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Thread: Going to College -- Or Not.

  1. #21
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    Quote Originally Posted by DaveJF View Post
    Engineering Degree here (not EE), ended up developing software b/c that's where the jobs were at the time.. Told my boys to get a degree if that's the best path to what you like doing, but I won't be paying for it. One served in the Corps and is now a few months short of a Journeyman Electrician License, other is crew lead for for a window replacement company & both are "ahead" of most of their (mid-20's) peers (and might or might not stay that way), but who the fuck cares if they provide for their families and don't loath their jobs?
    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.

  2. #22
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    Quote Originally Posted by Shiva Kaul View Post
    You don’t need prerequisites or a large textbook. What you need to know about single-variable calculus fits in 12 pages. Actually 11. Education doesn’t have to be a long, slow distance event.
    This is not going to be useful for someone who is not an autistic savant or has never touched calculus or more rigorous math before.

  3. #23
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  4. #24
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    Quote Originally Posted by Shiva Kaul View Post
    Bernstein explains differentiating a constant:

    This makes sense because it mimics a definition on the immediately previous page. Calculus Made Easy devotes a whole chapter to this sentence, and it's hardly the most verbose calculus text. Big textbooks can be useful, but they are counterproductive for many.
    Honest questions: Do you think kids in high school can be sufficiently initiated into “functional” thinking to digest Bernstein? And, would this be a sound approach to the AP calc exams?

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    Quote Originally Posted by asm44 View Post
    This is not going to be useful for someone who is not an autistic savant or has never touched calculus or more rigorous math before.
    I actually think a lot of students would respond better to 12 pages of very intense effort than to 400 illustrated pages following 2 semesters of prerequisites. Especially when a teacher is involved. The analogy to strength training is not idle.

  6. #26
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    Quote Originally Posted by VNV View Post
    Honest questions: Do you think kids in high school can be sufficiently initiated into “functional” thinking to digest Bernstein? And, would this be a sound approach to the AP calc exams?
    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.

  7. #27
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    Quote Originally Posted by asm44 View Post
    This is not going to be useful for someone who is not an autistic savant or has never touched calculus or more rigorous math before.
    Note that Bernstein’s title is “Calculus for Mathematicians”. Did he mean future or current Mathematicians?

  8. #28
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    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.

  9. #29
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    Quote Originally Posted by Shiva Kaul View Post
    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.

  10. #30
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    Quote Originally Posted by Shiva Kaul View Post
    I actually think a lot of students would respond better to 12 pages of very intense effort than to 400 illustrated pages following 2 semesters of prerequisites. Especially when a teacher is involved. The analogy to strength training is not idle.
    I think you are right.
    Shiva, you are an autistic savant and that is why we love you.
    How do we define what it means to have "learned" calculus?

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