Numbers: A Very Short Introduction

Very Short Introductions #260

by Peter M. Higgins

Numbers are integral to our everyday lives and factor into almost everything we do. In this Very Short Introduction , Peter M. Higgins, a renowned popular-science writer, unravels the world of numbers, demonstrating its richness and providing an overview of all the number types that feature in modern science and mathematics. Indeed, Higgins paints a crystal-clear picture of the number world, showing how the modern number system matured over many centuries, and introducing key concepts such as integers, fractions, real and imaginary numbers, and complex numbers. Higgins sheds light on such fascinating topics as the series of primes, describing how primes are now used to encrypt confidential data on the internet. He also explores the infinite nature of number collections and explains how the so-called real numbers knit together to form the continuum of the number line. Written in the fashion of Higgins' highly popular science paperbacks, Numbers accurately explains the nature of
numbers and how so-called complex numbers and number systems are used in calculations that arise in real problems.

Genres: Mathematics, Science, Nonfiction, Ebooks, Amazon

132 pages, Paperback

First published February 24, 2010

Reviews

[Sajjad thaier · Rating 3 out of 5]

كتاب بسيط وقصير ومحشو بكثيرمن المعلومات . أعتقد أنه يناسب المتخصصين في الرياضيات ومن لهم بعض الاطلاع او هواة هذا العلم الجميل . اظطررت لقرأته أكثر من مرة لكي افهم نصفه تقريبا . وهذا كافي لي الى الأن . وارجو أن اعود له في يوم من الايام .

[عياد بن يدر · Rating 4 out of 5]

في هذا الكتيب ستتعلم عن
كيف لا تفكر في الأعداد
متتالية الأعداد الأولية غير المتناهية
الأعداد الكاملةوغير الكاملة
التشفير الحياة السرية للأعداد الأولية
الأعداد المهمة
ماوراء أعداد العد
ماهي لالانهاية
الأعداد من منظور مختلف
وعن مجموعة من الرياضيين الذين ساهموا في الكشف عن الأعداد وطلاسمها

[Ezri · Rating 4 out of 5]

a cute, short romp through numbers & number theory which only occasionally feels like a dense mathematics text. non- mathematicians may enjoy this book by just skipping a paragraph or two when it gets too proofy and believing the author’s claims. aspiring mathematicians will find themselves breezing through a chapter only to spend about as much time on a single paragraph as in the rest of the chapter. this may just be part and parcel of doing justice to rigorous subject like mathematics in an introductory form, so hats off to the author. standout chapter: the one on the ancient roots of cryptography

[Albert Yakoub · Rating 4 out of 5]

من خلال هذا الكتاب فهمت نظريتي فيثاغورس واقليدس
الاسمان اللذان طالما اشعروني بالبلاهة في مرحلة الدراسة الاعدادية.
اما عن متتالية فيبوناتشي فكان دان براون اكثر براعة عندما قام بشرحها في روايته الرائعة ابدًا شفرة دافنشي.

[Pete · Rating 3 out of 5]

Numbers : A Very Short Introduction (2010) by Peter Higgins examines numbers.

For this review we have a celebrity reviewer, The Count from Sesame Street. Take it away Count.

Ah, ah, ah! Today, I, the Count, will be reviewing a book about one of my favorite things in the world – numbers! This book is all about the magic and wonder of numbers, from 1 to infinity and beyond!

In this book even the chapters have numbers that you can count. The first is ‘How not to think about Numbers’, the second is about primes. Then more sequences and numbers with perfect numbers are introduced. There is a chapter on cryptography that shows how primes can be used. Then a chapter ‘The Numbers tha Count’ – just for me! Then a chapter on numbers below the waterline of the number iceberg. Following this there is a chapter ‘to Infinity and beyond!’ and then a chapter ‘Numbers, but not as we know them which extends into complex and other numbers.

The book covers numbers and their theory up to the level of a few undergraduate math courses and in a book so short it is hard to follow unless you already know most of the theory.

