Maybe they teach advanced algebra during graduate studies, so you are not expected to know it at the entrance exams? At least in my experience that was the case -- I've only learned group and field theory while doing my CS master.
Todai has a strong traditional science profile and traditionally science deals mainly with calculus and statistics. This leads to less of an emphasis on algebra for these exams since they are based on the undergraduate curriculum. It is regrettable, especially for those like myself that came from a school that emphasised algebra and theoretical computer science and only taught advanced calculus at a graduate level.
This is applied math. There isn't any analysis, topology, etc, either.