Messages - Page 2
Solutions of the first assignment is on the web.
Geir
There are two more misprints on Ark8:
There is sign missing in problem 3b. It should read: the bn=-2 Im cn.
There is a factor 2 missing in the big sum in problem 10.b.
Corrected version is posted.
Geir
About the curriculum:
The adjustment of the curriculum from the theory of Fourier series amounts to:
The Section 4.10 is not part of the curriculum - except that the statement (not the proof) of Corollary 4.10.6 is part.
Geir
To day I finished what we will do in Fourier theory. On friday I'l start on chapter 5.
Geir
Due to the midterm week there will be no lectures next week (i.e., the week from 26/3 to 30/3). There will be no group on Thursday next week ( i.e., 29/3) , but the group on Friday (30/3) will go as usual.
Geir
There is a misprint in Problem 10 on Ark8: The function f should vanish outside [-h,h].
G
In ti day's lecture I finished 4.8. On friday I'll do 4.9 and hopefully have some time to start on 4.9.
G
About the curriculum:
As some important parts in Tom's notes are not covered in Tao's book, the official curriculum will be Tom's notes. (Example: equicontinuity and Arzela-Ascoli.) I'll will give a precise curriculum later on - but it will correspond closely to what we do during the lectures.
Geir
NB - about the mandatory assignment:
You will get the feedback at the latest at thursday march 15. Those which do not pass on the first try, will have a deadline on thursday march 22 for the second chance. That will be final - no third chance.
Geir
On friday I did section 4.6 until 4.6.7. To day we will finish 4.6 and go on with Fourier series. I ll try to do most of 4.8
Geir
On Monday I finished the proof of Abel's theorem about power series. I gave some background for Fourier series and started slowly on normed spaces and inner product. On Friday I'll do that more in detail, that means 4.5 and 4.6 in Tom's.
Geir
LaTeX-kurs onsdag 28. mars (nybegynnere) og onsdag 11. april (viderekomne) - begge dager kl. 16.15-18.00.
In to days lecture I did 4.1 and 4.2 from Tom's. On friday I'll do 4.2 and 4.4.
Geir
I am back among the living again!
Have posted Ark6.
Geir
Inevitably, there were misprints in the assignment. New version is posted.
Geir
The first mandatory assignment is posted - remember the deadline: 8. March at 14.30.
Geir
I have written a small note about the proof of Weierstrass approksimasjons teorem which I ll give to day. I did it in norwegian (sorry for those who do not speak that language), partly because everybody in the audiens understands norwegian, and partly because I write norwegian at least at double speed than english.
This is a preliminary version, probably (let me admit it: for sure) with some small errors, but I wanted you have before the lecture, so you can follow what I say.
Of course, updated version will soon come.
G
On friday I did Arzela-Ascoli and finished 3.5. To day I will do chapter 3.7 called "Polynomials are dense in C([a,b], R)". The main result is the Weierstrass approximation theorem. I will follow a path a little different from Tom. The mathematical content is the same in the two approaches, but I will not use a statistical language.
I will probably not be through with Weierstrass to day; I would guess we need one hour also on friday. And then we start on chapter 4!
For the moment I plan to do chapter 4 in its entirety (if time permits). I would guess some of things there are more or less well known, so I ll try to put emphasis on the new things and do the well known "with a rabbit's foot".
This means:
3.6, "Differential equations revisited" is not part of the curriculum.
3.8 "Baire's category theorem" is not part of the curriculum.
G
NB: Concerning the first mandatory assignment
You will get the problems Thursday February 23.
Deadline is Thursday Mars 8.
Geir
New corrected versions of Ark2 (where there was a mistake in problem 12) and Ark4 ( where there was a mistake in problem 3) are on the web.
There is also a small misprint in theorem 3.4.2 in tom's note, which can be confusing. You find the correction on the list of misprints.
Geir