>>11453650The guide you posted is garbage. Most of the books are redundant and aren't even necessary for something like Apostol or Spivak.
Yes, at some point you do have to "reinvent the wheel", that's what most higher level mathematics is all about. However, if this is your first time trying to learn a topic like calculus then doing pic related will just make you burn out, because learning things like proofs or set theory are boring without any motivation behind it. Like the other anon said, what is your goal with all this knowledge?
The strategy, if you actually want to become sophisticated in mathematics, is to go through computational calculus first to get an idea. The point is to develop mathematical maturity by going through computations and getting some motivation to actually dive deeper into what interests you. Mathematical maturity is gained not by forcibly reading logic and set theory, but by doing some surface level math like differential equations or linear algebra, and then appreciating why these fields and these computations are so useful and important to learn.
The second step, when you reached that level of maturity, you can now find the motivation to learn whats under the hood. As for what do you need to read, literally all of the following is what is needed:
1) Propositional and Predicate Logic
2) Proofs
3) Set Theory
Thats it. Literally just read the first three books on the list and you're set to learn anything in advanced mathematics. By studying more rigorous topics like abstract algebra, complex analysis, or topology you will gain appreciation for certain areas in mathematics.
Reading other books too will give you some appreciation for math as well, like maybe a book on the history of math, or a book on philosophy of math. Remember that all of this takes time anon. You cannot rush these things. You have to get a sense of why you are doing this. Don't focus on a tree without realizing you're in a forest. Best of luck.