Overall, I would highly recommend this book to anyone who loves numbers as much as I do. It’s a fantastic resource for anyone looking to improve their math skills or just wants to learn more about the magic of numbers.

And don’t forget, counting is always more fun when you do it with the Count! So go ahead and pick up a copy of this book and let the counting begin! Ah, ah, ah!”

This review was brought to you by the letter e and the number pi.

[John · Rating 2 out of 5]

This book is a real miss, sadly. As an introduction to number theory it is far too advanced for a novice and it is also far to basic for someone familiar with the field. It doesn’t know what it’s audience is and ends up satisfying no one.

[Jaber ab · Rating 1 out of 5]

لم استوعب من الكتاب سوي القليل
ربما لان بعض الامور لايمكن اختصارها والرياضيات قد تكون احداها
او ربما هي مشاكل في الترجمة او معضلتي القديمة مع الرياضيات

[Andrew Brassington · Rating 3 out of 5]

Somewhat accessible, but the theoretical developments in each chapter are wildly inconsistent and can be quite jarring. There are also some strange moments where certain mathematical processes are assumed to be known by the reader (such as rationalising a surd in the denominator) which seems inappropriate for an introductory text.

[Bob · Rating 3 out of 5]

Interesting at the outset, but I was completely lost in the final chapter. Not sure who the target audience is. People who know mathematics well know this info already. Others won’t be able to keep up I think.

[Michael · Rating 5 out of 5]

This was an enjoyable and engaging read. I recommend this book to anyone who is not a professional mathematician but has an interest in the world of numbers. As an applied mathematician myself, I appreciated the opportunity to revisit some fundamental questions about numbers and quantities. Along the way, I refreshed parts of my high school mathematics and gained new perspectives on topics I was already somewhat familiar with, such as the matrix representation of complex numbers and the irrationality of e.
The book begins with several chapters on the integers, which partly overlap with the "Very Short Introduction" volume on Number Theory (by Peter Wilson). However, I would say that the book by Wilson is more suitable for readers whose main interest lies specifically in the integers. In contrast, this book broadens the scope in later chapters to include combinatorial numbers, cardinal numbers, and the concept of infinity. The author does an excellent job of explaining the nature of irrational numbers in simple terms. The proofs of the irrationality of sqrt(2) and of the fact that irrational numbers have non-terminating, non-repeating decimal expansions are particularly clear and compact.
The treatment of complex numbers is also well done, covering their three most common representations in a concise and accessible way. Overall, this is a very good book for anyone who enjoys reading mathematics presented in a clear, engaging, and slightly less formal style, but still want to enjoy reading some exact proofs and understand the reasoning behind the mathematical theory.

[Moses · Rating 3 out of 5]

This book was, as its name suggests, very short, and it did have a lot of interesting content. While the writing was far better than some mathematical writing I've seen, it was still often dry and confusing. I had to spend a lot of time trying to figure out what Peter Higgins was talking about, although once I understood it I usually thought it was really cool.
For a more accessible introduction to number theory, I would recommend The Number Devil: A Mathematical Adventure , which is geared more towards children but, as a result, tends to explain concepts more effectively and with far better illustrations. It frustrates me that so many math books seem to lack high-quality illustrations, when pictures can be so helpful in conveying mathematical concepts (Numbers had a few illustrations, but nothing to write home about).

[Hunter Ross · Rating 4 out of 5]

I am rounding up (way up) because I listened to this and did not read it. This is a very difficult course to manage on audible. I had to constantly look things up. I would consider this at a higher level than "introduction." That said, some interesting points but at the same time divided between difficult and ind-numbing sections.

[Ahmed Ezzeldien · Rating 3 out of 5]

كتاب مفيد ومسلي نوعاً ما .. نظراً لأنه تطرق للعديد من الأشياء المعقدة عن الأعداد قد لا يستوعبها غير المتخصصين أو الدارسين .. ولكني استفدت بمعلومات عديدة منه بجانب أسلوبه الفكاهي والمبسط في مواضع عدة...

