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Numbers: A Very Short Introduction (Very Short Introductions) Paperback – 24 Feb 2011

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Product details

  • Paperback: 152 pages
  • Publisher: OUP Oxford (24 Feb. 2011)
  • Language: English
  • ISBN-10: 0199584052
  • ISBN-13: 978-0199584055
  • Product Dimensions: 17.3 x 1.3 x 10.9 cm
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Bestsellers Rank: 111,969 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Product Description


coridial guide to number theory (The Guardian)

About the Author

Peter M. Higgins is currently Professor and Head of the Department of Mathematical Sciences at Essex University. He is a research algebraist but has written five popular mathematics books that bring mathematical matters to a wide audience. He is the inventor of Circular Sodoku, which has appeared throughout the world in magazines, books, the internet, and on handheld computer games.

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8 of 8 people found the following review helpful By SusyBrownlowe on 23 April 2011
Format: Paperback
Fantastic! I was looking for something that didn't just talk about maths, but really explained it - and this was perfect. Peter Higgins writes in such an accessible style that the reader is carefully guided through the maths in a way that leaves you informed and entertained. For example, the chapter on cryptography was a revelation. For a "very short introduction" you come away with enough knowledge to impress even your most scientific friends - a great buy.
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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.
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13 of 19 people found the following review helpful By A. Rodgers on 17 Mar. 2011
Format: Paperback
[Update to review:

I fear that this long (and in places technical) review may give the impression that the book itself is a somewhat heavy and technical, which it isn't. If this review is too wordy or convoluted, be assured that the book does not suffer from the same faults. A glance at the Amazon preview facility should reassure any nervous prospective reader that the book is in fact friendly and inviting. In the (slightly edited) review that follows, I have necessarily concentrated on points which gave me some difficulty, which may give a skewed impression of the book as a whole.

If that's not enough, let me add that, having not been able to so much as look at a book on mathematics for nearly two years, I found that this book very gently and unthreateningly got me interested in reading and doing mathematics again.

It is not at all in the class of apparently 'popular', but actually difficult and technical, books such as Roger Penrose's huge and intimidating "The Road to Reality: A Complete Guide to the Laws of the Universe" (probably very readable and interesting, but only with considerable effort and time - you actually have to do tensor calculus, and so on!), or Avner Ash and Robert Gross's "Fearless Symmetry: Exposing the Hidden Patterns of Numbers" (which I think is utterly incomprehensible, for anyone other than Andrew Wiles himself!).]

This would be a good book to give someone who has already shown some interest in the subject, and might be thinking of studying a mathematical subject at university. On the other hand, the proverbial intelligent general reader, nervous of mathematics, and wanting only to be told something about it, rather than actually having to do it, might find their commitment challenged.
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Most Helpful Customer Reviews on (beta) 7 reviews
16 of 16 people found the following review helpful
Good But Challenging Introduction 28 April 2011
By Dr. Bojan Tunguz - Published on
Format: Paperback Verified Purchase
In most people's minds, math is about numbers and numbers are math. The connection is so prevalent that sometimes it's very hard to explain to people that you are actually doing math when all you do is write unrecognizable symbols on a blackboard or a piece of paper. Nonetheless, the study of numbers can open up vistas to all sorts of interesting mathematical objects, as well as a lot of interesting and non-trivial research on numbers themselves. For instance, integers are probably the most accessible of all numbers, and yet certain properties of integers are so hard to understand that even those professional mathematicians who have worked on them all their lives feel like they have only been scratching the surface of all the problems that one can possibly dream of.

This short introduction introduces the reader to the full richness of numbers, the way in which various sets of numbers arose, and various intriguing and fascinating properties that various collections of numbers have. The book is particularly detailed and comprehensive when it comes to discussing various sets of integers and their properties. I am a theoretical physicist with a lifelong armature interest in math, but even I have never heard of several collections of integers that had been discussed in this short introduction.

The book is very detailed, and it doesn't condescend to the reader. Many examples are given somewhat detailed proofs, and at no point does the reader get the impression that this is a watered-down popular math book. Many arguments can be challenging and need to be read carefully and if you are not willing to untangle them you will not benefit too much from the text. I certainly appreciated all the effort that has been put into making this book this educational and informative.

Unfortunately, the book's biggest strength is also its biggest weakness. This book will probably be on the advanced side for the most general readers. It is certainly amongst the most intellectually demanding of all VSI books. If you are up for a challenge, however, it will be the best introduction to numbers short of actually opening a textbook on the subject.
8 of 8 people found the following review helpful
A Fine Introduction to the Beauty and Mystery of Mathematics 11 Feb. 2012
By Joseph A. Schrock - Published on
Format: Paperback Verified Purchase
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.
20 of 24 people found the following review helpful
As clear an introduction to number theory as is possible 19 April 2011
By Michael Birman - Published on
Format: Paperback Verified Purchase
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
Good. Various aspects of numbers. 12 Sept. 2014
By Rudra Prasanna Mohapatra - Published on
Format: Kindle Edition Verified Purchase
Basic math skills desired. Or else partial understanding. Numbers, types, applications, few math giants, good book for person love for math not stat.
0 of 1 people found the following review helpful
Great Book 7 Oct. 2013
By Amazon Customer - Published on
Format: Kindle Edition Verified Purchase
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.
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