Numbers: A Very Short Introduction

Oxford University Press has created a superb series of small format books that introduce disparate academic subjects. These attractively designed, sturdily bound books easily slip into a pocket for convenient transport (except for one inexplicable exception: the introduction to Bertrand Russell which for some reason is 50% larger and bound by a glossy cover). I've collected many of the nearly 300 books in the series; storage is easy to do given their small footprint. This new addition to the series is Numbers and it is primarily written for those with nothing more than an elementary knowledge of mathematics but who are fascinated by the world of numbers and are unafraid of taking the plunge. Innumeracy is rampant with many intelligent people convincing themselves that mathematics is too difficult, too arcane to be understood. As one advances up math's ladder of abstractions it does tend to get a bit hair-raising but none of those difficulties are in evidence here.Author Peter Higgins has mastered the technique of using familiar language to describe the fascinating world of number theory. This short introduction concentrates on the behavior of counting numbers or integers, the simplest concepts in all of math. He begins by discussing the behavior of these most fundamental of mathematical entities. From there he leads the reader into the important realm of Prime Numbers (divisible only by 1 and themselves). Primes are reigning kings amongst numbers: the famous Riemann Hypothesis deals with them. Prime number theory inevitably leads to a discussion of cryptography (primes are the malleable agents of devising encryption codes). Higgins also discusses so-called Perfect Numbers (numbers like 6 that are uniquely the sum of its divisors: 1+2+3).The author then enters the more daunting world of complex numbers, the realm of the imaginary square-root of -1. This is probably the most abstract topic tackled by Higgins but his descriptions and language are not too difficult. He is always precise and clear and I found that a little concentration was all that was necessary to follow him on the path. Higgins concludes this fine little book with an introduction to infinity, featuring the peculiar universe of 19th Century number theorist Georg Cantor. It is an appropriate conclusion to this book because infinity is the key attribute of the world of numbers. I read this diminutive volume in a single sitting, found nothing overwhelming and I was always engrossed. If you're interested in learning a little more about numbers, have a few hours of spare time and are both curious and adventurous, you could hardly do better than this splendid introduction.Mike Birman

I just finished reading "Numbers: A Very Short Introduction". I'm pretty much a mathematical hobbyist -- thus not a "real" mathematician. However, my verdict on this book, as with other VSI books via Oxford University Press, is that it is quite pleasing reading, and that it is a fine introduction to elementary numbers, as well as the more mysterious numbers such as complex numbers, transcendental numbers, quaternions, etc.For people who are professional mathematics students, mathematicians, or those who merely like to dabble in mathematics, this book is an excellent (brief) overview of much of the currently discovered mathematical world. Who knows what additional mysterious numbers and concepts might evolve in human mathematical endeavors over the next century or two?From my perspective, this book is highly recommended for those who love to read about the world of numbers.

Two things I really like about this book.1. Physical Size - Just guessing off the top of my head, this book is probably about 5 inches wide, by seven inches tall. Plus, it's only about 120 pages long so it's pretty thin and the binding is flexible.2. Content - This book covers a diverse range of toppings and never stays on one thing long enough to get boring.Those two attributes combined, mean that it's small enough to fit in a pocket comfortably, and interesting enough to take out of that pocket and read. Plus, the book is written at the level of a layman. It's perfect for a middle schooler, or someone who wants a quick entertaining read.I'll probably be buying more books from this series in the future.

Good place to start understanding what numbers are and how they work.

I did not learn much from this little book but it may be useful to those who know next to nothing about numbers

The structure of the book and the topics it aims to present certainly make sense. Unfortunately, the author assumes too much mathematical competency from his audience. He goes too deep too fast and leaves out too many details, assuming the reader has the ability to fill in the blanks. This is often how graduate level mathematics textbooks are written, sparse with little handholding, and yet the book is intended for a general audience. Consequently, portions of this book will likely be frustrating to non-math readers who are interested in learning about the nature of numbers but may never have taken a rigorous math class before. Ultimately, after finishing the book I am left wondering who it was intended for, because if you have the competency to fill in the author's blanks, you probably have a strong math background, which would imply you don't need to be reading "a very short introduction" text.

Basic math skills desired. Or else partial understanding. Numbers, types, applications, few math giants, good book for person love for math not stat.

As advertised

This book is an easy and educational read with a logical, if sometimes head scratching format. If you are fascinated by numbers and maths in general you will enjoy this book.

A very good introduction to basic Number theory. I am using it to update and refresh my Mathematics knowledge that I first acquired in the early 1970s. I have a large number of these short Oxford Press books on various Mathematics, Physics and Computing topics.

Alright but could be better laid out

Bought in tandem with a Very Short Introduction to Mathematics to bring me up to speed on the subject. As someone with a blind spot for maths, who has resolutely steered clear of the subject since O-level maths fifty years ago, I found the book fascinating and a real eye-opener and not too difficult to follow.

A vast subject and very complicated if you think like a mathematician which I don't.I ended up more confused than I thought was possible and did not enjoy this book - I will stick to physics in future