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Functions modeling change: a preparation for calculus. (English) Zbl 0945.00001
New York, NY: Wiley. xiv, 554 p. (2000).
This is the pre-calculus text prepared by the well-known Harvard Consortium, suitable for a full-year secondary school course or a one-semester college course. Students should have previously completed a course in intermediate algebra. Some quotes from the preface: “Mathematics has the extraordinary power to reduce complicated problems to simple rules and procedures. Therein lies the danger in teaching mathematics: it is possible to teach the subject as nothing but the rules and procedures—thereby losing sight of both the mathematics and of its practical value.” “We focused on a small number of key concepts, emphasizing depth of understanding rather than breadth of coverage.” The guiding principles include the “Rule of Four: Each function is represented symbolically, numerically, graphically and verbally.” No specific software or technology is required, but some kind of technology with function graphing ability should be at hand.
The eleven chapters are: 1. Functions and Change. 2. Linear Functions. 3. Function Notation. 4. Exponential and Logarithmic Functions. 5. Transformations of Functions and Their Graphs. 6. Trigonometric Functions. 7. Trigonometry. 8. Composition, Inverses, and Combinations of Functions. 9. Polynomial and Rational Functions. 10. Vectors. 11. Other Ways of Defining Functions. A review of algebra is given in the appendices.
Each section of the book contains a good set of problems, most of which cannot be done by following a template in the text, but which include easy as well as more challenging problems. In addition, each chapter closes with a set of review problems. Answers to odd-numbered problems are given at the back of the book.
The book should serve well as a pre-calculus text, whether followed by the calculus texts of the Harvard Consortium, other “reform” texts, or traditional calculus texts.

MSC:
00A05 Mathematics in general
26-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
00A35 Methodology of mathematics
97-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics education
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