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Where can I find phd qualifying exams questions.Is there any website that keeps a collection of such problems? I need it for doing some revision of the basic topics.I know of a book but that do not have the full collection.

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Checking the links in the two first answers I remember what I was told during the presentation of my M.Sc. final exam: you must know what your thesis is about (really?!) and also the general stuff from undergraduate studies. This was funny since in graduate school they killed us with super year-long courses in topology, algebra or functional analysis (at least two of these three), plus some other optional courses, yet they remarked: it's your level in stuff of undergraduate level that'll decide whether you continue to PhD or not (with a mark of at least 85)...the same as Harvard and TAMU –  DonAntonio Dec 30 '12 at 11:47
    
UFL link above is broken. Here is the right link: gma.math.ufl.edu/past-exams –  Ashish Bhatt Jun 17 at 22:29

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These are the sets of qualifying/preliminary examinations of US universities that I collected some time ago for the same purposes as you. (Dave L. Renfro points out in a commentary below that he compiled a similar list a decade ago, the following includes new departments, updated old broken links and removes unavailable sources). These exams are of much help and some even include solutions!:

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@ Javier Álvarez: I don't know how much time it took you to assemble this list, but you might be amused at how long it took me to do this back in May 2000 (probably over 15 hours). See my comment at the StackExchange question Qual question archives?‌​, where I incorrectly said there that it was in 1999. There still seem to be a few (legitimate) webpages carrying my list, despite the fact that I last updated it in December 2001. –  Dave L. Renfro Jan 4 '13 at 19:28
    
@DaveL.Renfro: I had the list already assembled some months ago and was unaware of your list. What I did was merely keeping a bookmarks folder of the departments which had copies of old exams as I was visiting every single one of them to look for their research interests. It grew slowly as I was surveying webs to make a suitable list of graduate schools I would apply to. To put it here was just copy and paste after a text script to change the bookmarks to StackExchange format. I hope you do not see my post as an illegitimate one... as there are a few more items and no broken links. –  Javier Álvarez Jan 4 '13 at 19:46
    
Javier Álvarez: Oh no, I had no intention that your list was "illegitimate", if by that you mean copying my list. I haven't checked my links, but I imagine many no longer work (perhaps this is what you meant by "broken links") and surely many more departments have such a list now. Indeed, I'd be surprised if more than a handful of all U.S. Ph.D. institutions didn't have such a list now. I was merely commenting on how much easier it is to find such things now than it used to be. Some of the ones I found were on faculty webpages and were not announced/linked on the main departmental webpages. –  Dave L. Renfro Jan 4 '13 at 20:58
    
@DaveL.Renfro: ah, ok! Indeed, nowadays it is pretty straightforward to collect such a list of bookmarks. Most departments now have a section on "resources for graduate students" or similar, where they directly link samples or complete collections of official old exams (some even with solutions!). They have realized the usefulness of this so there is no need to dive in the personal webs of faculty (many of which are now "not found", that is what I called "broken links"), hence collecting this list was pretty easy after surfing through the graduate program sections to get the info I needed :D. –  Javier Álvarez Jan 4 '13 at 21:12
    
thanks for your huge effort –  Koushik Jan 5 '13 at 1:39

Some old qualifying exams from Harvard: http://www.math.harvard.edu/quals/index.html

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Try the collection at Texas A&M University. Although I am not a student of the university, I used the collection to practice for my own qualifying exams. Here is the link: http://www.math.tamu.edu/graduate/phd/quals.html.

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