## A Course of Pure Mathematics Centenary EditionCelebrating 100 years in print with Cambridge, this newly updated edition includes a foreword by T. W. Körner, describing the huge influence the book has had on the teaching and development of mathematics worldwide. There are few textbooks in mathematics as well-known as Hardy's Pure Mathematics. Since its publication in 1908, this classic book has inspired successive generations of budding mathematicians at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of the missionary with the rigor of the purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit. Hardy's presentation of mathematical analysis is as valid today as when first written: students will find that his economical and energetic style of presentation is one that modern authors rarely come close to. |

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good book

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this is and will always serve the people,s enquiring mind ,s about maths and its meaning to us in nour every day life,s and to learn from as well that we are onlyey human but for the enthuserist good perhap,s a bit more time reading the book for what it is and a lot more for nbstudents of the subject matter wf

### Contents

CHAPTER II | 40 |

Fig 13 Fig 14 | 56 |

Fig 16 | 65 |

MISCELLANEOUS EXAMPLES ON CHAPTER II | 67 |

CHAPTER III | 72 |

Fig 19 | 75 |

Kg 21 | 79 |

u | 90 |

Examples XLIX 1 Prove that if a 0 then | 259 |

CHAPTER VII | 285 |

CHAPTER VIII | 341 |

or diverge according as Z2n2m converges or diverges ie | 355 |

Examples LXXXI 1 If z is less than | 387 |

CHAPTER IX | 398 |

The general form of the graph of the logarithmic function | 400 |

where s 1 for large n and divergent if | 419 |

25 Cross ratios The cross ratio ziZ2 z3z4 is defined | 99 |

CHAPTER IV | 110 |

since lim jn | 131 |

so that I zn rn Thus zn | 163 |

CHAPTER V | 172 |

Fig 27 | 185 |

Examples XXXVIII lIffix lx except when x 0aadpx | 195 |

CHAPTER VI | 210 |

3 Differentiate | 227 |

CHAPTER X | 447 |

2 we may get a different value corresponding to every | 451 |

Suppose first that | 481 |

22 The transformation z Z If z Z | 483 |

Fig 58 Fig 59 | 485 |

APPENDIX I | 487 |

Fig A Fig B | 492 |

APPENDIX III | 498 |

APPENDIX IV | 502 |

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### Common terms and phrases

Abel's theorem absolutely convergent algebraical function angle assume axis bounded circle complex numbers condition conditionally convergent consider constant continuous function convergent or divergent convergent series corresponding cos2 cosh curve deduce defined definition denote derivative displacement equal equation example exponential exponential function expressed finite number follows formula geometrical greater Hence inequality infinite integral infinity interval inverse irrational numbers limit logarithmic Math mean value theorem multiple multiplication of series numerically less obtain oscillates finitely polynomial positive integer positive number positive or negative positive rational numbers positive values principal value proof Prove rational function reader real numbers real roots recurring decimal result satisfied Show Similarly sin2 sinh straight line suppose tangent Taylor's theorem tends to oo tends to zero Trip true values of x vanishes Verify write

### Popular passages

Page 6 - ... could often do things much better than my teachers; and even at Cambridge I found, though naturally much less frequently, that I could sometimes do things better than the College lecturers. But I was really quite ignorant, even when I took the Tripos, of the subjects on which I have spent the rest of my life; and I still thought of mathematics as essentially a 'competitive