Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry

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.

This book is an excellent source for review and reference. It contains three chapters covering the important concepts from middle school and high school geometry, algebra, and trigonometry. It is clear and concise yet surprisingly thorough. The author focuses on giving a conceptual understanding of the topics omitting unnecessary details. His explanations and derivations are clear and understandable with helpful illustrations when necessary. This doesn't necessarily mean that it is all an easy read; many concepts will require a good amount of focus and thinking to properly understand. There are example problems and at the end of each section there are practice problems. At the ends of the geometry and trigonometry chapters are all of the important formulas so they can all be seen together for easy reference. The chapters are completely independent of each other and the sections within each chapter are mostly independent of each other so it is easy and convenient to skip to whatever section is necessary to review or reference without the need to study background material elsewhere in the book.That being said, this book definitely covers the topics "in a nutshell". It would probably not be great for learning precalculus topics for the first time and I don't think that is what the author intended it to be used for. It could be an effective supplement to a class or another more thorough textbook, but alone it would probably be insufficient. The examples and practice problems are sufficient for someone who already has a basic understanding of the concepts, but a new student will almost certainly need more guidance and practice.

At 80, I decided that it was time to renew my math, and this book is just what I needed. It is like new and a good place to start.

I bought this book to review math so I can take a calculus course. I like how to the point it is. There is zero fluff. However, once in awhile, I notice pedagogical gaps. Small things,. Like not fully explaining an image. Nothing that can't be figured out. I don't regret the purchase.

I love this little book. I've been away from teaching for a few years and have forgotten/never known many of the things Simmons makes clear. For example: "The system of assigning coordinate points in a line enable us to study geometry with the tools of algebra, and this is what analytic geometry is all about." No techno-gibberish. It's all plain English which makes the book brilliant, deep, and simple all at once. This was written by a master teacher and masterful communicator.

As many say here: this is not a textbook, it’s a resource for reviewing Algebra 1/2, Geometry and Trig. Basically, it replaces four years of lost or low quality class notes with 50-odd pages of correct, legible and well-written text and some exercises. (If you think that’s depressing, one popular calculus guide summarizes those four years in five pages.) That said, this is so well-written (Simmons is famous for the clarity of his undergrad texts, such as Topology and Modern Analysis) that I’m planning on using it as guided tutoring material for my kid - I can explain it and he can then use the book as his notes.

The book is definitely not what I expected based on reviews. The book offers views, interpretations and insights on how to understand calculus. It doesn’t actually give instructions or ways to remember formulas. This book might be helpful to others but not so much for me.