Currently it's a first generation and if past events have taught me anything then it's best to wait for at least the second generation.
On the website it says that if I can't access the website form within the university network that I can ring them and get the discount. Also are you sure the Warranty is for 3 years for education students?
Ok - I wasn't sure if you'd get the full discount or not that way - but cool if they'll give it to you.
Regarding the three year warranty, yes I'm 100 per cent sure. It's not the university that provides the extended warranty because they (in the UK) do not supply the item, you have to go through the Apple Store (for the larger discount - they give a discount in store, but it's not as big, and without the longer warranty I think).
I'm currently using a macbook without apple care that was bought with an educational discount.
I don't have telephone support because I don't have apple care, but I still have a three year warranty - and I've confirmed this by entering my serial number on the Apple support page on their website - it shows just under two years of warranty left but no telephone support.
BTW - not sure how much research literature you'll have to read as a dentist (as in journal articles) - but you might want to consider investing in a piece of software called Papers - it's also on the iPad which is my sole reason for buying one.