- Paperback: 128 pages
- Publisher: Wipf & Stock Publishers (January 14, 2003)
- Language: English
- ISBN-10: 1592441300
- ISBN-13: 978-1592441303
- Product Dimensions: 6.8 x 0.3 x 9.8 inches
- Shipping Weight: 10.4 ounces (View shipping rates and policies)
- Average Customer Review: 73 customer reviews
- Amazon Best Sellers Rank: #50,018 in Books (See Top 100 in Books)
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Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry:
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About the Author
George Simmons received his undergraduate degree from the California Institute of Technology and his graduate degrees from the University of Chicago and Yale University. His previous books include 'Introduction to Topology and Modern Analysis' (1962) and 'Differential Equations with Applications and Historical Notes' (1972). 'Precalculus Mathematics in a Nutshell' was written after many years of teaching calculus courses convinced the author that a clearly focused, brief review of high school mathematics should be available -- one which highlights the important ideas of geometry, algebra, and trigonometry and makes them easy to understand and remember.
Top customer reviews
"In words: if two triangles are similar then the ratio of any two sides of one triangle equals the ratio of the corresponding sides of the other. By part (a) above, two triangles will necessarily be similar if two pairs of their corresponding angles are equal."
Sure you can understand it but there's so many ways to say it in an easier to digest, less run-on-sentency manner. It still does the trick, though, so I won't not recommend it. Just be prepared to pay attention while you study.
In an effort to correct this I bought Precalculus in a Nutshell, and the results were spectacular. In just a week I was able to finish the book and work on 95% of the problems (there are many!). Simmons goes a long way in removing any useless additional information from his book while keeping the explanations fresh. I've seen huge pre-calculus textbooks that seriously don't teach as much and as well as Simmons does: they are verbose, dry and dull. In less than 120 pages this book covers Geometry, Algebra and Trigonometry. These three parts are independent of each other, so you can read then in any order you want.
Even if Simmons aims for brevity, he always gives good examples (and solutions) to the topic being covered. Also, on each topic, he gives proofs for most formulas and concepts. And his proofs are so intuitive (but correct!) that when one understands one has to smile of the satisfaction. Of course, Simmons does not prove obvious things. For example, he himself argues that proving that one point is always in the middle of three points that lay in a line segment is painful to discuss, and says "...when examining a proof, the natural reaction of an intelligent student is irritation and impatience, and he is right." One word of advice though: some proofs are obscure in the sense that they are not completely laid out in just one block of the text. Simmons sometimes assumes you have a COMPLETE understanding of all the topics before the proof, so he goes over some details hoping you know what is going on. But this is not really bad, because he will always tell you for example: "Because of (a) above..." and this will be you hint to discover the influence of the topic (a) in that proof.
It must be said: the explanations of some topics are really brief (though not incomplete), so if you are in a hurry you can finish this book in about three days. I don't think you could work on all the exercises in three days, but anyhow if you are very short on time you could maybe do like 5 or 6 exercises per topic. That seems like a feasible goal for a three day limit.
Finally, Simmons does not cover every tiny little detail of pre-calculus in his book. He covers what he thinks are the most important topics. I agree with his choice, because looking back, these are the topics that I needed the most for my calculus, linear algebra, statistics and differential equations classes.