On Ph.D. Qualifying Exams

Question

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 doesn't have the full collection.

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: http://gma.math.ufl.edu/past-exams/ — , Jun 17 '14 at 22:29

score 153 · Accepted Answer · edited Jul 23 '19 at 22:04

153

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!:

edited Jul 23 '19 at 22:04

user557

12,359

answered Jan 04 '13 at 18:59

Javier Álvarez-Vizoso

15,674

13

@ 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 04 '13 at 19:28
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@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-Vizoso Jan 04 '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 04 '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-Vizoso Jan 04 '13 at 21:12
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thanks for your huge effort – Koushik Jan 05 '13 at 01:39
@K.Ghosh: you are welcome! – Javier Álvarez-Vizoso Jan 05 '13 at 07:36
@Javier A truly remarkable list and a Herculean effort! May I post a link to this list-with full authorship credit-at my in-construction website of free online mathematics source material? This will be a gift to graduate students everywhere fearing thier exams. – Mathemagician1234 Mar 20 '14 at 05:23
@Mathemagician1234 Sure! you may copy and paste the list of links as they are freely available! just mention a link to this forum's answer. – Javier Álvarez-Vizoso Mar 20 '14 at 08:25
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Most links are broken as of now. – user557 Jul 11 '19 at 23:17
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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. – user557 Jul 23 '19 at 20:52

score 26 · Answer 2 · answered Dec 30 '12 at 11:36

26

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

answered Dec 30 '12 at 11:36

arkadiy

381

score 16 · Answer 3 · answered Dec 30 '12 at 10:17

16

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.

answered Dec 30 '12 at 10:17

Haskell Curry

20,144

score 5 · Answer 4 · answered Sep 28 '20 at 10:29

Berkeley Problems in Mathematics (Problem Books in Mathematics) 2004 by Paulo Ney de Souza and Jorge-Nuno Silva.

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.

score 3 · Answer 5 · answered Sep 27 '20 at 07:03

3

The Written Qual Book by Daryl DeFord and David Freund.

answered Sep 27 '20 at 07:03

Xiangzhen Zhang

1,156

On Ph.D. Qualifying Exams

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