<p>To follow up on idad:</p>
<p>It may be quite different in engineering and in those fields where participation in lab work is important. But for other fields, it is important to get exposure to different perspectives and methods. Whom one’s advisor knows is quite important, as idad says. While members of the same department know their own colleagues and thus the value of a colleague’s recommendation, they also expect that a student who expressed interest in that colleague’s area of expertise would already have taken more than one course with that colleague (and they would also know the student as an undergraduate). Sure, taking undergraduate courses with a prof is not the same as writing a Ph.D. dissertation under the guidance of same prof. But, in general, it is expected that studying with others will be beneficial.</p>