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