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Passing those Ph.D. Oral Qualifiers
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Grad Life
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By kevin charlwood
Posted Sun Jan 08, 2006 at 10:49:27 AM PDT
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If you are a graduate student who will soon take your Ph. D. oral qualifiers, this article may be of interest to you. The point here is to give some useful tips, and avoid the horror stories that abound. If you are in the throes of preparing to take these exams, good luck!
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| Passing Those Ph.D. Oral Qualifiers
The 15th anniversary of my passing my Ph.D. orals (a.k.a. the "cum's", the "qual's" or the "comp's") came around recently and I took some time to reflect on the entire process of getting ready for them, and what the whole experience meant to me. Since "writtens" and "orals" are two
completely different balls of wax, so to speak, I'll focus my attention only on the oral exams. The process of getting oneself ready for such an
event is indeed time-consuming, and also a bit nerve-wracking. I include here some ideas and hopefully helpful hints to those of you in graduate school who still need to undergo this process....
The Ph.D. qualifiers at most schools serve as the first big "check point" in one's graduate career - pass these exams, and you move on in the
Ph.D. program to take more advanced coursework and begin your years of reading and research. Fail, and you may get to take them again, but the
second time around is apt to be even far less pleasant than the first go-round. Those who are examining you are testing you to see what you
know as well as what you don't know. And, they're looking to see how well you think on your feet, and your level of mathematical maturity. Do you
have a decent concept of the "big picture" in each area - that is, do you have a fairly deep understanding of the big ideas within each area and how they connect with other branches of mathematics? Basically, in a nutshell, are you ready to do serious mathematical research? That's what they're looking for....
When you are petitioning your department for the topic areas to be covered, and finding out who the potential examiners are, seize the moment
and speak to those faculty about their expectations. Don't be afraid to ask this - they actually welcome it when you show that you are taking the matter seriously enough to discuss examination topics and the overall scope of the exam in each area. My examiner for complex analysis came to my office, pulled two complex analysis texts off my shelf, leafed through
them, pointed to the tables of contents and said, "Know this, or it's a 'fail'." That certainly got my attention, but it also served to give me
some idea of how high a level he'd be testing me at as well.
I spent a solid seven months preparing, using the texts from the courses I had taken, as well as some of the "bibles" for each area, too.
I concentrated heavily on knowing basic definitions and examples/non-examples for important concepts, knowing named theorems and
their proofs, and how to solve many of the homework problems I had had in my courses. Probably the biggest help was to talk to Ph.D. candidates who'd taken the orals in past years, and ask them what was asked of them by their examiners. That really helped clue me in as to what to expect. And, lo and behold, some of those same questions came up again when it was my turn!! I also spent numerous hours with four other oral-qualifier candidates who were up for their exams at the same time I was; we took old
exam questions and took turns attempting to simulate the exam environment by practicing in front of each other. This too, was an enormous help to me, as it took some of the nervous edge off when the time came for me to sit for my exam.
For the day and time of the exam itself, try to arrange a date that's apart from the regular semester/quarter to help you clear your mind of
other distractions (kids from a class you're TA-ing asking about grades, etc.). At the exam itself, go in with a "battle plan" - if you have a
choice of which examiner goes first, go with your strongest area first, and so on. If you don't know an answer to something, by all means say, "I
don't know" - a wrong answer or some sort of "bluff" can send the examiner off down a different path finding out what else you don't know. Falling in to one of those traps has proved costly to more than one qualifier candidate I've known over the years. Usually, when you start answering a question and the examiner is convinced you know what you're doing, they'll stop you and move on to something else. I was amazed at how much
material was covered in my three area exams in under two hours!
For me, the entire process went very well as I had spent plenty of time preparing for the exam. Although I am now in a position which is
primarily teaching-oriented, the experience of learning deep ideas in mathematics helped to make me a much better teacher at the undergraduate
level. Going far beyond any topic(s) that undergraduates will see in their course work has given me a perspective on the discipline that
enhances my ability to "paint the big picture" for my students, and can help encourage students to continue their studies in mathematics.
From the perspective of the examiners, the readiness to do research is of course the main thing they're looking for. At the same time, you may be one of their colleagues some day, and they want to see that you are serious enough about doing mathematics and that you have spent ample time gaining the knowledge base that it takes to proceed with a research-level problem. The question is, "Are you ready to be one of them?"
Kevin Charlwood
Washburn University
kevin.charlwood@washburn.edu |
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