Creative Study Techniques for Math Theorems and Definitions

[DivisionByZro]

I'm a math major with lots of theorems/definitions to know by heart. I regularly use flash cards so I can study while I walk and wait. Basically, I quiz myself on if I can fully remember and perfectly state the definition/theorem. I have used summary sheets in the past, but find that they take too much time to write out nicely (By summary sheet I mean all the definitions/theorems and maybe relevant examples condensed on one side of a 8x11" sheet).

Also, it should be noted that lots of practice time (i.e. actually doing math) is assumed. I can't learn it by simply reading it, so I do put in my time.

My questions is: what types of technique do you use to remember these types of things? I always like hearing about the creative ways people use to study.

 

[flyingpig]

If you are memorizing in Math, then you are not doing it right...

 

[Number Nine]

For theorems? Never. To know a theorem is not just to know how it was proved, but to understand why it's true, in which case there's no memorization issue at all since you just explain it rather than recall it. Part of becoming stronger at mathematics is becoming comfortable enough with the subject that a theorem isn't just a sequence of steps that you recite to reach a conclusion, but an actual explanation that reveals something about the underlying phenomenon ("Oh! So that's why every n > 2 has a prime factor...").

I do occasionally use flash cards, though mostly when I've been slacking off and need to quickly memorize some facts/definitions for an exam (In which case I usually forget them as soon as the exam is over, so I try to avoid it).

 

[DivisionByZro]

If you are memorizing in Math, then you are not doing it right...

Wrong. Most of math is knowing how it works. I know how the math I'm doing works. I can explain and prove the theorems in my books. But there are still things (Formal definitions) that are nice to have memorized, especially when one hasn't had enough practice with the subject yet. The feeling I get is that people seem to believe I'm "memorizing steps", when that's not the case. There are always time when memorizing a definition saves a lot of page-flipping or ambiguity in conversation. That is all.

Edit: I created this thread to get to know of different study techniques in math/physics. I did not create the thread to get lectured, and especially not to incite non-constructive feedback. So, please, if you have anything useful and pertinent to add, then please do so.

 

[DivisionByZro]

I do occasionally use flash cards, though mostly when I've been slacking off and need to quickly memorize some facts/definitions for an exam (In which case I usually forget them as soon as the exam is over, so I try to avoid it).

This is one of the points I'm trying to get across; sometimes it is quite handy to have something quickly memorized, especially for the next-day lecture.

 

[micromass]

If you are memorizing in Math, then you are not doing it right...

Very wrong. While memorization should certainly be minimized, there is still a certain amount of memorization that one should do. Sometimes proofs can be very hard and some steps need to be memorized.

For example, you absolutely need to memorize things like Taylor series, because you can't repeat the (complicated) proof every time you need it.

That said, instead of rote memorization, I prefer the memorization by practise. If you used a theorem 10 times already, then you will certainly remember it.



For the OP: I have devised a nice technique that helps me in memorization. It consists of giving a 1-line explanation of a certain term, theorem or proof. The thing is that most professors and doctors can give an intuitive explanation of things without going it detail. Practising such an intiutive explanation does help. (however, you still need to memorize the correct conditions).

So what I did is I made a list filled with 1-line explanations of things (and I revised the list occasionaly). And whenever I forgot what a concept was, I checked back to the list and I read the intuitive explanation. Then I would try to use this explanation to remember the full rigorous definition. It usually worked.

 

[micromass]

Also helpful:

- Drawing pictures! If I want to understand the definition of an integral then drawing a pictures of the Riemann-rectangles below a function is worth more than the actual definition! Just memorizing the pictures is in most cases enough!

- Making a mindmap: basically, you write some subjects on a paper and you connect them. This is a huge help.

- Make a dependency chart: write down what theorem depends of what theorem and represent this visually. This is a very good exercise. (and some professors like to ask this as an exam question)

 

[DivisionByZro]

Also helpful:

- Drawing pictures! If I want to understand the definition of an integral then drawing a pictures of the Riemann-rectangles below a function is worth more than the actual definition! Just memorizing the pictures is in most cases enough!

- Making a mindmap: basically, you write some subjects on a paper and you connect them. This is a huge help.

- Make a dependency chart: write down what theorem depends of what theorem and represent this visually. This is a very good exercise. (and some professors like to ask this as an exam question)

Thanks! I really hadn't thought of the dependency chart. I will also try the one-line summary of theorems/definitions, it seems like it could have a lot of potential. Thank you very much Micromass.