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I have to write a research proposal for some (post doctoral) fellowship (for Mathematics/Mathematical Physics). The authority wants me to submit a short research proposal (preferably in two pages which includes bibliography). Can someone suggest what one should consider while writing such a proposal with a length restriction? I believe, I just have to highlight the main points of the the research and give a bibliography with it, but I may be wrong. The idea in my mind contains several steps. Should I give a time frame as well to finish each one? Please help.

Reconsidering once again, can someone tell me how to write good research proposals in areas like pure mathematics (I mean, like Non-commutative geometry, K-Homology etc. where, unlike some other subjects, number of papers, an average researcher can produce at the time of graduation, is less).

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I think this might be useful as complementary to the questions mentioned by Suresh. I heard for the first time about Heilmeier Catechism in one of the grant writing workshops. Since then I always think to Heilmeier questions while writing a proposal or paper.

I copy Heilmeier questions from DARPA website, however another version is available from Wikipedia.

  1. What are you trying to do? Articulate your objectives using absolutely no jargon. What is the problem? Why is it hard?
  2. How is it done today, and what are the limits of current practice?
  3. What's new in your approach and why do you think it will be successful?
  4. Who cares?
  5. If you're successful, what difference will it make? What impact will success have? How will it be measured?
  6. What are the risks and the payoffs?
  7. How much will it cost?
  8. How long will it take?
  9. What are the midterm and final "exams" to check for success? How will progress be measured?
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    You forgot "And why are you the right person to do this?" And with all due respect to Heilmeier, if you can answer all of those questions accurately (especially #8), it isn't really research. – JeffE May 15 '13 at 20:20
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    @JeffE: On the other hand, if you can't come up with partial answers to some of these questions, then you probably haven't formulated the problem well enough. . . . – aeismail May 15 '13 at 21:10
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I'm sure this depends wildly from area to area, and while I work in the theoretical side of CS, I claim no expertise on math research proposals. Having said that, there are some general guidelines.

Since you're applying for a fellowship, it's competitive. So you have to make a few points in your proposal:

  • [WHY] that the problem you're studying is interesting and worthwhile
  • [HOW] that your line of attack (briefly sketched) is plausible
  • [WHO] and that you have the right skills to execute this plan

and all of this in 2 pages !

Unless specifically asked for, I'd be surprised to see a timeline, especially with open-ended research. However, if the postdoc is for a fixed time, then the work being proposed should expect to produce some tangible results in that time frame if the plan works.

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  • "I'd be surprised to see a timeline": Depends very much on location. Here in Germany it's unusual not to have a very detailed breakdown—even timelines and work plans for individual tasks! – aeismail May 16 '13 at 14:14
  • We see that in DARPA proposals here too. But not in NSF proposals, and usually not in a postdoc research statement. – Suresh May 16 '13 at 18:49

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