MATH4/61112 Ergodic Theory (Reading Course)

Course structure

This is a reading course, supported by one lecture per week. I have split the notes into weekly sections. You are expected to have read through the material before the lecture, and then go over it again afterwards in your own time. In the lectures I will highlight the most important parts, explain the statements of the theorems and what they mean in practice, and point out common misunderstandings. As a general rule, I will \emph{not} normally go through the proofs in great detail (but they are examinable unless indicated otherwise). You will be expected to work through the proofs yourself in your own time. All the material in the notes is examinable, unless it says otherwise.

Please point out any mistakes (typographical or mathematical) in the notes.

Lecture notes

The notes for the course, together with exercises and solutions, can be found here

• Ergodic theory lecture notes (updated 29/4/13)

A list of corrections made to the notes is available here:

• Corrections (updated 29/4/13)

The following handout contains the background material on metric spaces that we shall need

• Notes on Metric Spaces

Assessment

The exam is a 3 hour written exam. There are several past exam papers on the course website. Note that some topics (for example, entropy) were covered in previous years and are not covered this year. Note that the format of the exam is different to previous years. This year the exam has 5 questions, of which you must do 4. If you attempt all 5 questions then you will get credit for your best 4 answers. The style of the questions is similar to a Section B question from previous years. Thus doing past exam papers will be a very useful way to revise the course. Each question is worth 30 marks. Thus the total number of marks available on th e exam is 4x30 =120. This will then be converted to a mark out of 100 (by multiplying by 100/120).

Past exams

Below are the past papers for the last 3 years.