Many people think of mathematics (incorrectly) as addition, subtraction, multiplication, and division of numbers. Those with more mathematical training may think of it as dealing with algorithms. But most professional mathematicians think of it as much more than that. While we hope that our students will perform algorithms correctly, what we really want is for them to understand three things: how you do something, why it works, and when it works. The problems we present to you in this book concentrate on these three goals. In this chapter, we’ll introduce you to Pólya’s list, a set of guidelines for attacking mathematical problems. This list has served as a guide for several generations of mathematicians, and it will guide us throughout the text as well. We include a brief biography of the mathematician behind the list in our spotlight George Pòlya. In the section Tips on Doing Homework, we discuss the importance of solving problems and provide the students with some advice for getting started.