|
Lessons from my Ph.D.: (1) Role of Math. In most fields of research, the most respected research mathematizes the field, that is, makes progress with math techniques and results. So for Ph.D. research, try to have math play that role. (2) Ugrad Preparation. To be successful with that role of math, have a good ugrad math background. Then maybe get some more math from independent study, work in a career, a Master's program, or whatever. Likely the math topics that both come first and are the most important are calculus and linear algebra. (3) Find a Good Problem. In your career, independent study, whatever, find a good problem to solve. Pick a practical problem and intend to get an engineering Ph.D. where a solution to that problem is regarded as good research. Make some progress on solving the problem. (4) Pick a University and a Department. Want a department that respects applied research, maybe in a school of engineering. Hopefully the university will state their standards for a Ph.D. dissertation, e.g., "An original contribution to knowledge worthy of publication." Look at their description of their Ph.D. qualifying exams. Do enough study at the ugrad or Master's level and/or independent study to be well prepared for the exams. If the department offers courses for preparation for the exams, in addition plan to take those courses. (5) Enroll. Become a grad student in the chosen department. (6) Progress. In your first year, take some courses, especially in subjects you already know well. Continue your research. Pass the qualifying exams. If you see some opportunities for doing some fast publishable research, as co-author, better as sole author, do that. Show the department that you have done publishable research. Then, sure, technically will have done a Ph.D. dissertation (I did that). (7) Finish. In your second year, finish your research project, stand for an oral exam, and graduate. Of course, if there is any question about your research being publishable, then just PUBLISH it. Done. |
To give some context as to my experience:
- PhDs are funded. You get a stipend and tuition is paid for. This funding is either through a research assistantship (RA), or a teaching assistantship (TA). Either way you are expected to devote 20 hours a week to this task, and the rest would be devoted to your coursework. Typically you take 9 credits per semester for about 4 years, and then after you enter candidacy (you're not really considered a PhD candidate until you pass qualifiers, before then you're a mere PhD "student") you reduce that to a 1 credit "dissertation maintenance" per semester.
- Grant money is the lifeblood of a PhD granting research-focused department. Here's how the economy of a typical CS department works:
-- Newly hired faculty are given a "startup grant" that they use to bootstrap a lab. Their motivation is they want to get tenure in 6-8 years. To do that, they will need to justify to the Dean that they are capable of generating sufficient grant revenue.
-- Grant agencies award grants largely based on published research papers. Therefore the primary directive of a new academic is to publish research, and use that to obtain grants. Hence the phrase "Publish or perish"; if a researcher fails to get enough grants when the tenure clock is up, they will usually be put out to pasture; failing to get tenure is the death knell for a young academic's career.
-- So they hire a couple PhD students as RAs and they work on producing research papers for conferences. The new academic uses the published research in grant applications (the first target is usually the CAREER award). Soon enough grant this grant money is flowing to the researcher and they use it to pay for all sorts of things. Chiefly though, it is used to pay for the stipends and tuition of graduate RAs.
- As an RA, you will be expected to spend 20 hours per week on grant funded research. This means you don't have room to explore your own research topics! All of the grant money is allocated for the funded grant research, not your own whims. The best you can do is carve out some interesting angle on the research that you can call your own.
- By the time you get to maintaining your candidacy, you're already knee deep in publications on the funded research project. The path of least resistance at this point is to bundle them up into a dissertation and defend it.
- If you have your own research agenda, now is the time to execute it as a faculty member at another University. One of their primary concerns during hiring will be: "How is your research agenda different from your advisors?" You will perhaps not be surprised to find that many candidates fresh out of a PhD program will not have their own original thoughts yet. This is why many departments prefer that a new PhD actually take some time doing a postdoc where they can gain some independence from their mentor.
Anyway, what I would say is that instead of picking a problem or a university or a department, pick a person you want to work with for the next 5-8+ years. Like I said, 2 years is very atypical. In my department, we have built in buffers that would make the minimum I think 3 years with a Master's, and even then I think the typical time would be 4 years.