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This is a great point, and I think it shows why people don't study math in their spare time. It's the same reason why most people aren't body builders with 5% b
by dvt 8y ago
This is a great point, and I think it shows why people don't study math in their spare time. It's the same reason why most people aren't body builders with 5% body fat: it takes a tremendous amount of hard work.
Not only that, but the work isn't glamorous or particularly creative. In my teens, I always though I was "bad" at math -- I never did the homework, didn't do the supplementary exercises, had an "intuitive" understanding that wouldn't translate when exam time rolled around, and I consistently got C's and F's.
In college, I decided to take things more seriously and I remember in Calc I-III doing literally every single problem in the books. If I missed any problem, I would do it over and over again until I got it right. "Miraculously," I started getting A's in math classes.
- imranq 8y agoSadly Calc iii is not “real” math, just an applied version of what newton created 300 years ago. Real math starts at analysis and abstract algebra. It is extremely inefficient to learn this kind of math completely by yourself since there is a specific ‘math intuition’ that is hard to gain without a great teacher.
- K0SM0S 8y agoI'd guess Khan Academy was among the first to provide such teaching. Is it "self-taught", I don't know (I think it qualifies, though). It can be done.
- ghufran_syed 8y agoThat seems a little harsh as a reply to the previous comment - calc 3 is math, but sure, upper division or graduate math also requires the ability to prove things, which is why people who did will in calc-3 might not necessarily do well in more advanced courses until they learn the additional skills. But it's not like the ability to apply theorems and calculate accurately is orthogonal to the ability to do proofs - the attention to detail and ability to keep track of the steps is certainly similar, I would argue.
- BigFish12 8y agoYou dont need to be a graduate in math to prove things. Check out the IMO and tell me it isn't real math, and it's only highschool level.