To the Student The bashful cannot learn, nor the irritable teach. - Hillel, Sayings of the Fathers, II, 6 With common sense and some algebra you can understand the world better than you can with common sense alone. That is the theme of this book on using algebra. Almost every problem is an application, a description in words of a piece of the world. No problems appear just in order to illustrate mathematical ideas. We will study the mathematics of automobile fuel economy, of inflation, of radioactive decay, and of population growth. You will learn to estimate numbers that are hard to measure, and to manipulate very large and very small numbers. To study this material you must already know some algebra, and you will master more while you learn to see the world in a mathematical way. But you will probably find less emphasis on the rules of algebra than you are used to. We concentrate more on how to read problems and make sense of what they say than on the laws that tell how to move mathematical symbols around on paper. The variables will rarely be the traditional x and y. They will more often be P (for, say, electric power consumption, measured in kWh per person per year) or T (for time, measured in years or seconds). The text is a sequence of worked examples designed to introduce new ideas in concrete settings. Read them. Listen to lectures about them. Then work problems. Mull them over, play with them, and talk about them with your friends. Just watching is not enough. Mathematics is not for spectators. If something in the text puzzles you, ask about it. Perhaps my estimate or my models do not match your experience. Perhaps something could be more clearly explained. Question. Argue. Look for understanding, not for revealed truth. Each problem, each technique, each answer is supposed to make sense. You may find that idea strange. Many students have been convinced by their experiences that the last thing mathematics can be is sensible. If you're one of them, I hope I can change your mind. While working through this book you will learn to use a calculator. For many of you that will be a new tool, and novelty makes learning exciting. We can use real data rather than simple numbers in the probs. Moreover, using a calculator does more than make arithmetic rable. It provides new routes toward understanding difficult ideas. The material that directly addresses your increasingly sophisticated use of the calculator is in indentations like this one. You will need a scientific or slide rule calculator, one with a key labeled "y to the power x," or something similar. Right now (1982) such calculators cost between $15 and $40. Your calculator must provide: * both common and natural logarithms (LOG and LN), * parentheses (or RPN, as on Hewlett-Packard calculators), * scientific notation, to display large numbers, * at least one memory location. If it uses rechargeable (or 1000-hour) batteries you will not be replacing them frequently. You will find more than one memory register very useful, though not essential. Other features may meet your long-term needs. Some calculators have built-in statistical tools. Some do common business calculations efficiently. Some are particularly suited for scientific work. The most exciting option you could select would be programmability, although a programmable calculator might cost more than $40 and is not necessary for this material. Buy the best calculator you can afford. Plan to keep it. This book was designed to cover useful and interesting material, the studying for its own sake. It may not be suitable preparation for advanced work in mathematics. In particular, this is not a standard calculus text, although it covers many of the topics included in such texts. It can, though, prepare you to take a short, applied calculus course. I hope that you enjoy learning the mathematics in this book. I've tried to find examples to interest you if you care about biology, economics, management, or sociology, or if you want to know how schematics can help you see the world in a new way.