If I had to repeat my youth, I would have taken up a good paying trade, like plumbing or similar. I mean, I am making good money with my made up job, probably better than most plumbers, but as a tradesman you really got a lot of freedom. Only the proles are truly free. I think your boys have made a great decision.
I will disagree with the economics books recommendations. If you are going to read one book on economics, it should be Keynes' General Theory.
Gary North’s thoughts on one’s job versus his calling:
Economics: Job vs. Calling | Mises Institute
A Job and a Calling Are Different. Don’t Get Them Confused in Your Life.
Bernstein's "text" is an extreme example. If they're starting from basic algebra like Subby, then they need to vaguely know what a set is, and the set-building notation {f(x) : x \in S}. But it may be preferable to just patch these holes than to reach for a massively padded textbook.
I would definitely not suggest it for AP calc. That's all about modeling word problems, memorizing integration and differentiation tricks, and working through algebra. But as many freshmen discover, acing this standardized exam is not the same thing as developing college-level rigor.
It's an inside joke. The title "___ for mathematicians" (or "for engineers") means short, self-contained, direct, and rigorous, i.e. lacking the frippery that others deal with.
I kinda got that. But it reminds me of how professors sometimes said “it’s important to revisit first principles” - but with far more elegance than the first time through. Which, assumes a certain level of competence - the vocabulary has been established, and the conversation is now in small society amongst near-peers.