Sorry, but it was the Romans who burned the Library at Alexandria. Islam (especially in its current form) has a lot to apoligize for but not something that happened six hundred years before the time of Mohammed.
The Library of Alexandria was finished off by the Muslims. The conquering Arab leader made the infamous comment to the effect of "That which is in the library which is contrary to the Holy Koran is wrong, and must be destoryed. That which is not contrary to the Holy Koran is superfluous."
The entire collection was used to feed the fires of the heating furnaces.