As a tool for you to self-evaluate how much you have learned in the first part of the course, I have made short document that highlights six topics we have looked at. Each topic tells you what you are expected to know at your finger tips (i.e. without looking it up) and gives a small problem testing your knowledge. Each problem should be solvable in about 5 to 10 minutes.
Two important things to note:
The curriculum is still chapters 3-5, not just this note.
This is entirely voluntary. If you don't want to do this you don't have to. (But I of course encourage you to do it)
The obvious way: read chapter 4 first and then chapter 5.
The quick way: read only chapter 5 but refer back to 4 when ever a proof from 4 is needed. Finally read Theorem 4.9. This is the way closest to what we will do in the lectures.
The best but slightly longer way: read the sections in this order 5.1, 5.2, 4.1, 5.3, 4.2, 5.4, 4.4. This way emphasizes how the Lebesgue integral on the real line is a special case of the general construction. It is the most complete way, but does require reading essentially the same thing twice sometimes.
As a tool for you to self-evaluate how much you remember from previous courses, I have made a short document that highlights 4 topics that I expect you to have seen before.Each topic tells you what you are expected to know at your finger tips (i.e. without looking it up) and gives you small problems testing your knowledge. Each problem should be solvable in about 5 to 10 minutes.
If you struggle with any of these problems, come and talk to me or Ulrik. The problems are meant to give us a jumping-off point for talking about things you used to know.
On Thursdays the lectures will consist of me talking a bit a about proofs, and you doing the proofs. Since some students have conflicting lectures at that time, I will make the problems we go through available after each session.
The exercise sessions for the course are at the somewhat unfortunate time of Friday afternoon. It is possible to move them to Monday afternoon (14-16) instead. We will discuss this in the first lecture.