Months ago on this site, I asked about how to learn word problems well. Some kind-hearted people replied, but I think I was asking the wrong question.
Instead, "How do I learn to derive a mathematical model for real-world phenomena I observe?"
Some examples: - If I'm studying temperature and volume of gases, how would I come up with Boyle's law on my own? How did he know he was dealing with linear, rather than exponential growth? How would I know when to introduce a constant?
- Let's say I'm evaluating search engines based on my own success with them. In my data collection, should I set the trials up to allow only a simple success or failure, or allow a more subjective 5-point scale? Once collected, Should I use linear algebra or statistics to model?
Even when I am pretty sure what branch of math to use for my inquiry (like probability for a card game, or trig for a problem involving cyclical features), I usually don't know where to begin.
I've always received A's in math through college (on a comp. sci. track): discrete math, linear algebra, calc 1&2, prob/stats. I also love learning on my own and have worked through most of the Schaum's outline on abstract algebra.
Yet it's frustrating to know a lot of theory, but not know how to apply it to problems of interest to me.
I'm happy to learn from books if you know of any good ones, or websites, or any other suggestions you have found to work for yourself.