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This text, intended for a graphing calculator required precalculus course, shows students when and how to use concepts, and promotes real understanding not just rote memorization. In addition, the graphing calculator is used as a tool to help explain ideas rather than merely to find answers. The book reflects AMATYC, MAA, and NCTM guidelines, and makes use of real world data in presenting a balanced algebraic and graphical approach to understanding precalculus concepts. The result is a thorough preparation for the calculus course.
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By Cornelis F. du Toit (MD USA)
My son is using this textbook at school in a 10th grade pre-calculus course. As a microwave antenna engineer I take a strong interest in my son's science and maths education, and try to help with supplementary material where I think it is needed. When I read the first sentence in the book, which states that "a real number is any number that can be written as a decimal", my heart sank. The language usage is as poor as the accuracy of the statement, and it did not bode well for what the rest of the book may offer. It then proceeds to explain that the set of real numbers contains several important subsets, and calls out the natural numbers, whole numbers and the integers out in 3 clearly separated paragraphs. But this is followed by a discussion on the use of brackets, before the rational numbers and later, the irrational numbers are described - you have to read the text carefully before it is clear that these are two more subsets of the real numbers. Clearly marked paragraphs for these subsets would have worked better.
While skimming though the rest of the textbook, my initial misgivings were confirmed by the general lack of rigour, and the over-emphasis on terms, formulas and nomenclature without consistently explaining and/or proving how these are derived. A good example of this is the formulas given in Chapter 3, pp. 334-341 for annuities and mortgages without any proof or explanation. These are presented as examples of exponential functions, but in doing so the mathematics is reduced to a subject more akin to the learning of facts rather than learning the art of deduction. It would have been better to present the section on finance after the section on geometric series, since you need that to explain the formulas. Indeed, the book admits to this "loose end" in Chapter 9, where it belatedly derives one of these formulas, i.e. the future value of an annuity, p. 743.
The text is well illustrated, with attractive and colourful tables, graphs and pictures. But the content should be better organized with more attention to rigour, thus I would not recommend this book.
By (Morris, MN)
The topics in this text have enough breadth to cover
Functions (algebraic, transcendentals, etc) and their Graphs.
One typical feature that is extremely disturbing is the fact that the authors decided to throw in mathematical terms without
defining them first. For instance, as early as Chapter 1.2,
the term "lim f(x) as x approaches ***" is introduced so that
the graphical concept "continuity" can be taught.
There is much more to
limits than just "plotting the graph, seeing where the curve goes". The purpose of PreCalc as suggested by its name is to prepare the students to take Calculus. And if we do not want to
cover some concepts correctly (algebraically and graphically - the motto of this text!) but only to do it in a touchy-feely sense, then please do NOT cover it in PreCalc. Do it in Calculus!
The only reason I ever used this is because someone else chose it for our multiple sections course!
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