>>17
How do you think I knew about them?
No idea, The first one you linked to a course in natural sciences, and I've never even heard of the second one (I'm pretty certain it's not on the first three years of the course, of which only the first are you forced to do any specific courses, let's not lose track of the point)
It's even more useful to study linear algebra or complex analysis or diffeqs *properly* so you have more than just a passing familiarity of such basic concepts.
Ignoring that I merely picked a course at random and that the contents of the course weren't the point, I might also add here that you're pretty much required to do an undergrad course on all of those (you can just about avoid linear analysis if you really want), try looking in the maths schedules instead of the natural sciences ones.
As for part III, it's an odd part of the tripos, from what I understand mainly the idea is try and get you, as far as possible, up to speed on developments in field to prepare you for research in them. Due to this the sheer volume of material covered I think is quite large, hence the approach to the examinations.
For parts I and II, from all the exams I've seen from other universities the cambridge exams require generally a higher level of ingenuity and original thought to actually do well.