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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Shaping of arithmetic. Berlin : Springer, c2007 (DLC) 2006932291 (OCoLC)80740189 |

Named Person: | Carl Friedrich Gauss |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Catherine Goldstein, (Mathematician); Norbert Schappacher; Joachim Schwermer |

ISBN: | 9783540204411 3540204415 9783540347200 3540347208 1280804068 9781280804069 |

OCLC Number: | 159934245 |

Notes: | Includes index. |

Description: | 1 online resource (x, 578 p.) : 36 ill. |

Contents: | I. A Book's History. - C. Goldstein, N. Schappacher. II. Algebraic Equations, Quadratic Forms, Higher Congruences: Key Mathematical Techniques of the Disquistiones. - O. Neumann: The Disquisitiones Arithmeticae and the Theory of Equations.- H.M. Edwards: Composition of Binary Quadratic Forms and the Foundations of Mathematics.- D. Fenster, J. Schwermer: Composition of Quadratic Forms: An Algebraic Perspective.- G. Frei: Gauss's Unpublished Section Eight: On the Way to Function Fields over a Finite Field.- III. The German Reception of the Disquisitiones Arithmeticae: Institutions and Ideas. - H. Pieper: A Network of Scientific Philanthropy: Humboldt's Relations with Number Theorists.- J. Ferreiros: The Rise of Pure Mathematics as Arithmetic after Gauss.- IV. Complex Numbers and Complex Functions in Arithmetic.- R. Bolling: From Reciprocity Laws to Ideal Numbers: An (Un)Known 1844 Manuscript by E.E. Kummer.- C. Houzel: Elliptic Functions and Arithmetic. V. Numbers as Model Objects of Mathematics.- J. Boniface: The Concept of Number from Gauss to Kronecker.- B. Petri, N. Schappacher: On Arithmetization. VI. Number Theory in France in the Second Half of the Nineteenth Century.- C. Goldstein: Hermitian Forms of Reading the Disquisitiones Arithmeticae.- A.-M. Decaillot: Number Theory at the Association francaise pour l'avancement des sciences.- VII. Spotlighting Some Later Reactions.- A. Brigaglia: An Overview on Italian Arithmeitc after the Disquistiones Arithmeticae. P. Piazza: Zolotarev's Theory of Algebraic Numbers.- D. Fenster: Gauss Goes West: The Reception of the Disquistiones Arithmeticae in the USA. VIII. Gauss's Theorem in the Long Run: Three Case Studies.- J. Schwermer: Reduction Theory of Quadratic Forms: Toward Raumliche Anschauung in Minkowski's Early Work.- S. J. Patterson: Gauss Sums.- F. Lemmermeyer: The Principal Genus Theorem.- List of Illustrations.- Index.- Author's Addresses. |

Responsibility: | Catherine Goldstein, Norbert Schappacher, Joachim Schwermer, editors. |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

From the reviews: "A book that traces the profound effect Gauss's masterpiece has had on mathematics over the past two centuries. ... The shaping of arithmetic is a major accomplishment, one which will stand as an important reference work on the history of number theory for many years. ... The editors and authors deserve our thanks for their efforts." (Victor J. Katz, Mathematical Reviews, Issue 2008 h) "It's a big book, with eighteen authors and almost six hundred pages, and it mixes the work of well-established scholars with that of recent Ph.D.'s. ... This volume deserves a wide audience, both among the mathematically able and among historians of nineteenth-century science." (Thomas Archibald, Institute for Science and International Security, Vol. 102 (2), June, 2011) Read more...

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