## 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 |

### Other editions - View all

A Course of Pure Mathematics... HardPress,Hardy G H (Godfrey Harold) 1877-1947 No preview available - 2013 |

### Common terms and phrases

according algebraical apply assume bounded called circle coefficients complex condition consider constant continuous convergent corresponding course curve deduce defined definition denote derivative determine differential Discuss divergent equal equation example existence expressed fact finite follows formula function geometrical give given graph greater Hence important increases inequality infinite infinity integral interval least length less lies limit Math mean value theorem means multiple negative obtain once origin oscillates particular polynomial positive positive integer possible proof Prove rational function rational numbers reader relation result roots satisfied Show side similar Similarly simple square steadily sufficiently suppose tends theorem Trip true unless values values of x variable write zero

### 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