem Sheet which contains a list of problems assigned, which will be discussed in the Exercise session; the file will be updated as the course goes on, so come back to download it at regular intervals for new problems.

Handwritten lecture notes

Handwritten notes for the lectures are available as additional informal reference (only to registered students). To download the pdfs, you need to log in to your My first (e.g. using the button here above), then you should be able to see the links to the pdf files here below.

Extra Resources online:

• Video presentation of the course;
• Slides of a colloquium talk on billiards I gave in the past (it contains an introduction which overlaps with the introduction to the course as well as an overview of some of my research in this area);
• For a picture of a non uniformely distributed billiard trajectory, see Figure 2 at page 3 of the following lecture notes;

Some fun related links:

• Tiling billiards animation by Ofir David

• 1BrowBlue1Brown explanation of two masses collision approximation of pi (solution to a Homework exercise!)

• More 3Blue1Brown on two masses elastic collisions, the explanation of the problem and another solution (without billiards) 

• The music of billiard tables, another video by Ofir David (with the idea of unfolding and a hint of solution to a Homework problem)

• Playing in an elliptical billiard table (no math...); some more footage here; 

• A Numberphile video on the illumination problem, with an interview to Howard Masur and a follow up;

• Cutting sequences in the pentagon, a 'Dance my PhD' video on , by Diana Davis; see also the 'The make of': FAQ video for explanations on how it was shot and the mathematics behind.

Billiards and Surface Dynamics I, which will run for the first 7 weeks only (4h per week + 2h exercise class) and cover only the first half of the syllabus.

References:

• Tabachnikov, Billiards and Geometry (available online, pdf here); German translation,  'Billiards and Geometrie' also available;
• Rozikov, Introduction to mathematical Billiards;