I don't know what you mean by "deep understanding"...? As for the practical applications, you'll need to enter the study of those practical topics to learn how the various tools are used.
Your question is akin to a child demanding to know the "deep meaning" of the alphabet, requiring to know all the ways that letters, etc, could possibly be used in a practical context, and all the history "justifying" their use throughout history, before consenting to learn his ABCs. The question is nearly unanswerable, and is not terribly relevant.
If you're wanting to know how scientists use this stuff, you might want to talk to some scientists. If you need to know how economists or engineers use this, then talk to them. If you want to learn the history of algebra, etc, then try studying some of the various books available on the topic. But math teachers generally just know the math, not the industry-specific stuff. We don't usually have the "real world" or "philosophical" information you seem to be wanting.