The reviewers of this paper, about a new method of dynamical tracer reconstruction ("PC proxy"), were interested in knowing more about the algorithm: how to determine the parameters and what makes it better than previous methods. In order to better understand it (only three years after the fact) I'm in the process of compiling a bunch of mathematics related to tracer transport, particularly in relation to how it's used in the paper. A lot of it I derived a long time ago, but whenever I want to work on this stuff the notebook where I did the last derivation usually isn't available so I end up re-deriving it. Now all I have to do is not lose the file--I've already misplaced an older collection of mathematical derivations. If anybody's seen it, maybe send me an e-mail.
Anyways, I've uploaded it to my homepage. It's still a work in progress so I will continue to add to and correct it. I should probably upload it to Github or some other code repository for better version control. I'm still waiting for a good science-based website for this type of thing. Maybe if I had the resources I might try starting something like this myself.
Another thing that strikes me is how time-consuming doing up these types of derivation in Latex is. Some software specifically for writing up and performing derivations could be really useful. And by this I don't mean symbolic computation packages like Maple or Maxima. I've always found these a whole lot less powerful and useful than one first imagines. Partly it's just the sheer volume of methods (the Maxima documentation is over 1000 pages long!) but also: all they seem to consist of is a whole bunch of built-in functions for manipulating equations one way or another. Not unlike a library for any standard procedural programming language, except instead of operating on variables, they're operating on what appears to the user to be mathematical expressions (but are actually structured variables in a programming language!)
What I'm talking about is something much simpler whose only purpose would be to write up equations in a pretty format as well as insert short sections of text and cross reference previous equations. A handful of shortcuts for Latex might fit the bill. One idea would be to just take simple ASCII math and in real time turn this into pretty equations, with macros for symbols that have no ASCII representation. The ultimate of course would be full WYSIWYG, maybe a bit like MathCAD, but without any actual math. I might try coding up something in lexx/yacc someday.
I'm also working on mathematical computations relating to multi-class classification and optimal adaptive Gaussian filtering.
Update: I've now posted this project on github. There is also an updated version of the compiled pdf on my homepage.