[.ca] Berkeley Problems in Mathematics (ISBN 0387008926)

Challenging problems, or just standard textbook stuff.:
The problem with the contents of this book is that they are mostly standard, or require a simple trick. Many problems also require quite a bit of knowledge in higher mathematics, which may be good if you want to test that. However, this book is not for problem solving enthusiasts.

What it is:
The books is a collection of problems of the Preliminary Exam at the Ph.D. Program in Mathematics at Berkeley. Most of them can b solved using undergraduate-level math, but the problems are challenging.

KK:
It's a good book for that part of the world ( I mean North America) since students are relatively weaker in math compare to Asia. So it's a gem if you want to get into UC Berkely but will be very standard for here ... I would say go for it and buy it but don't set your expectations high...

A real pearl!:
This book is a rare peak inside one of the best Ph.D. programs in Mathematics in the world. It allows you to try out and test yourself on the same problems that the best young and aspiring mathematicians are testing themselves. The problems are neatly arranged by subject and in increasing level of difficulty, and the solutions, are not only beautifully written, but somewhat surprising and unexpected for a seasoned student. I pull mine out of the shelf on the rainy days and try a few more, and when I get one, I really savour it!