I am writing a statement of purpose right now for US graduate schools in mathematics, and am I bit bogged down on figuring out the approximate ratio of my background versus my actual research goals. I currently have three paragrahs of background, mainly involving seminars and projects, and a discussion of the non-traditionality of my situation, and one of my actual research goals, and I am trying to determine if this is what is desired? The only source of examples I could find are here, and I am not sure if these are actually good examples of what is desired.

Edit: I keep using the wrong word since statement of purpose and Personal statement means different things to different departments (for example, Northwestern seems to want only one essay, which they call a personal statement)

  • When I was applying to schools, a few schools required something called a "personal statement" which was mainly "orgin of intrest" type fluff [sic] which I did not take writing seriously and I doubt committees took seriously either. All schools required a statement of purpose (which I think everyone takes seriously). The purpose of a statement of a purpose is to summarize your relevant experience with regards to research, identify the goals of your research and hopefully potential advisors/research groups, and not very much else. Fluff is (in my opinion) inappropriate. – PVAL Nov 3 '15 at 20:34
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    Northwestern seems to want only one essay, which they call a personal statement) — Don't listen to them. It's a research statement. – JeffE Nov 4 '15 at 1:56
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    One thing you want to guard against is coming across as too "precious" with your prior research experiences. As in "I did an REU project in [some obscure corner of graph theory], and I look forward to doing my PhD thesis in the same area since I'm basically an expert in it already." That's exaggerated, but you get the point. – user37208 Apr 6 '16 at 4:24

When I review graduate applications, the statement serves three purposes:

  1. If you are not a native English speaker, it may tell me something about your English proficiency. However, it cannot be relied upon too heavily since you may have gotten at least editorial help from a friend or even a professional.

  2. More importantly, it is an opportunity to demonstrate that you know something about a research area that interests you. This is more important for PhD applications than for MS applications, obviously. If you have already done some research, hopefully your recommendation letters speak about that. Your statement can sometimes be useful in showing that you keep up with some research area even though you haven't yet contributed to it.

  3. Finally, your statement can address issues in your application, like a period of low grades related to something in your personal life, a gap in your schooling/employment, etc.

There is in my opinion no correct ratio of personal versus research components; it depends on the individual.

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