## An Episodic History of Mathematics: Mathematical Culture Through Problem SolvingAn Episodic History of Mathematics will acquaint students and readers with mathematical language, thought, and mathematical life by means of historically important mathematical vignettes. It will also serve to help prospective teachers become more familiar with important ideas of in the history of mathematicsboth classical and modern.Contained within are wonderful and engaging stories and anecdotes about Pythagoras and Galois and Cantor and Poincar, which let readers indulge themselves in whimsy, gossip, and learning. The mathematicians treated here were complex individuals who led colorful and fascinating lives, and did fascinating mathematics. They remain interesting to us as people and as scientists.This history of mathematics is also an opportunity to have some fun because the focus in this text is also on the practicalgetting involved with the mathematics and solving problems. This book is unabashedly mathematical. In the course of reading this book, the neophyte will become involved with mathematics by working on the same problems that, for instance, Zeno and Pythagoras and Descartes and Fermat and Riemann worked on.This is a book to be read, therefore, with pencil and paper in hand, and a calculator or computer close by. All will want to experiment; to try things; and become a part of the mathematical process. |

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### Contents

Zenos Paradox and the Concept of Limit | 25 |

The Mystical Mathematics of Hypatia | 43 |

The Islamic World and the Development of Algebra | 55 |

Cardano Abel Galois and the Solving of Equations | 73 |

Rene Descartes and the Idea of Coordinates | 95 |

Pierre de Fermat and the Invention of Differential Calculus | 109 |

The Great Isaac Newton | 125 |

The Complex Numbers and the Fundamental Theorem of Algebra | 151 |

Bernhard Riemann and | 247 |

Georg Cantor | 261 |

The Number Systems | 275 |

Henri Poincare Child Phenomenon | 289 |

Sonya Kovalevskaya and the Mathematics of Mechanics | 305 |

Emmy Noether and Algebra | 319 |

Methods of Proof | 331 |

Alan Turing and Cryptography | 345 |

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