Projects - 2

I have recalled some basics about measure and integration theory, and this lead me to the idea to take this as the second topic for my master exam. Master exams at the University of Vienna consist of two parts, the first one is about your thesis, and the second one covers a subject which shouldn’t be related to the first part. My first idea had been to take linear algebra with H. Rindler as examiner, who is the dean of the faculty of mathematics. But now I think about deciding for measure and integration theory, the exam of which I had taken at K. Sigmund. The relation to functional analysis is given by measurability, Lebesgue-integrability and the -spaces.

I got the Christensen-book on Friday. The 3 new books I own now cost the hell of €241.59! Well, others buy a plasma TV, I buy mathematical literature.

Apropos: I’ve set up a time plan for working up the basics of functional analysis. Until the end of January, I want to recall properties of metrical and topological spaces as well as basics of measure theory, using my script of Prof. Cigler’s lecture about functional analysis and the book “Functional Analysis” by Werner. After that I want to go through the first seven chapters of the mentioned book until the end of March; chapter IV should be done by the end of February. I’ll have to go through about 6 pages per day, I think this should be possible.

In April I want to start doing Gabor analysis, and finally the topic of my thesis should be fixed in May.

Today I went to HGFei to receive three books: Gröchenig’s “Foundations” and HGFei/Strohmer’s “Gabor Analysis” and “Advances”; the first two are now my property, the third one is just a lend. I also ordered a copy of Christensen’s “Introduction”. I want to buy these books because of their high quality and their good aptitude as introductory literature, and I like to write down notes *into* books, which isn’t quite possible for borrowed copies.

We had a short talk about further proceedings. My task now is to read a lot. In two or three months I should have a good enough overview about the topic to be able to say what direction is most interesting for me. As final target, Christmas 2006 should be a reasonable date for the master exam.

One part of my thesis could be to do some “quality assurance” and documentation of the NuHAG Matlab toolbox. Also, I think I should create a port for Octave.

I bought the MathTimeProfessional fonts for LaTeX from PCTeX, Inc. and plan to combine it with Monotype Baskerville for the actual print of my thesis.

I’m still finishing to read the introduction chapter of HGFei’s book, after which I want to get myself familiar with some basics of Functional Analysis again, such as properties of , , , e.a.

Today I went to Prof. Baxa and showed him my exam reports. Although there were some “Gut” (“good”, i.e. B’s) among them, I cleverly combined them with some “Sehr gut” (“very good”, i.e. A’s) to get an average of “Sehr gut” in most cases. Topology will be my only “Gut” in the master exam report. But that’s OK, as I can’t call myself a very good mathematician.

Anyway, all in all I have finished the second part of my study with “Ausgezeichneter Erfolg” (“outstanding success”). All that’s missing now is a master thesis and the master exam.

Three months have passed since September, but I continued reading on the Short Introduction to Gabor Analysis by Feichtinger/Strohmer some time ago. Also, I did around a bit with Octave. I borrowed two books (Christensen, Blatter) from the NuHAG Library. Unfortunately I forgot to look for a copy of Gröchenig. As one of the next things I want to check out the NuHAG MATLAB toolbox and the PDFs about the basics of Fourier Analysis, the links of which HGFei sent me some time ago.

Also, I finally collected all exam reports and will hand them out to Prof. Baxa, together with the exam pass. The meeting with Thomas K. is still up to come, but I want to wait until I really understand what we’ll be talking about.

I found out that Prof. Kowol isn’t responsible any longer for rubber-stamping exam passes. This task has been taken over by Prof. Baxa, and not Prof. Cap, as I’ve been told first. As soon as I have all reports together, I will hopefully know the topic of my master exam and hand out my exam pass to Prof. Baxa.

Unfortunately, I couldn’t meet with HGFei before his 2 week holiday, so I will look after taking some other first steps within August: Meet with Thomas to get an idea if Matching Pursuit would be interesting for me, and get my exam pass filled out and signed by Prof. Kowol. Also, I will have some looks at introductions to Signal Analysis and get myself familiar with Matlab/Octave again.

This way, I want to have the topic for my thesis fixed until the mid of September.