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Precalculus mathematics in a nutshell: Geometry, algebra, trigonometry ebook

by George Finlay Simmons

In less than 120 pages this book covers Geometry, Algebra and Trigonometry

In a mere one hundred pages of blazing clarity, this book covers your entire middle school and high school mathematics, and then some. If you are like me and your teachers never got around to giving you a proof for the volume of a sphere, sulk no more. Instead, grab this book and curl up in a corner. and you will learn not one or two equally brilliant but completely different proofs for these most intriguing of mathematical facts. In less than 120 pages this book covers Geometry, Algebra and Trigonometry.

Simmons, George Finlay, 1925-. Mathematics, Precalculus. Books for People with Print Disabilities. Internet Archive Books. org on September 20, 2010. SIMILAR ITEMS (based on metadata).

Download books for free. George Finlay Simmons

Download books for free. George Finlay Simmons. Unlike many textbooks dealing with precalculus mathematics, this volume contains none of the unnecessary "padding" in the form of irrelevant digressions or obscure formalities that tend to confuse even the brightest students. Instead, Precalculus Mathematics in a Nutshell is organized and presented so that students may grasp this often misunderstood material with increased understanding - and decreased frustration. Categories: Mathematics.

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Title: Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry By: George F. Simmons Format: Paperback Number of Pages: 128 Vendor: Resource Publications. Publication Date: 2003 Dimensions: . 6 X . 6 (inches) ISBN: 1592441300 ISBN-13: 9781592441303 Stock No: WW441304. ▲. Have a question about this product? Ask us here. Find Related Products.

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"Geometry is a very beautiful subject whose qualities of elegance, order, and certainty have exerted a powerful attraction on the human mind for many centuries . . . Algebra's importance lies in the student's future . . . as essential preparation for the serious study of science, engineering, economics, or for more advanced types of mathematics . . . The primary importance of trigonometry is not in its applications to surveying and navigation, or in making computations about triangles, but rather 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" In this brief, clearly written book, the essentials of geometry, algebra, and trigonometry are pulled together into three complementary and convenient small packages, providing an excellent preview and review for anyone who wishes to prepare to master calculus with a minimum of misunderstanding and wasted time and effort. Students and other readers will find here all they need to pull them through.
I guess it would be difficult to thoroughly learn geometry, algebra, and trigonometry just from this text, but if it's been a few (or more than a few) years since you've studied these subjects, _and_ you were pretty comfortable with them when you first learned them, then this is the perfect book for brush-up. As my children are headed for high school, I decided to review all of precalculus, calculus, and related subjects (e.g. elemetary linear algebra), and this text turned out to be the perfect starting point. The author doesn't suffer fools gladly, but on the other hand he's not trying to prove how smart he is - he instead demonstrates how accessible his topics are. His introduction to the trigonometry section is particularly entertaining (I won't give it away), and darn it if he doesn't follow through on his promise. I can't see this book being outdone in its goals.
So cut and to the point it was kind of a shock, in a good way. A must have for any one interested or who works with mathematics.
What can you say about a math book? It's slim, easy to read, and to the point. I got it to teach my son trigonometry since I haven't used trig in over ten years. Its brevity is excellent for such a difficult topic and it's much better than trying to sift through a bulky textbook with tons of repetitive lessons and exercises.
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.
I come from another country where math education was different than what it is in the United States. Now I'm studying in American college and this book comes very handy when I need some extra help in some applied math problems in my science classes. Overall, the book has been a very good purchase! Text is easy to follow and problems are easy to understand with the help of this book.
As a professor who teaches Capital Markets in a Masters program in Finance, I only wish that all my students came prepared with this much math (let alone, basic calculus).

To answer criticisms first. This is not a book to learn pre-calculus math from, with no previous exposure -- the explanations are too condensed; the reader is expected to fill-in key steps from his/her previous knowledge.

However, for those reviewing topics for which they already have some understanding, I cannot think of a better book. It cuts down to the essence what often takes 500, verbose pages. It is a excellent summary that requires the reader to be active and think through the steps along the way.

Again, for those who have previously studied the topic, what would be a good follow-on for elementary calculus? Probably, either Spivak:

or Kleppner and Ramsey:

Personally, I would slightly prefer Kleppner and Ramsey (because it goes a little further, without sacrificing understanding).
This book is not intended for people who need to learn algebra, geometry, or Trig. It is a very quick and short review of these three subjects. Although short, it completely covers everything you need to know about these three subjects, with additional tips and tricks along the way from the author. There are exercises at the end of each section that help further the review. I personally like the section on geometry. It has simple to mind-blowing proofs. The Author purposely skips steps in his examples so that you "actively" read the book. The book is great, and I recommend it to anyone who is passionate about mathematics.
Precalculus mathematics in a nutshell: Geometry, algebra, trigonometry ebook
George Finlay Simmons
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Barnes & Noble Books; First edition (1997)
119 pages
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