Remembering Maths

Rhino

Typically in math, I can pick up most concepts fairly quickly; either from a class setting or from the book. The problem I'm having is remembering the simple rules.

Even very simple rules I tend to forgot. I can do a quick refresher and then hammer out a 100 problems. But without the refresher or quick review I just can't remember how to solve them.

Anyone else have this problem?

An example. In the front of my text there is a quick review of simple arithmetic on fractions. Add, subtract, etc. Easy stuff right? For the life of me I couldn't remember the rules even though I've solved thousands of these problems in grade/highschool/college - even as recent as last week. I can't remember, I glace back at the summary and "ah, I remember now" and hammer them out.

If someone were to stop me on the street and say "hey, divide these two fractions" I'm sure I'd draw a blank. That's just an example; not just fractions; but rules in algebra, geometry, etc. Any "rule" I tend to quickly forgot even though I can easily understand most of them and even put a lot of practice into doing problems.

I love math; but seems like this handicap is killing me. I spend more time review/refreshing on basic rules then I do actucally solving the problems.

Hamster_style

So, I think part of this might be that you're not particularly specific with what you're trying to remember. I do a lot of math, and I use a variety of tricks to remember things, but it depends on what you're trying to do. Remembering tricks for, say, whether something is divisible by 3 is way different than remembering what makes a region simply connected or how to evaluate a contour integral in the complex plane.

What specifically are you trying to *do*?

I'll try with your very general OP. What I usually do is remember some basic things and derive a lot of stuff based on that, in conjunction with mnemonic devices. For the former, a good way to explain how I think about it is how I remember sine or cosine in terms of e^(ix) where i is sqrt(-1). I know that it's of the form:

cos x or sin x = e^(ix) +/- e(-ix) all over 2 OR 2i

but sometimes I mess up the signs and whether there is an i in the denominator. Usually I just remember this by remembering Euler's formula, which is

e^(ix) = cos x + i * sin x

which, remembering the evenness of cosine and oddness of sine, makes it obvious which equation works.

EDIT: Finally, if I've *completely* forgotten even the equation form for cos x or sin x, I can just derive it from Euler's theorem completely. Euler's theorem is one of those things that is basic, like, say, positive numbers are greater than zero.

While that may be a complicated example (I have no idea what level you're at), the thing to remember is that there's a lot of relations between different mathematical formulas and theorems, and a *huge* part of both remembering them and using them is realizing these relations. This is much much easier than remembering a bunch of theorems out of the blue that, without context, have no real meaning. People don't do that with words; why do they do it with math?

As to the second point, a good example is SOHCAHTOA (sow - ca - tow - a, short a's) for remembering how sines, cosines, etc work. IE: SOC = sine is opposite over hypotenuse; cosine = adjacent over hypotenuse; tangent = opposite over adjacent. You can remember a bunch of stuff making those or looking for ones that already exist - also, xyzzy for cross products!

Final bit: God, reading that bit "remembering the evenness of cosine and oddness of sine", makes me realize that it reads kind of like a textbook. Scary much?