For many of us, the idea of a "classic" math textbook seems odd or even distasteful, but Paul A. Foerster's Algebra & Trigonometry: Functions and Applications has achieved just that reputation. A student and later colleague of Harold Jacobs, Foerster is similarly thorough and clear in his instruction, though somewhat less whimsical.
Designed to teach intermediate algebra, advanced algebra, and trigonometry, this single-volume text is the perfect follow-up to Harold Jacobs's algebra and geometry courses. Students ought to be self-teaching at this point, and while there is a teacher guide for those who aren't, most families pursuing more advanced math will get by fine with just the student book and solutions key.
How Does This Work?
Foerster wastes no time with unhelpful introductions or buffer lessons to ease students into the content. The first chapter, "Preliminary Information," does offer some review while making students aware of what they'll be learning. Chapters 1-8 cover intermediate algebra; chapters 9-12 cover advanced algebra; and chapters 13-15 cover trigonometry.
In the Foreword, Foerster says his text can be used as an algebra and trig book with applications, or as an applications book with supporting algebra and trig. Applications are simply mathematical models of real-world phenomena, and present a more practical aspect to the content presented.
Whichever of those two ways you choose to use Algebra & Trigonometry: Functions & Applications, you can decide whether, once completing the intermediate algebra chapters, you want to do the trigonometry or advanced algebra section first. The overall goal of the text is to present both trigonometry and advanced algebra as the foundations of calculus, which Foerster assumes students will go on to study.
Like Harold Jacobs's math books, this one is straightforward and clear, with plenty of pedagogical material and lots of example problems to help students get a good grasp of the concepts. Unlike Jacobs's books, doesn't make jokes or include cartoons or other humorous illustrations. Of course, by the time students are studying math at this level, such sweeteners are more likely to prove distracting than helpful.
This is a long book. Most high school students will need to take two years to get through it, though presumably a really motivated student could complete it in one 12-month period. As the content will be largely unfamiliar and difficult, however, it's best that even the most skillful students take as long as needed to really absorb the information.
Each of the fifteen chapters cover a single major topic broken into several sections centered around supporting topics. Every sub-section begins with student objectives and a teaching section before moving to extended problem sets; important laws and equations are highlighted in easy-to-spot blue boxes.
Answers to select exercises and problems are included in the back of the book; the accompanying solutions manual includes complete solutions to all in-text problems. As mentioned above, there is a teacher's edition for this volume, but it was unavailable at the time of the writing of this review.
Our Honest Opinion
This is an excellent advanced algebra/trigonometry textbook, though it isn't "fun." There are no happy animals guiding students on their studies, no jokesters who pop out of the pages with helpful hints, no color illustrations. Which is perfectly okay: this is serious math, and Foerster takes it seriously.
Algebra & Trigonometry: Functions & Applications isn't for all students. Good for any who want a more full-orbed understanding of essential algebraic and trigonometric functions, it's best for students who intend to go on to study calculus and for those who intend to enter a math-based profession such as engineering or physics.
Review by C. Hollis Crossman
C. Hollis Crossman used to be a child. Now he's a husband and father who loves church, good food, and weird stuff. He might be a mythical creature, but he's definitely not a centaur. Read more of his reviews here
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