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I'm trying to put together a mathematical article on how to obtain certain infinite series for some well known functions by a method of integrals (I like to call it "The Integral Method" - thank you), and I'm stuck on the structure of it. I have the following vague ideas.

  1. It should start by explaining what the article is about.
  2. It should have a part where it shows other ways to compute the infinite series (namely Taylor's method) and what are the similarities, differences, pros and cons of it vs. the method I'll use.
  3. It should introduce the basic notions of the tools to be used.
  4. The main body should be the proof of the series itself, with good guidance on the steps and explanations to make it good for a broad audience.
  5. It should give some ideas on how the method can be used for other functions, or give some ideas as to how the method could be generalized as Taylor's.
  6. A closing paragraph.

However it may seem I have a good idea, believe, I don't. I'm sincerely stuck and asking for help to any experienced publisher that could give me examples of articles to mimic or learn from.

Thanks in advance.

(I don't know how far this should go to math.SO so let me know. I haven't found any appropriate tags.)

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    @BenCrowell I should have stressed *simple sight*. Nevertheless, I invite you to give a look to it.2012-02-23

2 Answers 2

1

Go find yourself a copy of Steven Krantz's A Primer of Mathematical Writing (it can be had for less than 20 US dollars on Amazon).

... or Paul Halmos' How to write mathematics

... or try the set of notes titled Mathematical Writing by Donald Knuth et al which you can find floating around on the internet.

And if you like to learn by negative reinforcement, there's a video recording of Serre giving a lecture on precisely what to do if you want to write mathematics badly.

3

Terence Tao has posted some lucid remarks about writing on his blog at here.