Preface The justification for a concept lies exclusively in its clear and unambiguous relation to facts that can be experienced. - Albert Einstein Useful, straightforward, thought-provoking, and fun: qualities college students rarely ascribe to mathematics. But this text presents just such mathematics, for students who have studied some algebra and want to know more, either to pursue one of the social or life sciences or to satisfy their pure intellectual curiosity. The book consists entirely of problems in which mathematics models familiar phenomena, like automobile fuel consumption, depreciation, population growth, inflation, and the spread of epidemics. To investigate such problems requires algebra: a thorough study of linear equations, unit calculations, the estimation of large numbers. logarithms, e, and the trigonometry of right triangles. Throughout the book the nature of the problems studied dictates the approach to the mathematics-setting up models and drawing inferences, but little formal manipulation and no proofs identified as such. I believe that the abstract truths that make mathematics beautiful and useful are best left implicit at this level. I have found that students tend to agree. To master real data, the book teaches the use of the scientific calculator in parallel with the mathematics. Features are introduced as their need is felt. The calculator builds confidence because it frees the user to concentrate on mathematics without worrying about arithmetic. Students learn a new skill while enjoying concrete approaches to some traditionally troublesome abstractions like inverse functions and the rounding of answers to the appropriate number of significant digits. On pace and coverage: When I teach real problems at a reasonable rate students find the mathematics clearly helpful in solving those problems-they learn more, remember more, and enjoy more than they do when I hurry. If I try to cover too much material I revert to teaching algorithms rather than how to think about problems. Then student interest flags and less is learned more painfully. My right pace for a one-semester course allows me to cover all of Parts I and II, on Linear Algebra and Exponential Models (treating Chapters 6, 7, 14, and 15 somewhat skimpily), and either Part III (Quadratic Models) or Part IV (Trigonometry). In the five years since I first taught a course based on these ideas I ave learned from both students and colleagues exposed to this growing text. Particular thanks go to Peter Ash, Bernice Auslander, Don Babcock, Valerie Collins, Dan Comenetz, Pamela Dodds, Marilyn Frankenstein, Matt Gaffney, Paul Mason, Michael Monette, Betty O'Neil, Earl Porter, Barbara Ruth, Geza Schay, Robert Seeley, Mary Shaner, Lorraine Turner, Tan VoVan, and Wing Aero. Students who suggested problems may find those problems here, with their names attached. Andrew Gleason added a thoughtful reading of an early draft this material to years of talk about mathematics and its philosophy, pedagogy, and exposition. Alex Greene's editorial enthusiasm was just e spur I needed to turn rough notes and ambitious ideas into this finished book. Bob Morris kept UNIX running and answered formatting questions while Benjamin Bolker typed the manuscript. Little, Brown's reviewers, Dan Kemp (South Dakota State University), E. James Peake Iowa State University of Science and Technology), Shirley Sorensen University of Maryland), and, particularly, Charles Jepsen (Grinnell College), were receptive and helpful. Ian Irvine and Dave Lynch at Little, Brown managed the editing and production with open-minded or. My wife Joan was there through some hard times-I'm glad we share this good one. My children, Jessica and Benjamin, were there, too. Growing and learning and laughing with them have shaped me and hence this book. They are part of why I enjoyed writing it so much, so for them.