The book Berkeley Problems in Mathematics was a wonderful source of interesting, some different and challenging problems for (under)graduate students.

However, for a long time, I did not find see any changes in the printing of the book: it contains problems up to Fall $2003$.

Can one suggest some recent books of similar type, which contain (Under)Graduate Problems in Mathematics from various branches such as Algebra, Analysis, Topology, Differential equations etc., which are collected from an exam for Ph.D. program in a prestigious university or institute?

  • $\begingroup$ The Art of Problem Solving is not enough? artofproblemsolving.com $\endgroup$
    – markvs
    Oct 29, 2021 at 4:06
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    $\begingroup$ @markvs: AoPS seems to be mainly for (advanced) high school students, not (under)graduates $\endgroup$ Oct 29, 2021 at 4:14
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    $\begingroup$ @J.W.Tanner: AOPS contains a lot of different problems, including some problems of (under) graduate level. For example, Putnam exams, artofproblemsolving.com/wiki/index.php/… $\endgroup$
    – markvs
    Oct 29, 2021 at 4:19

1 Answer 1


Disclosure: I am one of the authors of the BPM.

At the time we wrote the book, end of the 80s, there was no similar material. There was a lot of problems book in Mathematics, but they fell on typically 3 categories:

In fact one source of inspiration in terms of general material was a book on the Princeton Physics Prelims:

Physics Prelim Book

which was a generalist book.

The only other generalist book I know is: Problems and Solutions in Mathematics by Ta-Tsien Li et al.

Problems and Solutions in Mathematics

Since then several publishers (Dover, AMS, Springer, World Scientific, ...) have published some nice problems books and series, among the remarkable are Masayoshi Hata's collection of problems in real analysis:

Masayoshi Hata's collection of problems in real analysis

The 4th Edition of our book is coming out this Fall (2023) and -- because of size -- may be split into several books - by subject.

  • $\begingroup$ Have the 4th edition of your legendary book been released? $\endgroup$
    – Akira
    Dec 11, 2023 at 13:45

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