Some of the assumed american and british spellings are a slight misconception. It's actually a difference between Cambridge and Oxford style. Oxford house style still spells words with '-ize' rather than '-ise', and also uses the serial comma. However, you will find that most people in the UK will think that only '-ise' is correct and that '-ize' is american. I've found that many book publishers in the UK still prefer to use '-ise' endings, surprisingly. But for most other american and british differences (color/colour, traveling/travelling, etc.) the british spellings are preferred.
Back to your original question, the spelling really depends on the person reading it and university protocol. I would hope most universities accept that you are an international student and write in american English. My tutors claim to not care if words are spelled british or american, so long as there is a consistency. This is a question you should definitely ask early in the term to make sure any essays won't be marked down because you wrote in american English.
