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Qual questions seem like a great way to study for a new topic, since they usually test slightly deeper understanding than typical questions in a textbook. Princeton has this great archive of questions here:

I was wondering if anyone knows of other universities with similar archives? I'm especially interested in questions from the special topics exam which is usually given orally to Ph.D. students in their 2nd to 3rd year. These tend to ask broader questions than the written exam taken during the first year and trying to answer these questions usually improves one's general understanding of a field.

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As someone whose name is on that list you posted, let me just say that truth value of the statement "[these] tend to ask broader questions than the written exam taken during the first year and trying to answer these questions usually improves one's general understanding of a field" strongly depends on the examiners and their moods on the day of the exam. – Willie Wong Nov 11 '11 at 16:15
@Willie: Yes, I've noticed that. Some students get much harder questions than others. I assumed that this has to do with what the examiners expect that the student can handle. :) – pki Nov 11 '11 at 16:26
@pki: you may be interested in this other question where I have just compiled a long list of links to qualifying examinations of U.S. departments: – Javier Álvarez Jan 4 '13 at 22:56

Harvard has one, Cambridge Tripos used to be harder (so I heard), Purdue also has some posted, and University of Florida's Math Department essentially answered your question (by copying from Dave Renfro) before you even asked by listing qual exams of other universities (UF's page seems to have disappeared completely; anyone who knows the replacement is free to edit).

And then there is Google...

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Written qualifying exams seem to be pretty easy to come by using Google. Transcripts/questions of the oral one is what I haven't been able to find. Thanks for the Florida link. These all seem to be links to questions for the written exam. – pki Nov 11 '11 at 16:31
Actually, Florida copied Dave L Renfro's post, as you can see at the bottom. I thought of that post when I saw the question. – Graphth Nov 11 '11 at 17:15
FYI, I remember spending an enormous amount of time (probably over 15 hours) assembling that list the first time (I posted 2 or 3 revised lists in the next year or two), because search engines didn't give you all that much back then (1999, I believe). What I did was get a list of every math Ph.D. granting university in the U.S. (from the Amer. Math. Soc. web pages) and then systematically went through all the web pages of the math department (including all faculty web pages). I had to do this because solutions were often posted under someone's web page and not mentioned elsewhere. – Dave L. Renfro Nov 11 '11 at 18:02
Links are dead... – Ant Jun 10 at 6:47

My alma mater has an an archive of them here. They don't have two different tiers of exams, but rather two pass levels: Master's and PhD (or, at least that's how it worked when I was there).

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