Since 1994 (when I set up my first web site) I've written an assortment of fragments on mathematics as web pages (using plaintext denotations which owe more to programming languages than to the squiggles and layout needed to transcribe what mathematicians with nimble fingers can scrawl onto a flat surface using chalk or a pen). As the mess has grown, so it has grown disorderly: I have little enough time to write, let alone perform coherent editorial work.

While I intend to continue adding to the existing chaotic mess, I eventually decided (in Spring 2000) that I need to set aside an area of greater order, in which to build up a (relatively) coherent account of the portions of mathematics which are indispensible for the physicist. I have even sketched out a plan (or sylabus) for this zone, though I will not claim to have stuck faithfully to it.

Given that I'm starting a fresh area, I've taken the opportunity to refine my earlier plaintext denotations and use a new version: naturally, I shall try to update earlier work to follow this, in so far as I find time to revisit them.

Physicists need to be able to discuss

- counting, arithmetic and permutations,
- vector and tensor spaces, using both real and complex scalars,
- differentiation and integration,
- smooth manifolds and their associated tensor algebra,
- information theory – entropy and Bayesian inference.

I intend to explain these and as much mathematical infrastructure as they require. There is much else of interest in mathematics, but that I shall discuss in a separate portion of my web-site.

Later, mayhap I'll expand the orderly zone to include category theory and other fun stuff: but the needs of familiar physics come first.

Written by Eddy.