Writing Feedback / Student exchange; the introduction part of my essay? [5]

I have to write an essay to apply for a student exchange program. Do you think this introduction part is good enough? Could you please tell me what you think and how I can make it better? I may have some mistakes about meaning or grammar.

Probably you know that the universities that accept foreign students aim to create an international and cosmopolitan atmosphere. So have you ever thought why they purpose such a thing? Because they believe gathering different cultures together would supply the possibility of thinking in different ways and reaching success. I write with great interest in applying for the position of the student exchange program which would give me the chance to meet a fully new culture and make use of its advantages.

Thanks for paying attention!