On Ph.D. Qualifying Exams 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.
 A: Some old qualifying exams from Harvard: http://www.math.harvard.edu/quals/index.html
A: The Written Qual Book by Daryl DeFord and David Freund.
A: 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.

A: 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.
A: 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!:


*

*University of Arizona Ph. D. Qualifying Exams

*Arizona State University Qualifying Examinations

*University of Alabama Qualifying Exams.

*University of Alabama at Birmingham Qualifying Exams

*SUNY Albany Ph.D. Preliminary Examinations.

*University of California-Berkeley Preliminary Examinations.

*Boston University Preliminary Exams.

*University of Colorado-Boulder Prelim Exams.

*Columbia University Qualifying Exams.

*University of Connecticut Prelim Exams.

*University of California-Davis Exams.

*University of California-Irvine Exams

*University of California-Riverside Exams

*University of Florida Graduate Exams.

*University of Georgia-Athens Qualifying Exams.

*Harvard University Qualifying Exams.

*University of Illinois at Urbana-Champaign Comprehensive Exams.

*Indiana University-Bloomington Tier I Examinations.

*University of Iowa Qualifying Exams.

*Iowa State University Qualifying Exams

*Johns Hopkins University Qualifying Exams.

*Kansas State University Qualifying Exams.

*University of California-Los Angeles Qualifying Exams.

*Louisiana State University Comprehensive Exams.

*University of Maryland Qualifying Exams.

*University of Massachussetts-Amherst Qualifying Exams.

*University of Michigan-Ann Arbor Qualifying Review Examinations.

*University of Minnesota Prelim Exams.

*University of Missouri-Columbia Qualifying Exams.

*University of Nebraska-Lincoln Qualifying Exams.

*University of New Mexico Qualifying Exams.

*University of North Carolina at Chapel Hill Comprehensive Ph.D. Exams (requires one to log in).

*Northeastern University Qualifying Examinations.

*Northwestern University Preliminary Examinations.

*Ohio State University Qualifying Exams.

*Oklahoma State University Comprehensive Exams.

*University of Oklahoma Qualifying Exams.

*Pennsylvania State University Qualifying Exams.

*University of Pittsburgh Preliminary Exams.

*Purdue University Qualifying Exams.

*University of Rochester Preliminary Exams.

*Rutgers University-New Brunswick Qualifying Exams and oral exams.

*Stanford University Qualifying Exams.

*Syracuse University Prelim and Qualifying Exams.

*Temple University PhD. Exams.

*University of Texas at Austin Preliminary Exams.

*Texas A & M University Qualifying Examinations.

*University of Utah Qualifying Examinations.

*University of Washington Preliminary Examinations.

*University of Wisconsin-Madison Qualifying Exams.

