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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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Is it going to be refereed? –  Will Jagy Feb 23 '12 at 0:15
    
@WillJagy I'm a total amateur on this. Not yet. This is a very recent project, so I don't really know where to publish it in. I've been advised to publish it a the College Research Journal or some name of the sort. I already have the main proofs done so maybe you can take a peek if you want. –  Pedro Tamaroff Feb 23 '12 at 0:18
    
I think Peter is talking about College Math Journal published by MAA. –  user21436 Feb 23 '12 at 0:43
    
@KannappanSampath Ha! You were away most of the day. –  Pedro Tamaroff Feb 23 '12 at 0:46
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Make sure that it demonstrates familiarity with the state of the art on this topic and contains appropriate references relating it to work that has come before. If a technique you use originates with Smith, give a reference to Smith's paper. If you're claiming that you've found the solution to something that was previously an open problem, give a reference to a fairly recent paper in which the problem is discussed and is indeed described as open. Make sure that your references are primarily to papers (not textbooks, etc.) and that they are primarily to recent papers, not old ones. –  Ben Crowell Feb 23 '12 at 1:18
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2 Answers 2

up vote 1 down vote accepted

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.

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

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