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Any book to study mathematics from first principles? Most materials are centered around college curriculums and I wonder if there is anything unconventional that is more insightful.
To be a bit more specific. I know the very basics of calculus, probability theory, complex numbers, sets. I don’t know these topics in any depth though. My understanding is very shallow so I’m interested in learning more about whatever’s most fundamental to other topics.
I think my mistake studying them in high school and the first year of uni was skipping over the proofs because I didn’t have the patience to follow through. So I can apply rules but I don’t have a solid understanding of why these rules exist. That’s what I’m most interested in.
Another thing that really confused me early on was arbitrary differences in notations. Eg Leibnitz versus Newton notation. So I’m interested in resources that don’t take notation for granted but actually explain the historical context and show how both represent the same idea.
