## 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. |

### 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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### Common terms and phrases

a₁ a₂ addition and multiplication American Mathematical Monthly applied assumed assumption axiom of choice axiomatic method binary operation Boolean algebra calculus of propositions called cardinal number circle commutative complex number concept congruent considered consistency construct contains corresponding deductive defined definition denote discourse dyadic relation elementary equal equation established Euclid's Elements Euclidean geometry Euclidean tools example exists FIGURE finite number following theorems given Greek Hilbert hypothesis implied independent infinite integers interpretation intersect inverse line segment Lobachevskian logic mathematical induction mathematicians means natural number system non-Euclidean geometry ordered field ordered pairs parallel postulate perpendicular positive integers postulate set primitive terms principle Problem projective geometry proof properties prove quadrilateral rational numbers real number system reductio ad absurdum right angles Section set of postulates Show sides space statements straight line subset symbols tautology transformation true truth table