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How can I read numbers and mathematical symbols comfortably, at a university level? [closed]

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User

( 3 months ago )


When I look at math, it's like my mind goes fuzzy. The only way to describe it is to relate to how when you read, you see the letters and words, but your brain picks up on the meaning?

When I see numbers, mathematical symbols and equations, I find understanding them incredibly difficult to. It's like trying to read Kanji (without knowing Japanese).

Something simple like 4+244+24 is easy, but as soon as I see 

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User

( 3 months ago )

Could it be that you're simply expecting too much? Mathematical formulas are designed to cram a lot of information into little space, but you still need to process all of that information, so you should expect your reading speed to drop dramatically each time you encounter a formula -- at least as measured centimeter by centimeter.

Furthermore (and I can only speak for myself here, but I think it is reasonably universal), there isn't really any spoken form of mathematics. We can read formulas aloud, but then the sounds we make represent symbols on paper -- in contrast to ordinary language, where the symbols on the paper represent sounds. If somebody speaks a formula to me, I have to reconstruct how it looks inside my head before I can begin to understand it. Formulas are a very visual language, with their meanings defined by how symbols appear side by side, or above and below each other, or surrounding each other. You should try to understand them by building some kind of visual model of the computation they describe, not by translating them into words.

I'm stressing this point because it sounds like you're panicking when you come across a formula because the little voice in your head that speaks aloud what you read goes silent. That's normal; it doesn't mean that you're missing some critical ability you're supposed to have. It just means that you need to treat the formula as a picture rather than words, because that is what it is. It's a picture that's sometimes made out of letters, but that's modern art for you -- you may need to approach it visually all the same.

And just as a picture is worth a thousand words, you should expect to spend as much time digesting each formula as it would ordinarily take you to read several paragraphs of ordinary text. It gets a bit quicker than that with practice, for some formulas, some of the time, but you shouldn't feel dissuaded because that doesn't happen instantaneously. Practice takes time.

Also: cheating is allowed. Very often, large parts of a formula are identical to large parts of a previous formula -- and the only thing that really matters is how it differs from the previous formula. In those cases it is expected that you'll just think to yourself, "oh, this thing is the same as that thing over there", without bothering to understand or remember exactly what "that thing" was in detail. You can just compare the relevant parts symbol for symbol without thinking.

In fact, this last point is part of the reason why formulas are designed to be compact and dense with information. It increases the chance that you can keep the entire formula in your visual short-term memory as you move your eyes from one formula to the next, and thereby make it easy to spot that some parts of them look alike, without even being conscious of the individual symbols. (Who knew all those inane "find 5 differences between these two drawings" problems you find in kids' magazines actually train a highly relevant mathematical skill? They do!)

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