Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry

by George F. Simmons

"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.

Genres: Mathematics, Science, Textbooks, Nonfiction, Reference, Calculus, Geometry

128 pages, Paperback

First published January 1, 1981

About the author

George Simmons was an American mathematician who worked in topology and classical analysis. He was known as the author of widely used textbooks on university mathematics.

Reviews

[Paul · Rating 5 out of 5]

Brilliantly done. Does a great job of showing how to identify core elements/proofs/algorithms of the subjects that can be used to extrapolate those to more proofs/algorithms. Great for the person who wants to not just "memorize" but to really understand.

[V · Rating 5 out of 5]

A goldmine of concepts that actually make sense. For someone who ignored maths in school because of teachers requiring to cram all the formulas without any explanations it was an eye opener. Its concepts are shown in a simple, intuitive and geometrical way - something what’s frequently missing in calculus classes nowadays. It is essentially a 3blue1brown book equivalent of all the basic maths collected and compressed to a single super dense yet simple to understand package.

[Bart · Rating 4 out of 5]

2009 will be the year I do the Calculus. This was a good review. It helped me get back into the Mathematics. Got an A in Calc I and II.

[Sungbin Kim · Rating 4 out of 5]

A great primer on Precalculus

[William Schram · Rating 4 out of 5]

Sometimes, we can learn a lot about a book from its title. The book I am reviewing, Precalculus Mathematics in a Nutshell, is a prime example. George F. Simmons wrote this book in the late 1980s. Thankfully, Precalculus math doesn't change too much.

I don't know much about the author, but I have other more advanced works by Simmons on my shelves. In the preface, Simmons mentions the punishment of New Math on American children. It came about to catch up to the Soviets after they succeeded with Sputnik. In practice, you had high school students who didn't know their multiplication tables.

As I said, the book covers mathematics you should know before starting a Calculus course. It covers Geometry, Algebra, and Trigonometry. The book doesn't lie about Algebra, suggesting everyone should learn it or even need it for their future. I found that refreshing.

The book has little hand-drawn pictures of the geometrical figures. It adds a charm that you don't find in more modern texts. Moreover, Simmons focuses on the most crucial points of the subject. Take Trigonometry, for example. You can learn it through navigation and surveying, but most Engineers and Scientists use it for periodic phenomena.

I recommend the book if you have trouble with Algebra, Geometry, or Trigonometry. The book is simplistic but gets to the point. On the other hand, you may find it lacking in some areas. The book is short and doesn't go too deep on any subject.

I liked the book for what it was, but I didn't get much new knowledge out of it. Thanks for reading my review, and see you next time.

[David Steyer · Rating 4 out of 5]

Overall I thought it was a really good book. I have purchased this book twice. The first time was when it was originally released by Barnes and Noble (or it may have been Border's it was that long ago) and the second time was when I wanted to actually read it. I have this read it and am donating it so someone else can enjoy.

The geometry section was a whirlwind and I enjoy Geometry. I understood it. I thought the algebra section was very easy to understand and so was the Trigonometry section. The book also has questions to apply yourself if you want to do them. Honestly, I did not. I refreshed myself with the formulas and thus it was a quick read.

[Gary Li · Rating 5 out of 5]

Six years worth of American public school math education packed into a slim little volume. And indeed the concepts are explained with far greater clarity here than in any of those ponderous tomes we had to lug around for so many years. It is always a source of marvel to me, that people managed to create all those hundreds and hundreds of pages of bloated drivel, when the math behind it is so elegantly concise, and so logically builds upon itself.

Which either speaks to the author's brilliance in pedagogy, or to the efficiency (or lack thereof) of said math education. As a victim myself, I suspect more of the latter.

[Ritesh Patel · Rating 4 out of 5]

Good for those who want a quick review before starting calculus. Even though it's small it contains proofs of most of the theorems and formulae. I specifically liked trigonometry section as it is very precise and straight forward without any unnecessary digressions.

[Brandonmack · Rating 5 out of 5]

PRECALCULUS MATHEMATICS IN A NUTSHELL:
GEOMETRY, ALGEBRA, TRIGONOMETRY
George F. Simmons

CHAPTER 1
GEOMETRY
"Any fool can know. The point is to understand."
- Albert Einstein

Brilliant book…it should be the aim of all high school mathematics students to know this little gem cover to cover!

[Kiryl Bushwackacowski · Rating 5 out of 5]

Perfect book to get one up to speed on precalculus mathematics.

[Hossam Abdallah · Rating 5 out of 5]

simple, to the point, and detailed.
It is awesome to learn math this way.

[David · Rating 5 out of 5]

I had always suspected these mathematical concepts could be taught in a compact, concise way. This book makes the concepts clear in as little space as possible.

EDIT: I just re-read this book 11 years later to brush up (I'm learning Calculus right now). My previous review is exactly right. It takes time to get through some of these pages, as they're all very dense with information. It is for this reason and its terseness that Nutshell makes an excellent go-to reference.

[Maxim · Rating 5 out of 5]

Excellent primer. I especially liked additional topics (Geometric Progressions, Permutations, Combinations, etc).

Another pro is that the author was able to cram approximately 200 exercises into such a small book.