I am no math genius, but over time I think I have picked up some approaches that generally work to help improve problem solving, and in particular, applying math to problem solving. I wasn't entirely sure if you were talking about focusing on a particular area. My answer is general. I hope it is useful.
Practice
In the end it comes down to practice. But how one practice's can make a big difference.
When you solve a problem you are working on, congratulations ... but you are not done with it. Look at it in other ways.
Change Constraints
One way I try to practice is by blowing things up to extremes. What if this was zero, what if that blew up to infinity, what if this was an infinite sequence. Things like that.
Here is a smattering of substitutions that I sometimes think of. This is totally random. You might imagine starting each of these bullets with the phrase "What if ...", followed by, "... how would that affect the problem".
- non-linear instead of linear
- stochastic versus not
- n dimensional instead of m dimensional
- statistical approach versus closed form
- not differentiable instead of differentiable
and so on.
Invent Your Own Problems
The "technique" I described above leads into this idea well. Invent a different problem by changing an existing one.
Teach
Teach things to others. Many argue that is the best way to learn something.
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