Anyone have a good suggestion of a mathematics textbook that would help me learn 'from the ground up so to speak' like how the article mentions, "He spoke of his mathematical work as the building of houses, contrasting it with that of mathematicians who make improvements on an inherited house or construct a piece of furniture."?
I am curious why a curriculum in the US includes four courses on calculus. Why isn't this just part of maybe three analysis courses for undergraduate studies?
Those are practical courses, meant to prep for linear algebra and differential equations — and various STEM tracks. As I recall, there were some proofs (eg, limits showing derivative rules; limits showing sums for integral rules).
We covered all the proofs in real analysis 1 (derivatives; sequences) and 2 (integrals; measure).
This textbook (work in progress but mostly complete) is an attempt to do exactly that: start at foundational math like group theory and topology and build up to higher and higher levels of math.
I worked through the first few chapters a while ago, and it's very good. My only issue is that sometimes he assumes knowledge of things that I didn't know about, but cursory googling was good enough for those situations.
