>>7799566 Math really isn't stressed too much in the US. The pace is intentionally kept slow starting in grade school so dumb kids don't fail because it makes dumb kids feel bad to be put in the math class for dumb kids, and god forbid anyone feels bad or gets a realistic assessment of their abilities. So at most US high schools, the highest math you can take is BC Calc, which is a year long course equivalent to Calc I and II. Then the universities want to keep you there for as long as they can so they can milk as much money as possible out of you, so you can't even take Real Analysis typically until you've done Calc I, II, III, and occasionally a basic Differential Equations class. Then, because most engineers don't have to take a math class beyond that to get their degrees, they have no reason to take Real Analysis. And because physicists maybe have to take a couple more applied math classes, they end up not taking Real Analysis. So the only people who really end up taking it are math majors, and it's typically in their junior year because that's when they've finally finished their prerequisites, assuming they started at Calc I.
Just as an example, I don't consider myself too smart but I'm a math major. Because I hated math for most of my life I didn't perform too well in high school and only even got into pre-calculus my junior year because I took a two week long summer course and got approval. And I only did that because my friends were in pre-calculus. I wanted to be in calculus with them so I worked a little bit harder and got an A-, so I got placed in AB Calc which is a year long course that covers Calc I material. I ended up loving the material, getting an A and passing the AP test so I could have skipped Calc I but my high school advisor told me that a college Calc class would be much harder. It wasn't and I wasted a semester repeating a class I already had credit for. But most people at my HS, which was a good HS, graduated at algebra trig or pre-calc.
>>7799553 German here. Went into engineering. Could only understand mathematics by rote, which is fucking tedious and makes learning a miserable experience, a bit like if you had programming lessons but only could compile your software once a week and then got a mark for it. Dropped out after a while.
So I don't think it helps in all cases. But then again, I'm literally brain damaged from depressive after-effects.
I disagree that real analysis should go before Calculus just the same as I would disagree if you said measure theory should go before your prob/stat 101 class.
Just stop being a crybaby, and if you're a math major, wait till take real analysis and have faith till then. It'll all make much sense.
If you're engineering, just wait till you see the applications in your field. It'll make you regain motivation once you see what you're learning it for, and also take real analysis (even if not required) because it'll provide that understanding you crave.
Study limits intensely until you develop a solid framework of knowledge on which to build calculus. How hard is it to understand the concept of rise/run, and then gradually increase the complexity of this understanding?
>>7799766 >>7799766 Some years ago I got a book called 'Introduction to Calculus and Analysis' with the idea that because I was going for pure mathematics, I should learn calculus the way a pure mathematician actually sees it.
>50 pages of the author non-rigorously constructing the set of the reals, from the naturals
>50 pages of definition of function and geometrical representation of funcitons
>50 pages of how to expand irrationals into infinite sums and then how to do this for functions
>50 pages semi-rigorously defining limits
I just wanted to learn how to fucking integrate for fucks sake. And believe me, there was more. You can pirate this book if you want for all I care. I got myself a typical 'Calculus I' book and fucked right off to applied town.
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