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# The Shaping of Arithmetic After C.F. Gauss's Disquisitiones Arithmeticae by Springer-Verlag Berlin and Heidelberg GmbH & Co. KG (Paperback, 2010)

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## About this product

### Key Features

- PublisherSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
- Date of Publication12/02/2010
- Language(s)English
- FormatPaperback
- ISBN-103642058027
- ISBN-139783642058028
- GenreMathematics

### Publication Data

- Place of PublicationBerlin
- Country of PublicationGermany
- ImprintSpringer-Verlag Berlin and Heidelberg GmbH & Co. K
- Content Note36 black & white illustrations, biography

### Dimensions

- Weight896 g
- Width156 mm
- Height234 mm
- Spine30 mm
- Pagination590

### Credits

- Edited byCatherine Goldstein,Joachim Schwermer,Norbert Schappacher

### Editorial Details

- Format DetailsTrade paperback (US)
- Edition StatementSoftcover reprint of hardcover 1st ed. 2007

### Description

- Table Of ContentsI. 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of Mathematics.- D. Fenster, J. Schwermer: Composition of Quadratic Forms: An Algebraic Perspective.- G. Frei: Gauss's Unpublished Section Eight: On the Way to Function Fields over a Finite Field.- III.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.
- Author BiographyCatherine Goldstein is Directrice de recherches du CNRS and works at the Institut de mathematiques de Jussieu (Paris, France). She is the author of Un theoreme de Fermat et ses lecteurs (1995) and a coeditor of Mathematical Europe: History, Myth, Identity (1996). Her research aims at developing a social history of mathematical practices and results, combining close readings and a network analysis of texts. Her current projects include the study of mathematical sciences through World War I and of experimentation in XVII th-century number theory. Norbert Schappacher is professor of mathematics at Universite Louis Pasteur, Strasbourg.His mathematical interests relate to the arithmetic of elliptic curves.But his current research projects lie in the history of mathematics. Specifically, he focuses on the intertwinement of philosophical and political categories with major junctures in the development of mathematical disciplines in the XIX\up{th} and XX\up{th} centuries. Examples include number theory and algebraic geometry, but also medical statistics. Joachim Schwermer is professor of mathematics at University of Vienna. In addition, he serves as scientific director at the Erwin-Schroedinger International Institute for Mathematical Physics, Vienna. His research interests lie in number theory and algebra, in particular, in questions arising in arithmetic algebraic geometry and the theory of automorphic forms. He takes a keen interest in the mathematical sciences in the XIX\up{th} and XX\up{th} centuries in their historical context.

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