Does anyone else ever get troubled by that vast array of mathematical formulas one has to apparently memorize to be successful in mathematics?
Does anyone ever get troubled by the vast array of facts one has to apparently memorize to be successful in the world?
You mean "memorize" as opposed to "learn"? By "learn" I mean "use often enough to understand what situations require that formula and know how that formula is derived". I find that much easier than memorizing formulas and far more valuable. There's a lot more memorization involved in learning a language than in learning mathematics. How old were you when you learned your native language?
i think there are extremely few formulas one needs to memorize in mathematics. if one understands the concepts, the formulas usually derive themselves.
I have a very poor memory, and had always worried about being able to memorize the formulas. I found that very little actually needed to be memorized, since derivations are fairly simple. I agree with mathwonk in that way.
Of Course there are a few results that there needs to have a certain degree of memorization. For example, a result like the Wallis Product. It is not too difficult to follow the proof and understand the concepts, but there are just a few steps that seem like the person who originally did those steps was just toodling around with some maths and stumbled upon it. And its nice that he stumbled upon a nice looking form of the product, when there are at least 5 other equivalent expressions. In my case, for the Wallis Product I had to remember some steps in the proof, when usually the steps are really quite self-explanatory (at least in hindsight).
You make it sound as if you are cramming for an exam. Memorizing is different then learning. You LEARN how to speak English, you don't memorize it.
I have always said: Memorizing for the low levels Learning for the high levels Forgetting for the geniuses Obviously in math, once you have done enough questions relating to that formula, then it will become second nature and you won't even need to think twice to recall the formula. You should learn the really basic ones, since the others are just built upon the basic formulas. If you truly understand how a formula works, then you can easily derive it when you needed it, although it may cause some inconvenience. Say, the trig identities for example. Some of them looks like God's Wrath...but you can derive them from basic ones if you know what you are doing. Of course, if you take IB Mathematics Higher Level, your Data Booklet has everything you need for you :P