Most efficient method of performing math research

I have an engineering background, but I would like to request advice on
which is the most efficient way of doing mathematical proofs or commence to
study a subject like wavelets.

In the past when I have studied a subject, I have done the usual read books,
write equations in a notebook, and so on. However, I do not find that
writing in a notebook and then reviewing my notes is not a very efficient
way to do math. There is no logical continuity; if I learn a new fact there
is no good way to add it to the original entries.

How do most people who are into mathematics do proofs and derive equations
while still keeping their notes in order? Is there a method that works best,
like writing in individual sheets so that the order of entries can be
modified and new pages inserted?

Any advice would be appreciated...anyone using tablet computers with pen
input? Which brand of computer?


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