Does this imply that the PageRank algorithm I wrote for a uni assignment is actually illegal? Or does this fall under "studying it"? Note that I'm from Europe.
Only if you made/used it commercially and also that Google did not decide you can use it
("What rights does a patent provide?
A patent owner has the right to decide who may – or may
not – use the patented invention for the period in which
the invention is protected. In other words, patent
protection means that the invention cannot be
commercially made, used, distributed, imported, or sold
by others without the patent owner's consent.")
And being out of the country, the US patent doesn't apply to you
("Is a patent valid in every country?
Patents are territorial rights. In general, the
exclusive rights are only applicable in the country or
region in which a patent has been filed and granted, in
accordance with the law of that country or region.")
("What rights does a patent provide? A patent owner has the right to decide who may – or may not – use the patented invention for the period in which the invention is protected. In other words, patent protection means that the invention cannot be commercially made, used, distributed, imported, or sold by others without the patent owner's consent.")
And being out of the country, the US patent doesn't apply to you
("Is a patent valid in every country? Patents are territorial rights. In general, the exclusive rights are only applicable in the country or region in which a patent has been filed and granted, in accordance with the law of that country or region.")