Broadly speaking, I want to read books like [1]. It looks like they use quite a bit of advanced nondiscrete probability. Since I prefer books written in definition - theorem - proof format anyway, I figured I might as well get analysis out the way :)
I am in the same boat. I get the feeling that most Calculus books are just a compilation of tips and tricks. So I am suggesting you invest time into learning real analysis proper. Right now I am learning from [1]. It follows Rudin closely and as opposed to many other analysis books meant to "better explain" stuff, it goes deep into the trenches and actually tackles the subject.
I think time invested into studying real analysis pays off because then you can later study measure theory, functional analysis and more advanced probability to deal with curse of dimensionality and whatnot.
edit: I started studying the book linked above starting from chapter 4 since the first 3 chapters are familiar from discrete math. Then did chapter 5, skimmed chapters 6(little linear algebra), 7, 8 (most "transition to higher math" books contain this stuff) and am currently in chapter 9.
[1]http://www.cs.cornell.edu/jeh/book%20June%2014,%202017pdf.pd... (Foundations of Data Science by Bloom/Hopcroft/Kannan)