Reference and theory are very useful, but context is how they are tied together in implementation.
Reference and theory are very useful, but context is how they are tied together in implementation.
Mathematics got a lot less interesting after I realized it amounted to a giant, informally-specified, mostly undocumented body of code designed to run on the human brain... from that perspective it's hard to see why one should prefer mathematics to a well-written software program that does the same thing.
So it's legacy code that runs on the oldest hardware that we have.. Plenty of people are interested in updating this code so that it runs on more modern platforms. Actually, this is my favorite way to drill into a piece of mathematics: port it to python.
Fortunately, nowadays, there is so much learning material that you have the opportunity to choose the one that suits you.
For example, I know that I cannot apply a theory upon reality. I have to start with examples and build my own vision by abstracting from a lot of examples. So I choose my learning material accordingly.
My current interest, at the moment, is monad. Believe me, there is a lot of abstract articles about that. But my entry point was a tutorial about implementing some stuff in Javascript, that happened to be functors, monads, etc.
Believe it or not, but I used that knowledge the week after in one of my Java projects. And my colleagues considered it was "a nice trick" (which is true!).
In one word, the learning process must be fluid. Don't try to force anything. If the book medium does not suit you, don't blame the book. Or yourself. Try to find another resource and keep learning.
This problem goes way beyond math and programming and into physics and general engineering. There are a surprising number of engineers who can manipulate the linear algebra tools but can't actually engineer structures or figure out linear circuits. EE filter design is another good example.
If you look at higher ed vocational training as kind of a prep-school or maybe a qualification filter for an apprenticeship it makes more sense. Once you figure out linear algebra you're qualified to apprentice to someone to teach you how to actually use it.