How Do You Prepare for Theorem Proofs in Math Exams?

[MathematicalPhysicist]

there are some exams (if not most of them) in maths that asks you to reproduce a theorem youv'e proved in class.
my question is: do you memorise the way of the proof, and try to write on paper by memory or you try to prove it again without looking at the notes ot textbook? (i mean when you are preparing for the exam).

obviously some kind of memorisation should be used here, do you think it's possible to do this by your own?

i don't think so, i think you need to memorise a lot of times the theorems (or everyday in the preparation time before the exam you should write the proof, i think this is the best way to remember a particular theorem by heart).

ofcourse it also helps to remember the rationale behind the proof.

 

[jbusc]

any time I've been asked to write proofs on an exam, it's because there is some key step that we learned that makes the proof trivial (no more than 10-15 lines). But then again I have only taken several proof-based courses, and nothing intensely proof oriented like real analysis or something like that.

 

[Kalimaa23]

Every math course I ever took had two exams : a theory part and a problems part.

The theory part was just that : theory. It was usually an oral exam, and the student is asked to describe a concept, formulate some properties or interesting links with other concepts...and then proof them. My way of doing this was thus :

- READ every bit of the proof. Make sure you understand every small step perfectly, quoting other proofs/lemma's as needed

- With the proof next to you, write it down. You'll be surprised how it changes your perspective compared to just reading it.

- Make a small diagram outlining the structure of the proof. Try to formulate the basic ideas in plain English "We want to show that, so we need to formulate it as, we can then use the properties proven in..."

You should now be able to reproduce the whole proof by yourself. If it doesn't work, repeat the steps above till it does. This allowed me to survive everything, including the 200+ proofs functional analysis course from hell in my last year undergraduate.