ChapterZero

I am feeling strangely depressed(?) right now. It looks so good outside, the sun is out and the breeze is strong and cool, but here I am at the library trying to get into reading. I came here originally to get away from the temptation of my computer and the tv at home in order to study my graph theory and read up on real analysis, but here I am typing away. I don’t think I love math the way I used to; it always seems that instead of studying it, I go find something else to do. Because it is too challenging, and I can’t read math books about the math I find interesting: either I am lost inside of 5 minutes, or it takes me an hour to digest the material on 3 pages.

Anyhow, I checked back out a book on Maple, because lately I’ve found myself thinking of some nifty and simplistic mathematical experiments that I would like to try out, but I don’t know any fast and efficient way to implement them. I certainly am not going to write a C program to generate the data, and then a MetaPost/Postscript Perl display engine– that would take forever, I would lose interest in the interim, and I would never be able to use the code more than once, unless I spent a week in writing it in the first place.

After all this messing around with low-level graphical languages, MetaPost and PS, I want something at hand that I can use to quickly plot up and experiment with any ideas that come to my mind. Maple fits the bill perfectly, but I have to learn it, and lately I don’t seem too good at learning any large computer-based systems. I guess it will be worth it, though.

So far in my reading, I’ve heard mention of the Risch Algorithm– a method for finding the integral of any elementary function. It sounds cool, and when I looked it up on Google, I found a message in an email digest of the Maple User’s Group from a guy who says he uses it by hand to do all his integration. Certainly that sounds interesting in practice, because I would be able to forget all those annoying heuristics that my math profs taught us to use to get integrals, but on the other hand, I know that at least one description of the algorithm runs on more than 100 pages!

I’ve also found lots of interesting references to function approximation techniques: Chebyshev, Pade, ChebyshevPade, Theile, etc. The methods in themselves are no doubt interesting, but I wasn’t looking at the particulars ( and not only because finding concise but usable description of mathematical techniques online is nigh on impossible), I was more interested in the thought patterns involved in finding the most accurate numerical approximations and the most efficient technique for use in a particular case.

Possibly relevant posts:

• A Possible Future (6/3/2005)
• Axiom vs other CASes (12/18/2003)
• Relaxing (12/16/2003)