How to start over learning math

[Anonymous No.10720762]

I was very successful in my mathematics education in the sense of getting good grades, but I cannot help but feel as if I am missing extremely fundamental concepts in all areas of mathematics in spite of making modest headway into post-secondary mathematics (Calculus II). Where do I go back to learn mathematics from the ground up, and is it even remotely useful for someone who simply has a curiosity as opposed to any realistic use for it?

[Anonymous No.10720772]

If it brings you joy then you should absolutely learn more mathematics.

That said if you’re looking for a little more foundational material I recommend working through A Transition to Advanced Mathematics or similar introductory logic/proof book. A lot of early mathematics is shallow for brevities sake. After tackling that move into some introductory analysis, linear algebra, and discrete math. When you go back later to shore up your weaknesses much of what you feel is escaping you now will seem obvious in retrospect.

[Anonymous No.10720789]

>>10720772
My real passion is chemistry, and at a point I found myself unable to meaningfully understand some concepts, mostly quantum, with my current understanding of mathematics. The further I go, the more I realize that I've completely neglected to approach math as a foundation for everything else as opposed to a limited, esoteric endeavor. Maybe I can rediscover some of my early vigor

[Anonymous No.10722252]

>>10720762
Before I started calc 2 I grabbed Spivaks calc and worked through the whole thing. It skips most applications you'll find in your Uni textbooks outside of analysis. Work through it from the beginning for an hour or two a day at the minimum. Dont skip anything or keep to a strict "every other problem" situation. Think about the problems and work through them the best you can. Shuffling through notes and reading answers doesn't count in this time. Don't cheat yourself. Even if you work on only a single problem in that two hours you're getting better at it. When you 100% believe you can't solve it or understand look at the answer only, not the work. Try again and figure out where you went wrong. If you still get it wrong work through it line by line using the long answer and strive to remember what you're doing and why.
If you do that reliably every day you'll come out being highly confident in your work compare to baby university shit.

[Anonymous No.10722587]

>>10720762
>Where do I go back to learn mathematics from the ground up, and is it even remotely useful for someone who simply has a curiosity as opposed to any realistic use for it?