Want Math/CS books that teach both the how and the why of the subject.

Calculus was developed by Newton and Leibniz as a way to tackle problems in physics. Later Real analysis was developed which gave a strong and mathematically rigorous foundation to the theory of Calculus. During its infancy Calculus was all about the "how"; after real analysis the "why" was added.

I believe learning only one side of the subject doesn't open up the entire capacity of the subject to your mind. You need to learn both the how and the why.

Mathematicians often fight over pure vs applied. Due to that books are also written like that. The how books are aimed at "engineers" and the "why" books are abstract and seldom contain the "hows".

Example: Strang's Linear Algebra is all about "how". Axler's Linear Algebra Done Right is all about the abstract treatment of the subject.

I have only talked about math books above. I am not much aware about how CS books fair in this aspect.

I want to know about books in both CS and Mathematics that teach both the how and the why of the subject. It shows how to practice the material in real life problems and why the material is true by showing a rigorous theory behind it, if there is a theory. Otherwise it says that this is yet to be proven.

If you know no such comprehensive book on a topic, you may suggest some online course (if that is available) or a set of books that seperately teach the how and why and complement each other very well.