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Where can I find Ph.D. 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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    $\begingroup$ 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 $\endgroup$ – DonAntonio Dec 30 '12 at 11:47
  • $\begingroup$ UFL link above is broken. Here is the right link: gma.math.ufl.edu/past-exams $\endgroup$ – user157687 Jun 17 '14 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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    $\begingroup$ @ 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. $\endgroup$ – Dave L. Renfro Jan 4 '13 at 19:28
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    $\begingroup$ @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. $\endgroup$ – Javier Álvarez Jan 4 '13 at 19:46
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    $\begingroup$ thanks for your huge effort $\endgroup$ – Koushik Jan 5 '13 at 1:39
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    $\begingroup$ Most links are broken as of now. $\endgroup$ – user634426 Jul 11 '19 at 23:17
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    $\begingroup$ I've updated most links. I wasn't able to find working links for ASU, Alabama, UNC (the one I added requires you to log in), Columbia. $\endgroup$ – user634426 Jul 23 '19 at 20:52
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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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Berkeley Problems in Mathematics (Problem Books in Mathematics) 2004 by Paulo Ney de Souza and Jorge-Nuno Silva.

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Download preface, sample pages 1 and table of contents in https://www.springer.com/gp/book/9780387204291

In 1977 the Mathematics Department at the University of California, Berkeley, instituted a written examination as one of the first major requirements toward the Ph.D. degree in Mathematics. Its purpose was to determine whether first-year students in the Ph.D. program had successfully mastered basic mathematics in order to continue in the program with the likelihood of success. Since its inception, the exam has become a major hurdle to overcome in the pursuit of the degree. The purpose of this book is to publicize the material and aid in the preparation for the examination during the undergraduate years. The book is a compilation of over 1,250 problems which have appeared on the preliminary exams in Berkeley over the last twenty-five years. It is an invaluable source of problems and solutions for every mathematics student who plans to enter a Ph.D. program. Students who work through this book will develop problem-solving skills in areas such as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra. The problems are organized by subject and ordered in an increasing level of difficulty. Tags with the exact exam year provide the opportunity to rehearse complete examinations. The appendix includes instructions on accessing electronic versions of the exams as well as a syllabus and statistics of passing scores.

This new edition has been updated with the most recent exams, including exams given during the Fall 2003 semester. There are numerous new problems and solutions which were not included in previous editions.

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The Written Qual Book by Daryl DeFord and David Freund.

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