puzzling out the proofs for concepts so utterly fundamental to math by myself that it’s like if Genesis 1:3 was And God said, 'Let there be integer,' and there was integer
puzzling out the proofs for concepts so utterly fundamental to math by myself that it’s like if Genesis 1:3 was And God said, 'Let there be integer,' and there was integer
I'd suggest doing introductory analysis prior to topology. Having a bit of concrete experience with the topology of R helps motivate a lot of the basic definitions and results.
Pretty sure that is covered under 'calculus' in English-speaking countries. Is that not so?
Only if it's the math major version of the course at elite institutions, at least in the US. Typical versions of calculus will probably at best discuss epsilon-delta definition of a limit. They won't discuss topics like connectedness or compactness, and when covering the Riemann integral they will use a version that only works for continuous (and can be extended to piecewise continuous) functions, but the definition can't answer some basic questions like "is this function Riemann integrable".
Huh? Wow, I guess the west is this barbarous. Seriously, those topics were covered in the first semester in my case, with the primary textbook also taking a topological approach (without introducing topology explicitly - just working with the metric notion of open sets, though).
Commercialised access to higher education has been a scourge upon your education, or seems.