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VINE VOICEon February 4, 2001
This book is a great tool for those who have been away from algebra, geometry, and trig for a short while. The author treats one to a 'no nonsense' crash course in basic concepts. This being the case, the book is fast paced and very crisp. There is not much 'hand holding' here. Topics are explained quite well and to the point with a good number of exercises.
One caveat though. If you have been away from math for say 10 - 20 years you will often get lost wading through the material. The text does assume that one's thinking process is still attuned to basic skills such as the "two sign change" rule in a compound expression. Therefore if you find that you have forgotten the tricks involved in things like factoring you will be better served to first go with say "Practical Algebra: A self teaching Guide" and "Geometry and Trig for Calculus". Both by Selby et al.
However, if you've been away from math for only a short time (< 5 years), by all means get this book.
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on January 23, 2005
As a dyed-in-the-wool math-phobe (with but one year
of high-school algebra and a year of high-school
geometry 15 years earlier), I thoroughly chewed through
this little book over a summer and then launched
into the first semester of Calculus (taught in the
traditional style, not "Calculus-reform style) at a
rather rigorous Math/Science/Engineering oriented
university. In that Calculus class, I generally got
100% on each quiz and exam (and most of my classmates
with a more typical pre-engineering background
did not). Take it for what it's worth, but I credit
this book. Very compressed, but very clear. You will
note that I successfully substituted this book for two
semesters of the usual pre-calculus math sequence,
and I doubt this would have worked for me if the book
were missing any important pre-calculus material.
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on June 8, 2001
This is one of my very favorite math books of all time. As a survivor of the deplorable California education system in the sixties and seventies, I had to teach myself math because most of my teachers didn't either didn't know how to teach basic math or else they didn't understand it themselves. I used this book! I have had my copy for around twenty years and it is all beaten up and filled with highlighting and notes. I have shown it to friends whenever they needed help and they have asked to buy my copy off me, but I refuse to sell it. I send them here instead.
Also, I recommended this book to a friend and walked her though the basics so that she regained her cofidence and knowledge enough to pass the GMAT within a couple of weeks!
In my opinion, this book gives it all to you -- the basics -- without getting "cutesy" or patronizing -- which is what many of the new "easy to understand" precalculus books unfortunately do. Nor does it leave out substance, which is what you need if you are trying to pass or master this subject. What more could you ask?
One thing to keep in mind, though, if you want to practice your math, use this book with an additional book of problems. There really isn't enough problems in the book for practice. But then, that was not the author's intention, anyway. You should know that when you buy it, though.
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on February 18, 2011
I am a guy who learned to love mathematics in college, but believe it or not, I was kind of a clown in high school. It is in this way that my pre-calculus background sucked. I got really good grades in my calculus and differential equations classes on college, but the sad thing is that I had to learn pre-calculus in a brute force approach: when trying to understand some topic, if that topic required an important pre-calculus concept (e.g., something as simple as factorization during some techniques for integration) I had to learn that concept on-the-fly. You can imagine then how horribly dispersed were my ideas of pre-calculus.

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.
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on August 9, 2011
I want to preface this review by saying that I scored 750 in math on the SATs, and consistently got excellent grades in math throughout high school. I'm not trying to brag, I just want it to be clear that this is not the review of someone without any math background.

I last took math in high school six years ago, and needed to brush up on precalculus for a premed math placement exam. I read the reviews, and thought it looked perfect as a review of material I'd already covered in high school to get ready for a test demonstrating that I'm ready to take calculus. I was impressed by the clear language and distillation of information that the book provided. I've never understood until now exactly *why* the angles in a triangle add up to 180 degrees, though I'd used that fact countless times in my studies.

When I got to the problem sets, however, I felt stumped. I'm able to do about half the problems using the information provided in the text. The other half, however, require a knowledge of precalculus that would seem to make this book unnecessary. I managed to find information to solve some of these problems online, but with others I was left wondering where to begin, rereading the text as though I might find some fact I had overlooked. The written material is very useful at distilling big ideas into comprehensible words and pictures, but I found the problem sets lacking in helpful context. Most of the problems offered no explanation as to how they could be solved.

I get that the book says "in a nutshell" in the title. Caveat emptor. I don't blame George F. Simmons for my difficulty with his book, but I personally found the problem sets very confusing, and the text of little use for solving many of them.
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on September 4, 2004
The book's title says it all. At a time when thousand-page tomes on basic geometry, algebra, and trignometry full of worthless color pictures have become commonplace; it is refreshing to see a book that shows just how simple and beautiful basic mathematics can be.

I would recommend this to anyone who appreciates mathematics--not just students.
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on August 23, 1998
This is one of the best concise texts on the subject of Precalculus Mathematics. It covers all one needs to know to make them comfortable in dealing with the deep dark world of higher mathematics. I found the book so outstanding that I use it as a precourse my Fundamentals of Engineering Review course where calculus and higher math must be totally understood to pass this tough State Board Exam. Excellent work!
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on October 24, 2005
This is an absolutely SUPERB text covering three of the most hated subjects in the entirety of the world! Akin to O'Reilly 'Nutshell' titles, this "Nutshell" book is exactly what its namesake implies: this is not a comprehensive or definitive tome of hundreds of pages to make you a geometry/algebra/trig pro. Therefore, don't expect it to be such. (Some people review non-definitive texts on Amazon, give them like one star, and complain that they believed the book was incomprehensive...DUH!)

While George Simmons has a very fresh, crisp, and fluid writing style which makes concepts easy to grasp, he doesn't stop to explain basic concepts or "on the cuff" calculations. Therefore, this very small and "skinny" book would be excellent for someone who may need some memory refreshing of particular topics or a quick overview of certain subjects. And it is in this manner that this book greatly succeeds; in fact, I plan on using it as a desktop reference into the the very forseeable future, probably forever.

Another notch on this book's belt are George Simmons' drawn examples. They are simple, straightforward, and blatantly expand the text in reference to the appropriate figure. These apparently handwritten sketches look like something out of da Vinci's notebooks!

A hands down winner, no question. (This review is in reference to the 1997 edition of this book, ISBN# 0760606603.)
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on February 5, 2000
Simmons' book cuts to the chase. Instead of wasting time with 800 to 1,000 (or more!) pages of tedium -- you can review, work problems, and get on to calculus! It is as simple as it can be -- but is no simpler.
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on November 10, 2006
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.
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