Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry

It's my understanding that sticking to the point was one of the objectives of the author and reasons for writing this book, and it delivers on this very well I thought, whilst at the same time covering a lot of ground. It is made up of three standalone chapters: Geometry, Algebra and Trigonometry, all of which I found enjoyable and informative. For me, the author's clear thinking and expertise shines through throughout the book, though I am not a mathematician I should note. The trigonometry chapter focuses on the trigonometric functions (sin, cos etc.) and emphasizes that they are not just all about navigating or assessing the height of a tree, but also (and according to the author most importantly) "the mathematical description of vibrations, rotations and periodic phenomena of all kinds". As it happens I already knew this and it was part of why I bought a pre-calculus book, i.e. I wanted to better understand the mathematics often used to describe AC electricity, so I was pleased to find this slant was taken. The Algebra chapter went further than I had expected, introducing logarithms, determinants and systems of linear equations, geometric progressions and series, arithmetic progressions, permutations and combinations, the binomial theorem and mathematical induction. The Geometry chapter like the rest of the book keeps to the essentials. There are also exercises interspersed throughout the book that consolidate and deepen the reader's understanding (and confidence perhaps). The reader is very well supported by this book, but also encouraged to go away and contemplate why some of the given results are true. I thought it was a great book for beginners or those looking to refresh their knowledge. I bought the paperback version, which was absolutely fine despite appearing to me to have been printed to a smaller than intended paper size.

this is a very good book. its very short too, only 119 pages. if like me you prefer vintage textbooks its a bargain. as you can imagine PDF textbooks are all over the internet nowadays, but its far better and more convenient to have the printed book in my opinion (as opposed to printing out the entire PDF on loose A4).

Really useful preparation for my calculus study. Clear and to the point.

I appreciate the tone of the book which is friendly and inviting, as well as the incremental approach whereby the author builds up your knowledge bit by bit.There are questions at the end of each of the three sections. Answers are given for the straightforward ones but you are left to figure out the difficult ones yourself. This had me mulling over things for days, which can be beneficial because it gets you thinking and experimenting, but often I had to resort to Google for clues. Some guidance would have been helpful as in some cases I couldn't find any help online and just gave up.The proofs are given in a very understandable style, but sometimes you are just presented with rules, for example operations on fractions. I still don't know why they work.Overall a good book, 1 star deducted for the missing bits.

This book broke down the formulas in a clear, concise way.

Excellent book well written and useful.

Really good book.

Excellent book. Concise, to the point, and very well written. I recommend it to everyone looking for a math refresher before studying calculus, linear algebra, and mathematical economics.

Superb!!!

This book is very small but contains a huge amount of information. It is concise and entirely readable, allowing would be mathematicians to study efficiently. I have gone on to do very well in my university level math, this in no small part due Precalculus Mathematics in a Nutshell. I still refer to it to this day!

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.

Great recap of geometry, algebra and trig. Handy reference, would recommend to anyone wanting a refresher on these topics.

Useless book. Too basic.The author just wrote it to get rich.