Monday, September 27, 2004

"My crystal ball sees a lot of math in your future ..."

My recent experiences reading papers about mathematical models of biological systems can be summed up by something like this:

[start reading the section describing the model]
"Ok, I understand where that equation comes from ..."
read equation, do a bit of algebra in my head]
"Ok, I understand where that equation comes from ..."
read next equation, try to do it in my head, fail, scribble a bit on a piece of paper]
"Ok, got that bit"
read next equation, scribble a lot, finally get it]
"Uhm, ok, I guess"
read next equation, scribble a lot, don't even get close to it]
"Ok,I'll just take your word for that"
[read next equation, have zero clue what they're even talking about]
"I guess it's time to skip to the next section ..."

So, it's become pretty clear that I'm going to need to learn a bunch more math if I want to be in a position to understand and critically analyze existing models as well as build my own. The high-level list of math that I think I need is

- linear algebra [always thought this was boring, so never wanted to take it as an undergrad]
- statistics & probability [beyond "what is the probability of a die showing 4 after one throw ?" ;-)]
- differential equations, both ordinary and partial [I took one course on ordinary differential equations, but all the stuff I covered takes up just the first half of the introductory, undergrad course on differential equations offered here ...]
- multivariable calculus [learned some of this in college, so hopefully it shouldn't be too hard to relearn]
- nonlinear dynamics [that's the theory underlying all those pretty pictures of chaos and fractals that were so popular a few years ago]

In other words, it's a depressingly long list. If I wanted to take courses on all of these, I'd be here a really long time, so that's not really an option. If I'd known this is where I was going to end up, I'd have traded a couple of my "oh, why not ?" undergrad courses for more useful material ;-)
I suspect that I'll take a couple of courses and just have to learn the rest myself as I go along. Fun times ...


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