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Memorizing math and physics "building blocks?"

  1. Jan 15, 2015 #1
    I know a lot of courses like linear algebra have a ton of "building blocks" that one must memorize. Yes, you can derive these things yourself, but this often takes to long.

    Does anyone here use any tools like SuperMemo to memorize math theorems or physics laws/equations/etc?

    Also, I just started taking a dynamics course and some formulas for the polar coordinate system are incredibly time consuming to derive (namely acceleration). Are things like this worth memorizing? Does anyone have advice? Thanks
     
  2. jcsd
  3. Jan 15, 2015 #2
    Usually the important things you end up remembering just because you use them often enough.
     
  4. Jan 16, 2015 #3
    This. No amount of flashcard websites will make up for just doing 100 problems with the required theorems.
     
  5. Jan 16, 2015 #4

    jtbell

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    Staff: Mentor

    Ask your professor whether he expects you to be able to remember complicated (but still important) formulas for an exam. My favorite example of these are the formulas for divergence, gradient and curl in spherical and cylindrical coordinates. I've always told students that they will have a reference sheet available for things like this (e.g. a copy of the table in the inside cover of their textbook).
     
  6. Jan 16, 2015 #5
    Linear algebra, in particular, is a subject where you don't have to memorize much by rote, if you are doing it right. In some sense, I have most of the subject "memorized" (I mean what's covered in an undergradate course). I know it by heart. But I understand it, I don't just remember the results without knowing why they are true. I can re-derive the theorems in a fraction of a second, visually in my mind. For example, I know that the determinant is a signed volume of a parallelopiped spanned by the column vectors, so if it is zero, then you get a degenerate parallelopiped, so that the vectors don't span the whole space. Sometimes, you can memorize results by rote as a crutch if you don't have time or inclination to try to understand them, but it's hard for it to stick that way, and your ability to apply it will be more rigid. If you need to use a result that is slightly different, but uses the same idea, if you have understanding, you can make that modification, but know it by rote only, then you're stuck.

    I think understanding is more important than memory, but I do use spaced repetition, which SuperMemo, I think, is based on. I just got a feel for how much review I needed and how to space in order to plant things in long term memory.

    Probably not if it's super complicated. But sometimes, the seemingly complicated is actually simple, if you look at it from just the right viewpoint. It takes experience to know how to do that, though. Completely aside from whether it's useful (it generally is, when successful, but the question is whether it's worth spending the time to figure out, which it may not be for really ugly formulas, and in any case, you can always come back to it later), I like to try to visualize even fairly complicated stuff, and sometimes that does the trick of making it simple (and memorable).
     
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