@abg, you just flushes away my airs for you, how can you say that Energy 'becomes' discrete? That's proven to be false and you know that. Energy's always been discrete in every way, unfortunately we're unable to measure it's discrete states at "normal" temperatures, therefore we treat energy as a continuous function. I think it's called Hund's rule, incredibly boring subject. I wish some people were not allowed to teach or to become professors.
Near the zero-point (approximately zero Kelvin and approximately one possible state [thus entropy equals approximately 1]) the effect of discretized states is easier observed, because the amount of possible states is largely reduced (according to the Boltzmann-distribution). Furthermore, I think that zero point energy and the absolute zero actually refer to the same point on a temperature scale, but please correct me if I'm wrong.
Apart from the fact that this point may or may not exist [I think it doesn't], we're unable to observe this possibly lowest state probable. But let's not start that discussion in here.
@D33 What do you want to put in your paper? And how long {do you want it}/{does it need} to be? Giving a short overview will be totally different from a discussion about specific topics. Hmm, ninth grade maths, that's going to be a though shot. It's been a while (7 years) since I was that age, you did got integrals, right?
BTW: I'm studying chemical engineering, and as well as you I read some books about QM, but I did some subjects about it as well. So in that case abg might be a better source.