# Semester page for MAT4400 - Autumn 2016

The exam was today (I hope you did well). You can read a suggested solution here: /studier/emner/matnat/math/MAT4400/h16/exam/solution.pdf

We will have a question session on Wednesday the 30th of November from 13:00 to 14:00 in room 1036 in the math building.

The idea is for you to come in and asking specific questions to me and Ulrik about the curriculum or old exam problems.

I have received the following nice three exam questions (in two files):

They test measurable functions, convergence theorems and product measure. All of which is relevant.

Problems 2 in particular is very good. It gives a sequence of functions f_n that converges pointwise to a function f, but where

lim_n \int f_n d\lambda \neq \int f d\lambda.

Having an understanding why you cannot use the MCT or the DCT here is good.

The syllabus is now updated.

Here are three ways to read Chapters 4 and 5 in McDonald and Weiss:

**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 covered 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.

A solution for the mandatory assignment is (finally) available here.

As a way for you to prepare for the exam, I propose that you try to make your own exam questions. This would work as follows:

- You read through some of the exams from previous years to get an idea of what exam questions look like.
- You review what we have learned in the course this year.
- You try to formulate exam questions that test the most important aspects of the course.

If you hand in your questions to me, either in person before Friday the 18th or by email before Sunday the 20th, I will look through them and tell you if I think they are of an appropriate level. If you permit it, I will post your questions online for the benefit of your fellow students. I might also go through some of your questions at one of the lectures.

Doing this is entirely voluntary. However, I think it will help you do better at the exam. It will make you review and reflect upon what we have learned in the course. Trying to think of problems that te...

Here are some of the exams from the past years:

When you read through them, please remember that the curriculum changes slightly from year to year.

For a more complete list see here: www.uio.no/studier/emner/matnat/math/MAT4400/oppgaver/ . But remember as you go further back, the curriculum changes more and more.

I have put up a written solution to exercise 13.26 that we went through at the lectures.

I have also made some short notes about the difference between curly L^p and L^p.

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)

Due to low interest the office hours are being shortened. I will now have office hours every Thursday from 14:00-15:00 in my office: 630 in Niels Henrik Abels Hus.

In a very close election you chose Vegard Vinje to be your student representative. His email address is: vegarvi@student.matnat.uio.no .

The dates for the mandatory assignment have been shifted by one day. The assignment will now be posted on the 6th of October and the deadline for submitting will be Thursday the 27th of October before 14:30.

The mandatory assignment will be posted on Friday the 7th of October and the deadline for submitting it will be on Friday the 28th of October.

I will have Office Hours every Thursday from 13:00-15:00 in my office (630) in Niels Henrik Abels Hus.