Re: Most efficient method of performing math research

On Sat, 21 Jul 2007 23:37:06 -0400, "Junior" <junior1@xxxxxxxxxxxxx>
wrote:

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?

Index cards work very well.

* easily reordered
* can be shuffled to test knowledge out of context
* save time by only writing a question, no answer.
* instead of an answer, just put a page number to refer to
* cards are easily editable (eraser) or just replace the card

The skill is to write just the right questions.

* ask definitions
* ask notation
* ask concepts
* ask statements of theorems
* ask formulas
* ask methods
* ask the motivation for concepts
* ask how a theorem, formula or method is used
* ask for comparisons
* ask true/false questions
* ask for examples and counterexamples
* ask simple, quick, representative exercises

Use the cards as flash cards.

Go through a pile quickly.

The ones you're sure about, put in the done pile.

If you're not sure, or if you don't know, or if it's taking too long,
put the card in the action pile.

For an entire course there might be as many as 500 cards.

If you've been studying all along, most you'll be sure of.

Let's say 30 cards cause trouble.

Back to the book for those.

A few hours later, check the 30 cards again.

100%?

Voila. You're ready to ace the final. By shuffling, you've proved to
yourself that the knowledge is "on-demand" and "random-access", hence
your confidence level is very high. You know in advance you're getting
an A.

Bottom line: a simple, low-tech, time-efficient solution.

quasi
.