>>10980498desu, during my studies, I have seen no correlation between the specialty and the quality of teaching.
I had an abstract algebra course given by an analyst, a topology course given by a number theorist, a course on amenability given by a geometer and all were excellent. However, I also had a PDE class given by a famous analyst that was terrible.
There is no reason to believe that an algebraist would give a better introductory algebra class than an analyst. It sounds counterintuitive, but if you think about it, there is such a gap between the research that your professors are doing and what you are learning that it makes no difference whatsoever.
It's like asking who, between math and physics majors, is the most qualified to teach a sixth grade student about distributivity.
In either case, they likely are not using any of the stuff they are teaching you or they are using it under so many layers of abstraction that they do not consciously think about it anymore.
It has much more to do with how invested they are in teaching and reviewing things than what research they do.
