This is a little bit more up my street than the maths one I just tried to answer! The stuff of nightmares was that...!
We're actually having a similar sort of debate in the UK at the moment about what 'Britishness" is so I'll draw on that in my answer.
Ok American Culture = misunderstandings and disagreement.
* America is now a mix of lots of different ethnic groups - how might Hispanics, African Americans, Dutch, Native Americans and other settlers define 'American Culture"? There would be differences in their definition thus possible misunderstandings and disagreements. Are they any you could interview for your paper?!! (Now there's a thought!)
* America is a mix of different religions. Does Christianity define American culture when there are so many other faiths in the country?
*Is American Culture defined by music?
*Is American Culture defined by Americans or the perception of Non-Americans such as myself? For example I see Americans as alot more outgoing, self confident and positive than people in the UK. In the UK people tend to be a little more self deprecating and to be a little too modest. I am more like what I perceive to be the American personality - cheerful, friendlyt, self confident and opinionated! Am I accurate in my perception of your cultural personality or am I inaccurate?
*America has quite a short history as a country in many ways, Thus whose culture is the 'real' culture? That begun in the 1700s or that which preceded with the Native Indians/Indigenous population. Or are they one and the same? What do people think? (Again you could ask people here)
I suppose American Culture causes so much misunderstanding and disagreement because it is so difficult to define! How do we define it? By ethnic group? By music? By religious faith? By history? By the personality of the people? Whose perception - Americans or Non Americans? And does Culture really matter anyway?
Most countries have a very defined cultural identity, even Scandinavia, the Mediterranean and Central Europe like Austria and Germany have a strong sense of identity. How do these countries manage to retain a strong sense of self/cultural identity despite immigration, while the likes of the US, the UK and Australia have a less well defined cultural identity as a result of immigration and ethnic integration? Out of the three the UK seems to have the strongest identity, that could be because of the empire? I'm not entirely sure of the real reason.
Don't worry - there will be lots of books on the question of culture and it's definition in your local llibrary.
An interesting and very contemporary topic. I hope I've given you some ideas!! xxx