Berkeley Problems in Mathematics
Paulo Ney de Souza, Jorge-Nuno Silva, Paulo Ney de Souza
The problems in this book are excellent, they are both entertaining and instructive. I thought I knew calculus, linear algebra, and all of the other typical undergraduate subjects very well, until I purchased this book. After working several problems, mostly without success, I realized that there is a big difference between knowing theorems and knowing how to use them. Since then I have worked these problems daily to improve my "working knowledge," and it has made me a much better mathematician. Learning the definitions and theorems is just the first stage of mathematical knowledge. In this form your knowledge is simply something stored in memory. In the second stage, you must turn it into something more like "software," something that is an active part of your thinking. The only way to do this is by solving problems, and for undergraduate mathematics, this is probably the best book of problems you will find. Highly recommended.
