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To me the polar coordinate trick show why maths are hard for me. When I've seen this integral for the first time, I was indeed clueless. But then there's this
by wiz21c 10y ago
To me the polar coordinate trick show why maths are hard for me.
When I've seen this integral for the first time, I was indeed clueless. But then there's this trick. The problem is that, when I look at the integral, with the math I know when I encounter it for the first time, it's very hard to infer that the trick is possible by just looking at the integral.
But maybe I don't know enough math to have the "bag of tricks" ready in my mind.
- jgrahamc 10y agoI did quite a lot of mathematics and your last line is correct. There are lots of hard concepts in maths that you end up getting your head around but then you end up with a toolbox of things to work with.
- k__ 10y agoThis often eluded me in university. I had the feeling before uni, these "tools" were shortcuts for a bit more complicated processes. But the magnitude of "complicated" got risen rather high in uni. In highschool I could simply cobble together the solution while working on it at an exam, but this "cobbling" often would take a few days for higher math. Math went from a "get rules"-subject to a "memorize all the shortcuts"-subject So university math was suddendly the same as highschool history, which I hated, and less like highschool math, which I loved.
- pif 10y ago> Math went from a "get rules"-subject to a "memorize all the shortcuts"-subject I'm sincerely sorry for you, you clearly had no luck in the choice of uni/prof. It must have been painful.
- k__ 10y agoIt was. It's a miracle that I got through it somehow. Calculus was especially hard. Linear Algebra was rather nice.
- therein 10y agoIt really sounds like you had a not-so-great teacher for your math courses at the university. What makes me think this way is I shared the exact same sentiment for math that you did in high school. I hated memorization and things took a turn for the better the moment that teachers stopped giving formulas already derived through calculus and started using calculus in front of me to get to the final usable form of the formula.
- vostok 10y agoI think it's pretty clear once you know that there's an answer. This kind of metagame is pretty useful on contests. You have something that looks like e^(-x^2) and you know that you need to multiply it by x to get something with an elementary anti-derivative. Other useful tricks are differentiating under the integral sign, building a sequence of integrals (I_n), solving in complex numbers, writing some sort of equation with the value of the integral, and so on.