## The Nature and Growth of Modern MathematicsThe 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; erogodic theorems; epsilon-delta arithmetization; integral equations. |

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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 |

### Common terms and phrases

abstract aggregate algebra approximately arithmetic axioms binary binary operation binary relation Boolean Boolean algebra calculus called cardinal number Cartesian Chapter complex numbers computed concept considered coordinates corresponding curve defined definition differential equations differential geometry distance domain elementary elements Emmy Noether equal equivalent Euclidean Euclidean geometry Euler example fact Figure finite formula frequency function Galois Gauss geometry graph Hence Hilbert hypercomplex illustrated indicated infinite number integral integral domain interval Klein Leibniz linear logical mathematicians matrix means measure modern modulo motion multiplication namely natural numbers Newton normal subgroup obtain pair physical plane position possible postulate prime probability problem proof propositions pure strategies Pythagorean quaternion random variable reader real numbers relation result Riemann sample space sequence solution statistical strategy subgroup subset substitute surface symbols symmetric group theorem theory tion topology transformation truth table University vector velocity zero