Mathematics is about theorems, science is about experiments. But theorems are expressed rigorously in formal logic...what about experiments?
The "old fashioned" way would be to write up a lab report and carry out the experiment! However, nowadays, there are some programs to simulate experiments.
For example, the KDE Education Project has a few programs for physics, astronomy, and chemistry. Sadly, no biology (although I wouldn't know what that would look like...).
Additionally, if one is writing notes on history, there is a beautiful globe program one could use...
At any rate, for classical physics, this is perhaps the ideal set up. It allows the reader to play with the experiment, which is the entire idea of an experiment(!), and if so possessed one could set it up in real life.
Plus this is free, a small perk.
There is the Step program which is useful for classical mechanics.
Better, the physical systems being studied can be represented as a program.
And when you get to numerical analysis, you can perform a "How accurate was this?" series of exercises ;)
It is multiplatform, so anyone on Windows, Mac OS X, or *nix can use the KDE Education suite. It may be worth while to consider :)
However, I wonder if there is not a better program out there? The qt framework is always a wee bit heavy duty.
It would be nice if someone invented a scripting language that produced flash videos, or something along those lines...since qt runs slow on my 733MHz Pentium 3 processor :'(
I have not thought about writing up chemistry notes, although I feel if I write biology notes then it would become necessary to study chemistry.
Personally, chemistry seems to be a sibling to physics, it just is concerned with different scales. So experiment is very important in chemistry, and it is just as repeatable as in physics.
The Kalzium suite simulates chemistry to a degree. Everything is always "to a degree"!
I am unaware of any similar such program for biology...but there are few experiments which are reproducible in biology!
Perhaps something like "virtual fruit flies" or "virtual peas" would be nice to study genetics, but I think it would be best to do it the "old fashioned way" (i.e., actually carry out the experiment!).
Take Home Message
If you are a mathematician writing notes on science, and are unable to perform the experiments: write a program.