## The Mathematical Experience, Study EditionWinner of the 1983 National Book Award! "...a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..." - The New Yorker (1983 National Book Award edition) Mathematics has been a human activity for thousands of years. Yet only a few people from the vast population of users are professional mathematicians, who create, teach, foster, and apply it in a variety of situations. The authors of this book believe that it should be possible for these professional mathematicians to explain to non-professionals what they do, what they say they are doing, and why the world should support them at it. They also believe that mathematics should be taught to non-mathematics majors in such a way as to instill an appreciation of the power and beauty of mathematics. Many people from around the world have told the authors that they have done precisely that with the first edition and they have encouraged publication of this revised edition complete with exercises for helping students to demonstrate their understanding. This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about. It will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications. The text is ideal for 1) a GE course for Liberal Arts students 2) a Capstone course for perspective teachers 3) a writing course for mathematics teachers. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto (elena.marchisotto@csun.edu) upon request. |

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### Contents

V | 1 |

VI | 5 |

VII | 6 |

VIII | 8 |

IX | 9 |

X | 13 |

XI | 17 |

XII | 20 |

XLIV | 203 |

XLV | 212 |

XLVI | 217 |

XLVII | 226 |

XLVIII | 227 |

XLIX | 233 |

L | 241 |

LI | 247 |

XIII | 24 |

XIV | 26 |

XV | 29 |

XVI | 31 |

XVII | 35 |

XVIII | 36 |

XIX | 38 |

XX | 48 |

XXI | 56 |

XXII | 59 |

XXIII | 64 |

XXIV | 70 |

XXV | 75 |

XXVI | 76 |

XXVII | 85 |

XXVIII | 87 |

XXIX | 97 |

XXX | 121 |

XXXI | 128 |

XXXII | 138 |

XXXIII | 142 |

XXXIV | 150 |

XXXV | 152 |

XXXVI | 156 |

XXXVII | 163 |

XXXVIII | 168 |

XXXIX | 174 |

XL | 179 |

XLI | 184 |

XLII | 188 |

XLIII | 196 |

### Common terms and phrases

abstract aesthetic algebra algorithm analysis analytic answer applied mathematics argument arithmetic axiom of choice Bibliography calculation called circle complex concept conjecture construct continuum hypothesis course Davis digits Douglas Campbell elements ematics essay Euclid Euclidean geometry Euler example existence experience fact figure finite formalist formula Fourier Fourier series function Further Readings G. H. Hardy Hersh Hilbert human hypercube idea ideal infinite set infinitesimal infinity integers intuition John Higgins knowledge Lakatos logic mathe mathematical objects mathematical proof mathematicians matics means ment method natural numbers non-Euclidean geometry nonstandard notion number theory parallel postulate philosophy of mathematics physical Platonism Platonist Polya prime number prime number theorem problem proof proved question real number reason restricted set theory rigorous sense sequence solution square statement straight line symbols theorem thing tion triangle true truth University Press York zero