Writing statement of purpose for admission to "scientific open days" at prospective graduate school

[nwa]

A university where I will be applying for graduate school has a two-weeks "open days" programme, where there will be several courses that present the research done by every research group in the math department; and several scheduled meetings with the faculty members and current PhD students.

For the (quite competitive) admission to this programme, a statement of purpose is required to explain the research interests and motivations of the candidate.

How would you go about writing it? What kind of information, qualification, and motivations may admission committees be looking for in a candidate for such a programme?

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If you happen to have some samples of statements of purpose for such occasions, I'd greatly appreciate a link.