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Title: Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry
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Manufacturer: Wipf & Stock Publishers
List Price: $17.00
Our Price: $14.44
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| Customer Reviews: |
| Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry by Wipf & Stock Publishers Too brief to be of value | The structure and focus of this book can be summed up by the author's comments on page 92. Simmons laments the size of trigonometry books, noting that they contain "hundreds of pages of unnecessary padding, consisting mostly of obscure formalities and irrelevant digressions. This padding is like smog, or dust in the eyes - it makes it impossible for even bright students to gain any clear view of what the subject is about or what it is for." He then states, "This chapter is a slightly expanded version of my standard 50-minute lecture."
The idea that one can impart all of trigonometry in one 50-minute lecture is absurd. Furthermore, the chapter on geometry is only thirty pages long and the chapter on algebra is sixty pages in length. This demonstrates that the emphasis should be on the nutshell in the title, because all that you get from this book is a small kernel of the broad expanse that is precalculus.
For example, the topics covered in the algebra chapter are:
*) The real line
*) Integral and fractional exponents
*) Polynomials and factoring
*) Linear and quadratic equations
*) Inequalities and absolute value
*) The concept of a function
*) Lines, circles and parabolas
*) Logarithms
*) Polynomial division
*) Determinants and systems of linear equations
*) Arithmetic and geometric progressions
*) Permutations and combinations
*) The binomial theorem
*) Mathematical induction
As you can see, this comes out to approximately four pages per topic. It is impossible to present anything other than the simplest of examples and explanations in so short a time. Such brevity is counterproductive, which is why I rank the book so low.
| | Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry by Wipf & Stock Publishers Precalculus Mathematics in a Nutshell. | It is easy to appreciate the high praise that Simmons's book receives from most reviewers, and, it is also easy to understand some reviewers' displeasure with the fast pace and brevity of the author's treatment of the curriculum. Simmons says [Preface to my copy of the 1997 hardcover edition], "I have eliminated most of the repetitious and unnecessary material often included in precalculus mathematics textbooks. I have also tried to achieve the utmost brevity that will still permit students who are willing to work at it to understand the material. If I overstep the bounds here and there, and provide explanations that are too concentrated for clarity, I welcome suggestions from teachers and students for improvements that can be included in future editions."
This is conceived as a 'brush up' for readers who have some years between themselves and their last math classes. A modest history and/or aptitude with mathematics is assumed, but not all notation or terminologies are explained when they first appear in the text; if you find this to be a problem, a decent dictionary should quickly resolve any questions.
Simmons takes full advantage of the "picture's worth a thousand words" principle, providing many excellent drawings to help explain concepts presented in the sections on geometry and trigonometry. The reader can spend abundant time in this rather small book, if he/she wants to work through all of the problems in the exercises and appendices, or they can move through it a bit more quickly by proceeding selectively, jumping past problems that look less challenging and/or concepts that are already understood (there'll be plenty of work here even for those who skip many problems!). The book can also serve as a reference for those of us who do some kinds of calculations too infrequently to recall the formulae. The book may be maddening, it may be fun (it will probably be both), it adroitly fills an important niche (or two). | | Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry by Wipf & Stock Publishers Short book, fast pace | | This introduction is for driven college seniors or graduates, not first timers. It is slim and it gets you "there" fast, but the few examples do not amplify or extend the material. The hand drawings help at times to understand what the author means. The infrequent examples also don't help you solve the problems, many of which are without full answers. The book is quirky. The author assumes you understand ratio, proportion, and phase shift in this introductory book. | | Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry by Wipf & Stock Publishers Excellent Refresher and Reference to Pre-Calc Mathematics | By all means, get this book even if you've just recently taken geometry, algebra or trig. Not only is this a good refresher, but also a good reference book. Simmons' explanations and drawings are so precise, so logical, and so coherent that not only could I remember what I learned 9-13 years ago, but I found enjoyment in doing the problems. For the first time ever, I saw the point to geometry.
Here is one of my favorite quotes from the book: "... even though very few people become surveyors or navigators, the students who study [trigonometry] books are expected to undertake many lengthy calculations about heights of flagpoles, the widths of rivers and the positions of ships at sea. The truth is that the primary importance of trigonometry lies in a comopletely different direction- in the mathematical description of vibrations, rotations, and periodic phenomena of all kinds, including light, sound, alternating currents and the orbits of the planets around the sun. What matters most in the subject is not making computations about triangles, but grasping the trigonometric functions as indispensable tools in science, engineering and higher mathematics..."
If it were possible, I'd rate this book six stars. | | Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry by Wipf & Stock Publishers overly brief | | This book provides explanations that are too cursory to serve as more than a good reference to formulas and proofs. At times the explanations are very quick and undetailed when it comes to some of the more complex derivations (for example, the 21 variations of the basic trigonmetric theorems), and at other times the book is overly thorough when it comes to some entirely basic concepts that don't require much of an explanation. While this book is sufficient to provide a slight refresher to someone who has previously learned all of the material, it doesn't have the content necessary to thoroughly relearn the material and by no means can it be used to teach this information to a first-timer. |
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