Lessons from my PhD
Lessons from my Ph.D.:<p>(1) Role of Math.  In most fields of research, the most respected research <i>mathematizes</i> the field, that is, makes progress with math techniques and results.  So for Ph.D. research, try to have math play that role.<p>(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&#x27;s program, or whatever.  Likely the math topics that both come first and are the most important are calculus and linear algebra.<p>(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 <i>engineering</i> Ph.D. where a solution to that problem is regarded as good research.  Make some progress on solving the problem.<p>(4) Pick a University and a Department.  Want a department that respects applied research, maybe in a school of <i>engineering</i>.  Hopefully the university will state their standards for a Ph.D. dissertation, e.g., &quot;An original contribution to knowledge worthy of publication.&quot;  Look at their description of their Ph.D. qualifying exams.  Do enough study at the ugrad or Master&#x27;s level and&#x2F;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.<p>(5) Enroll.  Become a grad student in the chosen department.<p>(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).<p>(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.<p>Done.