[npp]

Some higher-level math will be important, other parts will not be. The parts that will be more useful are more on the analysis side (real analysis, complex analysis, functional analysis, convex analysis, Fourier analysis, probability theory). These are higher math and are very applicable, or are prerequisites to understanding the applied stuff (convex optimization, dynamical systems, control, ...).

It helps to know what a topology is, but not much more, and you would learn enough "on the way" in learning analysis properly. It helps to know what groups are, because they do show up in practical things, but you don't really need to know full-up "group theory". (They show up because they capture the idea of symmetries, and it is useful in certain practical situations to talk about something being symmetric with respect to various transformations, e.g. under permutations or rotations or whatever. But in this case you don't tend to do much analysis actually using group theory beyond this.) A whole course on abstract algebra is not necessary unless you're interested. It may help in some indirect way of "helping you think better", it may not.

See, say, http://junction.stanford.edu/~lall/engr207c/ as an example of an EE course that does a fair amount of math.

(Also, above, I don't mean 'applicable' in the very indirect sense of "helping you think better" -- I mean people use it to do real stuff. Whether you want to do that stuff is another story -- there are certainly good things in EE/CS that don't require this kind of math.)