## Vita Mathematica: Historical Research and Integration with TeachingVita Mathematica will enable teachers to learn the relevant history of various topics in the undergraduate curriculum and help them incorporate this history in their teaching. It contains articles dealing not only with calculus, but also with algebra, combinatorics, graph theory, and geometry, as well as more general articles on teaching courses for prospective teachers, and describes courses taught entirely using original sources. Judith Grabiner shows us how two important eighteenth century mathematicians, Colin Maclaurin and Joseph-Louis Lagrange, understood the calculus from these different standpoints and how their legacy is still important in teaching calculus today. We learn from Hans Nils Jahnke why Lagrange's algebraic approach dominated teaching in Germany in the nineteenth century. Wilbur Knorr traces the ancient history of one of the possible foundations, the concept of indivisibles. This volume demonstrates that the history of mathematics is no longer tangential to the mathematics curriculum, but in fact deserves a central role. |

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### Contents

Historiography and Sources | 1 |

Two Dialogues Gavin Hitchcock | 27 |

From the Scientific Revolution to the Present | 113 |

Judith Grabiner | 131 |

The Development of Algebraic Analysis from Euler to Klein | 145 |

Technical Colleges in Germany during the Nineteenth Century Susann Hensel | 191 |

The Role of the National Science Foundation in the Rise of Theoretical Computer | 209 |

An Explanation Ubiratan DAmbrosio | 245 |

Measuring an Arc of Meridian Marie F rancoise Jozeau and Michele Gregoire | 269 |

African Origins of False Position Solutions | 279 |

Origins and Teaching of Calculus | 301 |

Barrows Theorem Martin Flashman | 309 |

The History of the Concept of Function and Some Implications for Classroom Teaching | 317 |

How Many People Ever Lived? James Tattersall | 331 |

Notes on Contributors | 339 |

345 | |

The Necessity of History in Teaching Mathematics V Frederick Rickey | 251 |

Teaching with Original Sources | 257 |

### Common terms and phrases

Abﬁ al-jabr algebraic analysis algorithm analytic ancient Andre Weil angles Apollonius applied Archimedean Archimedes arithmetic Babylonian mathematics Bakr’s Berlin calculus Cambridge century Chinese Chinese mathematics circle College complex computer science concept cone cube cultural curve cylinder deﬁned deﬁnition Dirichlet Elements ematics engineering equal ethnomathematics Euclid Euler example Felix Klein ﬁeld ﬁgure ﬁnd ﬁnding ﬁnite ﬁrst ﬁve Foundation functions geometric Georg Cantor Getaldic Getaldic’s given Greek Greek mathematics history of mathematics Ibid ibn al-Banna ideas indivisibles inﬁnite inﬂuence integrals Joseph Liouville Karl Weierstrass Kovalevskaya Kummer Lagrange Maclaurin math mathematicians mathematics education Mathematik matics measure method models paper Paris Philosophical problem proof published pupils reﬂected root scientiﬁc seminar sides signiﬁcant solution solve speciﬁc square Stevin STIFEL tangent teachers teaching techniques theorem theory theta functions tion tradition translation triangle University Press Weierstrass York

### References to this book

Mathematical Expeditions: Chronicles by the Explorers Reinhard Laubenbacher,David Pengelley Limited preview - 1999 |

Handbook of International Research in Mathematics Education Lyn D. English No preview available - 2002 |