HN Academy

Not many people realize that the literature you mention is the field of "analysis of algorithms", which is a sub-field of (or, in practice, somewhat different from) computational complexity theory / theory of algorithms. Robert Sedgewick (CS professor at Princeton, and an early PhD student of Knuth) has a great book with Flajolet on Analysis of Algorithms [1], and in one of the lectures from his course [2] makes a distinction between the complexity analysis usually taught in basic undergraduate algorithms courses (he calls O-notation not the scientific method, in a certain context in the lecture) and AofA (which involves saying "Running time is ~aN^c" instead of saying "Running time is O(N^c)", and also actually measuring against real programs) — watch the video or read the slides; it's an interesting distinction.

And the Purdue website [3] is even better at giving a sense of the field.

[1]: https://aofa.cs.princeton.edu

[2]: https://aofa.cs.princeton.edu/online/slides/AA01-AofA.pdf / https://www.coursera.org/learn/analysis-of-algorithms/lectur...

[3]: https://aofa.cs.purdue.edu

Its both. Here are some links:

Video Lectures are here: https://www.coursera.org/learn/analysis-of-algorithms

and the book:

http://aofa.cs.princeton.edu/home/

Also a youtube - short history of algorithm analysis by Sedgewick is worth a watch:

https://www.youtube.com/watch?v=qap2MyBTSZk