Master's Thesis

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.