Just for clarification, Vance will only stick with each of these topics so long as it seems fruitful. He wants to take advantage of the great library and doesn't want to waste his time on topics that don't offer enough unique information.
Also, he realizes he can research some of these things in the future. His ambition for studying them now is because he believes the perspectives may be different from this timeline, possibly allowing him to learn lost information. Military Tactics and History, though high on the list, may be glossed over if he feels everything he's learning can be just as easily studied in his own time. Topics like religion, though near the end of the list, may require more time if he hits them.