**by Alexandre Borovik, Tony Gardiner**

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It is increasingly clear that the shapes of reality - whether of the natural world, or of the built environment - are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself 'tick', and to appreciate why its shapes, patterns and formulae provide us with precisely the language we need to make sense of the world around us. The second part of this challenge may require some specialist experience, but the authors of this book concentrate on the first part, and explore the extent to which elementary mathematics allows us all to understand something of the nature of mathematics from the inside.

The Essence of Mathematics consists of a sequence of 270 problems - with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline.

The book consists of six chapters of increasing sophistication (Mental Skills; Arithmetic; Word Problems; Algebra; Geometry; Infinity), with interleaved commentary. The content will appeal to students considering further study of mathematics at university, teachers of mathematics at age 14-18, and anyone who wants to see what this kind of elementary content has to tell us about how mathematics really works. ### Table of Contents

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The Essence of Mathematics consists of a sequence of 270 problems - with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline.

The book consists of six chapters of increasing sophistication (Mental Skills; Arithmetic; Word Problems; Algebra; Geometry; Infinity), with interleaved commentary. The content will appeal to students considering further study of mathematics at university, teachers of mathematics at age 14-18, and anyone who wants to see what this kind of elementary content has to tell us about how mathematics really works.

This open book is licensed under a Creative Commons License (CC BY). You can download The Essence of Mathematics ebook for free in PDF format (6.4 MB).

Chapter 1

Mental Skills

Chapter 2

Arithmetic

Chapter 3

Word Problems

Chapter 4

Algebra

Chapter 5

Geometry

Chapter 6

Infinity: recursion, induction, infinite descent

Title

The Essence of Mathematics

Subject

Science and Mathematics

Publisher

Open Book Publishers

Published

2019

Pages

400

Edition

1

Language

English

ISBN13

9781783746996

ISBN10

1783746998

ISBN13 Digital

9781783747016

ISBN10 Digital

1783747013

PDF Size

6.4 MB

License

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