This book is accompanied by a companion website:

www.wiley.com/go/farlow/advanced-mathematics

The famous mathematician, George Polya, once remarked that mathematics is not a spectator sport, and to learn mathematics, you must do mathematics. Otherwise, he argued, you are simply a mathematical spectator.

In the context of this book, Polya’s observation means that while reading the book, the reader is a mathematical spectator, after which the reader develops serious mathematical skills and becomes a mathematician by solving, untangling, playing with, etc., yes, even enjoying the problems in the book.

Solving mathematical problems is similar to other endeavors in life, even activities far afield from mathematics, like swimming or playing a musical instrument. We acquire skills in these activities by trial and error, by practice, by making observations, throwing out what does not work, and keeping what does. After a while, we become adept, even proud of our skills, and more often than not, enjoy such activities, that earlier we might have disliked, even abhorred.

I seriously hope the reader will enjoy and develop mathematical skills from the problems in this book, as much as I enjoyed making them.