College Algebra, 4th Edition

Book Preface

For many students a College Algebra course represents the first opportunity to discover the beauty and practical power of mathematics. Thus instructors are faced with the challenge of teaching the concepts and skills of algebra while at the same time imparting a sense of its utility in the real world. In this edition, as in the previous three editions, our aim is to provide instructors and students with tools they can use to meet this challenge.

The emphasis is on understanding concepts. Certainly all instructors are committed to encouraging conceptual understanding. For many this is implemented through the rule of four: “Topics should be presented geometrically, numerically, algebraically, and verbally.” Technology facilitates the learning of geometrical and numerical concepts, extended projects or group learning help students explore their understanding of algebraic concepts, writing exercises emphasize the verbal or descriptive point of view,and modeling can clarify a concept by connecting it to real life. Underlying all these approaches is an emphasis on algebra as a problemsolving endeavor. In this book we have used all these methods of presenting college algebra as enhancements to a central core of fundamental skills. These methods are tools to be used by instructors and students in navigating their own course of action toward the goal of conceptual understanding.

In writing this fourth edition our purpose was to further sharpen the clarity of the exposition while retaining the main features that have contributed to the success of this book. We have reorganized and rewritten some chapters (as described below) with a view to making the book usable in a wider variety of instructional approaches. We have included more use of the powerful capabilities of the graphing calculator. In the examples and exercises we have tried to give meaningful applications that we hope will give a sense of how useful a mathematical description of the world really is. Our premise continues to be that conceptual understanding, technical skill, and real-world applications all go hand in hand, each reinforcing the others.

Many of the changes in this edition are a result of our own experience in teaching College Algebra. We have benefited from the insightful comments of our colleagues. We have listened to our students and added examples, or clarified the statement of an exercise. We have also paid attention to the many suggestions sent by users and to the comments of our reviewers.