## A concise history of mathematics, Volumes 1-2 |

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Page 228

Jacobi based his theory of elliptic

series and called theta

u are quotients of theta

Jacobi based his theory of elliptic

**functions**on four**functions**defined by infiniteseries and called theta

**functions**. The doubly periodic**functions**an u, on u and dnu are quotients of theta

**functions**; they satisfy certain identities and addition ...Page 234

Dirk Jan Struik. In 1851 appeared Riemann's doctoral thesis on the theory of

complex

influenced by hydrodynamical considerations. He mapped the (my)plane

conformally ...

Dirk Jan Struik. In 1851 appeared Riemann's doctoral thesis on the theory of

complex

**functions**u + iv = f(x + iy). Like D'Alembert and Cauchy, Riemann wasinfluenced by hydrodynamical considerations. He mapped the (my)plane

conformally ...

Page 235

The first of these papers analyzed Dirichlet's conditions for the expansion of a

integrable.” But what does this mean? Cauchy and Dirichlet had already given

certain ...

The first of these papers analyzed Dirichlet's conditions for the expansion of a

**function**in a Fourier series. One of these conditions was that the**function**be “integrable.” But what does this mean? Cauchy and Dirichlet had already given

certain ...

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### Contents

The Beginnings | 1 |

Geometrical Patterns Developed by American Indians | 6 |

The Ancient Orient | 13 |

Copyright | |

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### Common terms and phrases

algebra ancient antiquity Apollonios appeared Arabic Archimedes arithmetic astronomy Babylonian mathematics became Bernoulli calculus calculus of variations Cantor Cauchy century A.D. circle classical complex numbers computational conception conic cubic cubic equations curves D’Alembert date back decimal deﬁned deﬁnite Descartes developed differential equations Diophantos discovery Egyptian Egyptian mathematics Euclid Euclidean Eudoxos Euler existence ﬁgures ﬁnd ﬁnite ﬁrst fractions functions Gauss Greek mathematics Hellenistic Hindu Hindu-Arabic numerals history of mathematics ideas Indian inﬁnite inﬁnitesimals inﬂuence integral known Lagrange Laplace later Leibniz mathe mathematicians matics method modern Newton Nineteenth Century notation number theory Oriental papers Paris Pascal period place value plane problems projective geometry published Pythagorean quadratic quadratic equations rational Riemann rigorous Roman Empire scientiﬁc sexagesimal so-called solution solved square symbols T. L. Heath texts theorem tion tradition translation triangle trigonometry vols Weierstrass Western Zeno’s