Qualifying Exams: How to Interpret This?

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Main Question or Discussion Point

I recently spoke with a Math professor of many years. He said that qualifying exams are
a young person's game and that he believed that neither himself nor most professors could
pass these exams without serious preparation. Is he right? If so, what does this say about both the worth of these exams and the necessary preparation to be a research Mathematician?
 

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  • #2
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The reason that most professors probably couldn't pass is that you typically have to pass multiple exams. An analyst probably couldn't pass the algebra exam and vice versa. They are usually just a test of the material that you should have learned in your core courses so they're not a big deal if you paid attention.
 
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I'm not sure. I'd probably have to study reasonably seriously to pass quals again. It's a right of passage. There's something to be said for over-learning. You learn it at 95% mastery at the time if what your goal is only to retain it at 80% mastery and so on (I just made the numbers up). I think studying for the quals also had the effect of making me slightly more problem-oriented than I was because when I studied for them, I already knew the theory well enough, and it was mostly a matter of being able to learn how to apply it. It's also a weed-out thing. It's partly about proving that you can learn something at high enough level if needed. However, I'm not sure how well-established it is that they are predictive of future success. I breezed through my quals without too much trouble, but I'm crap at research, and I know people who barely squeaked through quals, and then did pretty well at research. It could be that I have some sort of untapped research talent that was not realized in practice, partly due to lack of interest and inclination (plus, calling it quits after my PhD), but I feel like I'm not even remotely good at it.
 
  • #4
officialmanojsh
Actually, you needn't work hard for your exams. You must just concentrate on what you want to pursue in! Example : being a mathematician!, focus on every theorems and functions that Maths contain. You needn't focus on any other subjects only a little knowledge should be known to you regarding other subjects! And you need to know how to play and make something new with existing theorems!!! According to me : imagination is more important than knowledge!
 
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Officialmanojsh, where did you get your PhD? If the answer is "nowhere", maybe you shouldn't be giving advice to people trying to earn one.

I'm not sure I agree with the premise. I know of one case at a major (but not top 10) university where the students complained the qual was too hard. The department chair took it - cold - and put his in the stack to be graded. He got the highest score in the class.
 
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But one would imagine that after teaching all these classes over the years the material would become
second nature.
 
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he believed that neither himself nor most professors could pass these exams without serious preparation
But one would imagine that after teaching all these classes over the years the material would become
second nature.
Which is it? Professors can't pass these exams, or professors can because they are teaching. I'm prepared to believe either statement, just not both at the same time.
 
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WWGD
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EDIT: Then please read carefully . He, the professor I spoke with, believed... I on the other hand believe, or would imagine that these
professors, after many years of teaching would be able to handle the material. I am just curious,
this professor had done some pretty serious high-end research. Is it too simplistic to conclude that thorough knowledge of the material in the quals. is not necessary to be able to do serious research (there is also the fact that this is just one opinion, though I sort-of agree with him, given that I have asked some professors these questions and many were unable to answer them on the spot)?
 
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