Writing is an Art!

Some useful tips for writing

* The problem is to communicate idea.
First, you must have something to say, you must organize what you want to say,
and you must arrange it in the order you want it said in, you must write it, and re-write it several times.
You must be willing to think hard about and work hard on mechanical details such as diction, notation, and punctuation.

* Say something
To have something to say is by far the most important ingredient of good exposition
-- so much so that if the idea is important enough, the work has a chance to be immortal even if it is confusingly misorganized and awkwardly expressed.

* Speak to someone and write for someone

* Organize First
To organize a subject means to decide what the main heading and subheadings are, what goes under each, and what are connections among them.
A diagram of the organization is a graph, very likely a tree, but almost certainly not a chain.

* Think about the alphabet
Invest an hour or two of thought in the alphabet: you'll find it saves headaches later.
A good consistent notation can be a tremendous help.
Good notation has a kind of alphabetical harmony and avoids dissonance.

* Write in spirals
According to spiral plan the chapters get written and re-written in the order 1, 2, 1, 2, 3, 1, 2, 3, 4, etc.

* Organize always
It goes like this. Begin with whatever you have chosen as your basic concept-love, say-- and do right by it: motivate it, define it, give example, and give counter examples.

* Write good English
Good English style implies correct grammar, correct choice of words, correct punctuation, and perhaps above all, common sense.
An author must have thorough mastery of the grammar and vocabulary of that language as well as of the vernacular.
The only way to learn it is to live with it for years.

* Honesty is the best policy
Clarity is what's wanted, not pedantry;
Understanding, not fuss.

* Down with the irrelevant and the trivial

* Do and do not repeat
One sense in which repetition is frequently regarded as a device of good teaching is that the oftener you say the same thing, in exactly the same words, or else
with slight differences each time, the more likely you are to drive point to home.
Another sense in which repetition is bad is summed up in the short and only partially inaccurate precept: never repeat a proof.

* Use words correctly
The general rule is to use the words of logic and mathematics correctly.
Replace "any" by "each" or "every", or recast the whole sentence.

* Use technical terms correctly
Avoid technical terms, and especially the creation of new ones, whenever possible.
Think hard about the new ones that you must create; consult Roget's thesaurus; and make them as appropriate as possible.
Use the old ones correctly and consistently but with a minimum of obtrusive pedantry.

* Resist symbols

* Use symbols correctly

* Content, aim and organization, plus the vitally important details of grammar, diction, and notation
- they are the essential ingredients of good lectures, as well good books

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* source:

How to write Mathematics
by P. R. Halmos