Approach to mathematics (tips?)

[Daveyzombie]

I feel like my approach to mathematics is strange, sometimes I just think about memorizing something when I see something new. I feel like memorizing something is the fastest way to learn because once you memorize it the logic seems to reveal itself.

I'm trying to learn trigonometric identities now and I am having a difficult time solving them and provide proofs.

I have no problem memorizing the identities but solving them is quite difficult for me.

So I was wondering how you people here on PF approach new math concepts and how you might learn them. Maybe there is something I can try that I am not doing.

 

[symbolipoint]

Memorizing formulas and identities only gives you very limited understanding, too limited. Learn to draw good reference graphs and make diagrams. Fit your expressions to those, meaning label the parts and use this to either make derivations or conduct proofs.

 

[mfb]

You don't understand what you do if you just memorize various formulas. That approach might work in the early years of school, but it will fail quickly once you get to actual mathematics.

The only mathematics-parts I ever memorized actively were names of theorems and some details of them no one ever uses - for an exam.

 

[S.G. Janssens]

I think it is good to memorize the structure and the "idea" of certain longer proofs. Some proofs contain steps that do not follow naturally from those that precede them. When I prepare a talk, I aim to memorize enough to be able to fill in the gaps "on the go", but not much more than that. Mostly that works, sometimes it doesn't. In the latter case it's bad luck.

 

[Daveyzombie]

Thanks for all your input. I'll trying a new approach to learning something. I saw a video on youtube about the Feynman method and I've been trying that out too.