The level of mathematics assumed for the text is quite modest. The reader is assumed to have had two semesters of calculus although much of the book is pitched at a lower level. There is a smattering of topics such as Markov chains that require a bit of matrix background. Chapter Nine explores using a computer as a tool for problem solving. Including this chapter in your syllabus adds some modest programming skills to the assumed knowledge.
Each of the first eleven chapters consists of a brief introduction to a mathematical technique followed by a few worked examples and a generous number of problems. The problem solving advice contained in the book is pretty limited. A brief, one page summary of Polyaâ€™s four-step method is about all you will find. It is the problems that make this book worth a look. Nearly every mathematical puzzle that I can recall is represented in this book. If you believe (as I do) that problem solving can only be learned by solving problems, then this is the book for you.
Jeffrey A. Graham teaches at Susquehanna University. His interests include numerical analysis, differential equations, inverse problems, and mathematical biology.