Think of it like reading. When you see a word you don't understand, do you look up its definition? How do you remember that definition?
I get the feeling most people approach math like they are reading a foreign language. They have to frequently look up translations instead of walking around with a working knowledge. The problem comes from not remembering translations after the initial look up.
If im struggling with the concept I do, If not than usually only if Im bored
Read theorem.
Apply example to understand how the theorem works.
Write proof based on insight from example.
If unable, do more examples.
Then write proof.
Once you do this enough, you gain an intuition on how to proceed. You'll know what techniques to apply in your proof and you can test lemmas and corollaries.
You can also find counter examples to theorems by changing the qualifiers of the theorem if you don't understand a particular aspect of it.
Where did you learn your proving methods? A course? A book?
>How do you remember that definition?
Force of will and associations, generally, but, most of all, frequent use. I suspect you are right - point taken, friend.
This sounds fantastic, and although I can imagine your meaning quite well, could you provide an example? Alternatively, could you provide a link to a video which shows this kind of methodological approach, or, even, a text recommendation?
I don't know of any books, but here's a hw problem that I had in number theory.
Theorem: if a,b are positive integers both not 0, then a = qb + r for some integer q and 0
I made a mistake. b > 0
*tips*
Where are you from user?
Literally the only real way to study math is doing a little bit of reading from the textbook and doing a shit ton of practice problems
OP if you're still in this thread just do practice problems a couple nights in advance before a test. If there is a practice test, take that and then practice where you struggle. If you are just trying to get into math, start with popmath. That will get you interested then work your way to more practical math.