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What are good books for learning about math? Not textbooks, but books that provide insight into mathematical phenomena.
Yeah, well ...Not textbooks
I got you! You can recommend some introductory textbooks which would just build my base for mathmatical concepts and thinking in algebra, geometry, number theory, calculus. Also to mention I am in high school.So you can recommend accordingly.Thanks!Yeah, well ...
It's like wanting to read russian litterature without learning russian.
A bit off topic. But do you have a recommendation for multi-variable analysis? I took a class recently using Spivak: Calculus On Manifolds. It was a bit too dense for me, and I don't think I learned anything from that book. I was able to scrape a B- minus in the course ( I got lucky, since I studied a bit a bit of point set topology, so the initial chapter was review). However, after the Inverse function theorem, I was a bit lost.It is a good book, but not for me at this current time. I am reading Hubbard: Vector Calculus, Linear Algebra, and Differential Forms. Very readable for me, but was hoping for something with a bit more rigor, but less than Spivak. So that I may be able to master Spivak.
Thank you once again. I received my copy three days ago. It is very illuminating. I wish my course would have been based on this book, instead of Spivak. To me, Spivak appears to be a Tour De Force to get Stokes Theorem with the minimum amount of things needed.In the old days people liked Williamson Crowell and Trotter, and I liked the very rigorous Calc of several variables by Wendell Fleming. Lang's Analysis I is also good for many things. that was the title in about 1970, maybe has a new title now.
a used copy:
https://www.amazon.com/dp/0201041723/?tag=pfamazon01-20
the same book with a new title: Undergraduate analysis:
https://www.amazon.com/dp/0387948414/?tag=pfamazon01-20
In particular, I thought spivak's treatment of stokes theorem was useless, to me at least, in being very abstract and unenlightening. Lang's treatment for a rectangle on the other hand, at the end of his book, made it seem so obvious that I never worried about it again.
of course they are the same, just don't look it. I.e. on a rectangle, stokes theorem is just fubini (the spell checker wants this word to be "tubing") to reduce to the fundamental theorem of calculus in one variable. Then the more abstract version is just done by parametrizing a more abstract set by a map from a rectangle, and pulling the statement back to the rectangle. on a manifold one can arrange this setup by using a partition of unity, so just understanding it on a rectangle is the main idea.