## 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 |

Copyright | |

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### Common terms and phrases

Abel affine transformation Al-Khwarizmi algebra American Mathematical Monthly angle approximation Archimedes area inside arithmetic axioms binomial calculate Cantor Cardano casting out nines Cauchy ciphertext circle coefficients College Mathematics Journal complex numbers Consider coordinates countable course curve denote Descartes digraph dirhems Dirichlet elements ellipse Emmy Noether encryption equal equivalence class Euclid Euclidean Euler example fact Fermat's Figure formula function fundamental theorem Further Reading Galois Gauss Gaussian integers geometry Gottingen graph ideas induction infinitely irrational numbers length letters mailbox Math mathematicians method mod 9 multiplication natural numbers Newton number system number theory parabola Pascal's triangle plane Poincare polynomial positive integer power series prime numbers problem in class Project proof prove Pythagorean theorem Pythagorean triple quadratic equation rational numbers real numbers result Riemann segment sequence side solution solve Sophie Germain Sophie Germain prime square root subsets tangent line Turing write Zeno's paradox