Advice for PhD students

Some advice from various people for PhD students:

From Adam Marcus, an RPI alum in CS and math.
From Mark Dredze and Hanna Wallach (pdf). (Here, NLP=natural language processing.)
A collection of links from Srinivas Akella.

Most of this advice is from people working in computer science, but a lot of it is broad enough to apply to research in mathematics or other fields.