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Questions about the Doctor of Philosophy (Ph.D.) degree, including requirements such as dissertations and university programs leading to a Ph.D.

0 votes

How deeply should one understand other people's work before building on them?

You don't need to know all the proofs. That wouldn't be practical. If it helps you prove your result or uses a common technique then it could be worth learning. Otherwise you would be spending lots of …
Mehta's user avatar
  • 2,098
5 votes
2 answers
3k views

Are undergrads applying to top math Phd programs expected to have taken core graduate clases?

mapping theorem, abstract algebra including Galois theory, point-set topology, and algebraic topology, as well as integration on real manifolds and Stokes' theorem) good enough to get into a top-20 math PhD … I ended up taking almost all the undergraduate courses offered at the liberal arts college I went to but I still think it's not enough, because most of the Harvard PhD students apparently take lots of …
Mehta's user avatar
  • 2,098
1 vote

Interesting vs tractable PhD topics

I think that a good PhD adviser will guide you to a project that is interesting and doable. Look for potential thesis advisers and see what their past students have done. …
Mehta's user avatar
  • 2,098
12 votes

Is it a good practice for PhD students in STEM to have supervisors who have no expertise in ...

I know some PhD supervisors with quite different fields (even in different disciplines) from their students' but they usually say that it is their students' responsibility to do research (as a completely … There are graduate students who lament their PhD advisor decision and say, "I was completely on my own." That is not a good thing! …
Mehta's user avatar
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