## The Nature and Growth of Modern MathematicsNow available in a one-volume paperback, this book traces the development of the most important mathematical concepts, giving special attention to the lives and thoughts of such mathematical innovators as Pythagoras, Newton, Poincare, and Godel. Beginning with a Sumerian short story--ultimately linked to modern digital computers--the author clearly introduces concepts of binary operations; point-set topology; the nature of post-relativity geometries; optimization and decision processes; ergodic theorems; epsilon-delta arithmetization; integral equations; the beautiful "ideals" of Dedekind and Emmy Noether; and the importance of "purifying" mathematics. Organizing her material in a conceptual rather than a chronological manner, she integrates the traditional with the modern, enlivening her discussions with historical and biographical detail. |

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### Contents

From Babylonian Beginnings to Digital Computers | 1 |

Mathematical Method and Main Streams Are Launched | 18 |

Mathematical Reasoning from Eudoxus to Lobachevsky | 41 |

Algebra from Hypatia to Hamilton | 61 |

Equations Human and Inhuman | 83 |

A Universal Language | 100 |

Forefathers of Modern Mathematics and Their Legacy | 134 |

A Calculus for Heaven and Earth | 167 |

A Special Group and Its Application | 434 |

Geometry for UniverseBuilders | 449 |

PostRelativity Geometry | 478 |

East Meets West in the Higher Arithmetic | 497 |

The Reformation of Analysis | 528 |

Royal Roads to Functional Analysis | 550 |

Infinite Hierarchy | 577 |

Angelic Geometry | 598 |

Determinism and Its Creators | 204 |

The Elements of Strategy in War and Peace | 246 |

Probabilistic Models Great Expectations and Randomized Strategies | 258 |

General Games and Statistical Decision Theory | 275 |

From Dice to Quantum Theory and Quality Control | 291 |

Realm of Random Variables | 316 |

Demons Energy Maxwell and Gibbs | 344 |

Sweet Manuscript of Youth | 368 |

The Unification of Geometry | 401 |

The Leonardos of Modern Mathematics | 625 |

TwentiethCentury VistasAnalysis | 639 |

TwentiethCentury VistasAlgebra | 656 |

TwentiethCentury VistasLogic and Foundations | 684 |

Retrospect and Prospect | 698 |

719 | |

Index | 723 |