Good thing I saved a copy of this before publishing. WordPress lost 300 words of it when I hit “publish”.
The effort is not without its share of logistical concerns. The Wikiverse has different stylistic demands, different typesetting requirements, and by all accounts a foolish and barbaric editing culture. On top of that, numerical methods are entirely concerned with computation, which requires readers to do some programming. There is also the matter of keeping myself on track and writing the damn thing.
I intend to solve most of these problems indirectly (that is, avoid them) by writing the material here on WordPress. I can do formatting for different outlets at the end when my creative corticals are fried and only a cynical-critical husk remains of my soul. I intend to write everything as closely to pure LaTeX formatting as I can manage in blog format, and saving the copies on my hard drive(s) as .tex files.
For programming examples, I intend to use Sage because it is freely available and open-source. Almost anyone who can read a wikibook can install it and follow along. There is danger in this, because I’m a novice programmer and have only a passing familiarity with Sage’s numerical capabilities. By the end of the project, I have no doubt that neither of those things will be true, but it’s worth budgeting some time to cram in the beginning.
For algorithms, I want to follow IEEE style if such a thing indeed exists. But I haven’t found anything except LaTeX code.
I intend to follow basic writing guidelines and style with respect to prose as well as the style guide published by the American Mathematical Society. But I’m not content to write a well-formatted piece of shit. I want to write a good math book, which will automatically set it apart from most of the trash that constitutes mathematical literature. I don’t just want to present material, I want to transmit it. These ideas are in my head, and I am going to use every bit of psychology at my disposal to penetrate my readers’ idiot skulls and put it there, too. Because all pretense aside, we all have this in common: we are stupid and lazy, given any say in the matter. So I won’t give them any more responsibility than I have to.
I’ll adhere to the technical writing philosophies of the brilliant Head First editors at O’Reilly. But I have a couple of personal touches to add.
I like my technical ideas the way I like my filesystems: simple and deep. That means short sections, and subsections, and subsubsections. It also means a small subsubsection for each little idea that serves as the building block for a larger, more complex idea.
I believe the way to create quicker understanding is to have lots of easy exercises, especially if you can do them in your head (you can do more of them that way). Textbooks with 50-page chapters and four bone-crushing exercises do not teach new concepts. They merely exercise the mathematics a person has already learned. I’m not against difficult problems in the abstract, but they have their proper place in the learning process: after the easy ones. If you’re teaching that force equals mass times acceleration, the first couple of exercises should look like this:
- If a particle weighs 2 kg and is undergoing an acceleration of 3 m/s^2, what must be the net force on the particle?
- If a particle weighs 1 kg and is subjected to a net force of 2 N, what will the resulting acceleration be?
And so on, gradually introducing vector representations, negative signs, and so on. No introductory exercise should take more than 30 seconds of concentrated effort.
Illustrations. If I had my way, there would be no words without an accompanying diagram of some sort. There would be no algebraic proofs without graphical explanations*. You might say I’m a dreamer, but I’m not the only one. I won’t hit that mark, but I’ll aim for it.
I think I’ve mentioned the economic importance of including mnemonics in textbooks themselves. We live in a specialized society, and and information-based economy to boot. It falls to those specializing in the transmission of ideas to work extra hard to make sure those ideas are understood, practiced, mastered, and remembered- all as quickly as possible. Gone are the days when learning relied on the diligence and genius of the student; they died with the scarcity of information. Now that information is abundant and time is scarce, we must change the way we think about teaching. It’s simple supply and demand.
These additions aren’t idle speculation either. I’m prepared to defend my approach.
*Actually, it’d be interesting to try to generate such illustrations with a computer as you perform manipulations…Another time, though.