## Mathematics: A Very Short IntroductionThe aim of this book is to explain, carefully but not technically, the differences between advanced, research-level mathematics, and the sort of mathematics we learn at school. The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understanding of paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questions about the mathematical community (such as "Is it true that mathematicians burn out at the age of 25?") ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable. |

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Explaining basic concepts very nicely. We think we understand, we know. But his explanation gives more insight of the things.

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A very good introduction to mathematics. But, don't expect the "mathematics" you see in school. This book is about mathematics as mathematicians understand it.

### Contents

Numbers and abstraction | 17 |

Proofs | 35 |

Limits and infinity | 56 |

Dimension | 70 |

Geometry | 86 |

Estimates and approximations | 112 |

o Some frequently asked questions | 126 |

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### Common terms and phrases

180 degrees abstract method angles answer approximate argument axioms becomes calculations Chapter chess circle complicated concept cube curved defined definition dimensional distance divided edges equation Euclid's exactly example fact Figure follows four-dimensional four-dimensional sphere give given golden ratio graph grid hyperbolic geometry idea infinite decimal infinity Koch snowflake large number line segment logarithm manifold mathematical proof mathematicians mathematics means molecules multiply natural logarithm negative numbers number of digits number system objects obvious odd number parallel postulate pentagons philosophical polygon possible prime number prime number theorem problem proof properties prove Pythagoras question real numbers rectangle result roughly rules sequence shape side lengths simple smaller sort space speed sphere spherical geometry square root statement straight line surface tells theory three dimensions three-dimensional Timothy Gowers trefoil knot triangle two-dimensional understand vertices visualize whole number words