Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry

Book Preface

For a variety of reasons, many bright people find it difficult to learn in high school the mathe­matics they need to know in order to continue effectively with their education. My purpose in this little book is to try to help by pulling together the essentials of the subject into three convenient small packages: geometry, algebra, and trigonom­etry. Most college mathematics teachers would be overjoyed (and astounded} if their students came to them from high school in full command of this much background material, but most high school graduates today do not even come close.

The three chapters that make up this book were written at different times with different aims. They are almost completely independent, and each can be mastered without reference to the other two. Chapter 3 contains several repetitions of earlier material which I have left in place so that students who wish to study only trigonometry can easily do so. Each chapter has many exer­cises, and answers are provided along with a number of fully worked-out solutions.

Precalculus mathematics is not an infinite shapeless mass that no one can hope to master. In order to demonstrate this, I have eliminated most of the repetitious and unnecessary material often included in precalculus mathematics text­books. I have also tried to achieve the utmost brevity that will still permit students who are willing to work at it to understand the material.

If I overstep the bounds here and there, and pro­vide explanations that are too concentrated for clarity, I welcome suggestions from teachers and students for improvements that can be included in future editions.  Even though few students enjoy studying math­ematics, many find it necessary to do so. If this book can occasionally ease the pain and smooth the learning process for these students, it will · have done its job.