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## Learning the "language" of math?

I just got a new book: "Mathematics for Physics and Physicists" by Walter Appel.
But, all the stuff in there is like another language to me almost. The thing is, that it actually seems quite basic and not too hard to understand (after I spend about an hour or so looking up notation and terms they use).

It starts off just going over the foundation of the integral, starting with Riemann sums and all that, but everything is done with set theory, and topological spaces, normed vector spaces, and a lot of symbols I'd never seen before.

To be honest, I'm not discouraged I think it would be awesome if I could learn this stuff, but it just begs the question.. why have I not been taught that stuff in school? I've already made it through Calculus 3 and differential equations but have never seen any of this. You'd think that it would be taught. What I'm covering now in the book is taught in Pre-Cal, but the way it's done here makes my Calculus 3 class look like 4th grade math.
Then on top of that, this book is supposed to be for physics students entering graduate school (which isn't too far off for me) and yet the book just starts using all of those math tools like if we should already know it.
The book was originally in French though, so perhaps it isn't catered to how dumbed down the schooling is over here in the US.

So I'm wondering, how did the rest of you learn those things? Right now I'm just looking each one up case by case on wikipedia.. I'm doing ok so far, but it would be nice if there was just a single source I could go to and read all about it and then tackle the book without having so many questions. Any ideas?

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 Take a nice introductory course to real analysis/read the textbook for one. You'll be swimming in norms and metrics and topologies.

Also,

 why have I not been taught that stuff in school?
Because you've only taken Calc 1-3 and Diff Eq. It's best to understand the most concrete examples before you generalize them.

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