## Foundations and Fundamental Concepts of MathematicsThird edition of popular undergraduate-level text offers overview of historical roots and evolution of several areas of mathematics. Topics include mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, and more. Emphasis on axiomatic procedures. Problems. Solution Suggestions for Selected Problems. Bibliography. |

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### Contents

MATHEMATICS BEFORE EUCLID | 1 |

EUCLIDS ELEMENTS | 26 |

NONEUCLIDEAN GEOMETRY | 51 |

HUBERTS GRUNDLAGEN | 79 |

ALGEBRAIC STRUCTURE | 113 |

FORMAL AXIOMATICS | 147 |

THE REAL NUMBER SYSTEM | 173 |

SETS | 212 |

LOGIC AND PHILOSOPHY | 243 |

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addition algebra angles applied assumed assumption axiom axiomatic calculus called circle common complete concept concerned considered consistency construct contains corresponding deductive defined definition denote discourse distinct elements employed equal equation equivalent established Euclid's Euclidean geometry example exists fact field FIGURE finite foundations four function geometry given greater Greek hold hypothesis idea implied important independent infinite interpretation intersect inverse known least less logic mathematicians mathematics matter means method multiplication natural numbers number system obtain operation ordered origin pairs parallel plane positive integers possible postulate set primitive terms principle Problem proof properties propositions prove rational numbers real numbers relation result right angles rules segment Show shown sides space statements straight line Suppose symbols Theorem theory transformation triangle true truth