Books for understanding the essence of mathematical disciplines?

Question

Books

There are small problems with understanding applied mathematics.
I often solve problems in various sections (terver, linal, matan), but it all comes down to googling and the subsequent search for a suitable algorithm in order to simply take and, roughly speaking, substituting everything into the formula, get the answer.
And I know it's wrong to do that.
Are there any books that explain the meaning of the direct operations performed during the calculation in tasks? For example, giving a basic idea of ​​what the normal distribution is and where it came from; why the Jacobian is needed; what is the rank of matrices and so on for? By analogy with the visual mathematical statistics of Lagutin and 3Blue1Brown , it is important that the book gives a visual representation of, it is possible with informal definitions.
If someone has similar books in mind, I will be glad to advice. It is also possible in English. Thank you!

Answer 1

"What is mathematics?" Richard Courant and Robbins, Herbert

Answer 2

To understand - you need to start not from terms, but from phenomena and processes.
1. First, work out the whole process step by step as you would to solve the problem (practice sorting the numbers in the array).
2. Then, you will already clearly understand: what exactly you need to find at each step.
3. And after you understand what to look for, you will already look for the name of what you want to find and the description of this step, and there Wikipedia is not far away.
There are always many solutions to one problem, and only one of them is the most optimal and shortest (God's algorithm).
To find it, you need (based on item 3) to look through all the available alternative solution methods regarding the one that is the first suitable for solving your problem and then try to optimize it as much as possible with a constant check of the optimization result.

Answer 3

Fichtengolts course of mathematical analysis to help you.

Answer 4

There is no "why". It was just invented and then used. In order to understand, they say, why and from where - you need to open the proofs of the corresponding theorems. That's all.