## Matters MathematicalFrom the Preface: ``This book is based on notes prepared for a course at the University of Chicago. The course was intended for nonmajors whose mathematical training was somewhat limited ... Mastery of the material requires nothing beyond algebra and geometry normally covered in high school ... [I]t could be used in courses designed for students who intend to teach mathematics ... We want the reader to see mathematics as a living subject in which new results are constantly being obtained.'' |

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### Contents

Sets and Functions | |

Number Theory | 33 |

Permutations | 99 |

Group Theory | 129 |

Finite Geometry | 153 |

Game Theory | 195 |

Infinite Sets | 221 |

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### Common terms and phrases

addition affine plane algebraic answer assumption Axiom called cardinal cards Chapter common commutative consider correspondence countable counting course cycles defined definition described discussion distinct divisible elements equal exactly example Exercise exists fact factor field Figure finite formal four function geometry give given Hence hold infinite instance intersection introduced inverse least leave Lemma Let G lines look mathematics means modulo multiplication namely Note objects one-to-one mapping operation parallel permutation play positive integers possible powers prime prime number probability proof properties prove question rational reader real numbers remaining remark result ring rules satisfy Show squares subgroup subsets Suppose theorem theory tion transpositions true unique verify write