[Badr Mokrai · Rating 5 out of 5]

كتاب جميلة جدا، يحاول من خلاله الأستاذ بيتر أن يبسط أهم مبادئ الرياضيات و يفسرها، احترم المؤلف التسلسل التاريخي و هي أحسن طريقة تقديم تساعد على فهم المواضيع المعقدة
حاول الكاتب التبسيط ما أمكن بالصور التوضيحية و القصص، لكن تبقى الرياضيات خاصة الأعداد المركبة الحديثة عصية على الفهم

[Douglas · Rating 3 out of 5]

A good introduction, but with nothing new if you know something about the subject, and no surprises. A bit too mathematical in places. Ironic, I know, but I would have appreciated the effort to make this useful to a curious lay reader. It’s not.

[Marko Beljac · Rating 5 out of 5]

The last chapter was deep - the section therein on complex numbers and matrices very important for physics, especially quantum physics. Many I see say they don’t know what the audience of the book was supposed to be - fair point.

[Natasha Holme · Rating 4 out of 5]

So much more about numbers than you would ever wish to know.

[Cesar F · Rating 3 out of 5]

Fascinating ...I listened to it so it was difficult to follow-up. It showed me however a perspective ai did not have before

[Kris · Rating 3 out of 5]

This is likely to be too terse for those without advanced mathematics training. For those with training, not much here will be fresh or novel unfortunately.

[Brother · Rating 2 out of 5]

To make a book about numbers you need to be inventive to capture the reader or you get a school book. This book is stiff and pretty much a school book without homework.

[Lydia · Rating 5 out of 5]

Another high-quality instalment of the VSI mathematics series. Author Peter Higgins accompanies the amateur reader on an intriguing and challenging excursion into the vast universe of all the kinds of numbers out there. Topics include the endlessly fascinating world of the primes, how to protect top secret information from nefarious code breakers, as well as a nice relaxing stay at the Hilbert Hotel. - From the counting numbers to the transcendentals to quaternions, there is a lot to be discovered for the interested, engaged reader.

[Maurizio Codogno · Rating 4 out of 5]

Si fa presto a dire numero

Avevo già preso il volume "Matematica" della collana Very Short Introduction. A che serve allora un altro volume sui numeri? Beh, come dico sempre la matematica tende a fare a meno dei numeri. In questo libretto si parla invece di numeri veri e propri, di tutti i tipi. A me non hanno detto molto i capitoli iniziali con i numeri figurati e l'approccio usato per definire il concetto di numero; devo però aggiungere che andando avanti nella lettura - non che ci voglia molto, vista la struttura della collana - ho trovato che la trattazione diventava più interessante. Segnalo in particolare il capitolo che mette insieme i numeri complessi e la trigonometria, dove Higgins - con un gioco di prestigio... - mostra come due diverse notazioni come le coordinate cartesiane e polari permettono di ricavare con facilità una serie di risultati a prima vista complicati da dimostrare. Probabilmente inutile per chi sa già di matematica, ma interessante per i curiosi che vogliano avere un'idea di come i matematici pensino ai numeri.

[Bob · Rating 5 out of 5]

An excellent volume on the subject of numbers. In a clear fashion, this book takes numbers all the way from the naturals (1, 2, 3 , ...) through infinity. Then explains, quite effectively, the basics of Cantor's levels of infinity.

The treatment of transcendental numbers was of special interest to me, and I appreciated the author's observation that transcendental's are "the dark matter of the universe of numbers." How true, and what a neat way to look at them!

[Jose · Rating 2 out of 5]

Very interesting but it must be the hardest book to read in the 'Very Short Introduction' series! Near impossible to read without a college level math background!

[Mills College Library]

512.7 H6367 2011

[Ahmed Omer · Rating 4 out of 5]

يساعد على إنعاش المفاهيم الرياضية التي تقادمت على طول السلم التعليمي, الفصل المتعلق بالتشفير أمتع فصل