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The shaping of arithmetic : after C.F. Gauss's Disquisitiones Arithmeticae

Author: Catherine Goldstein, (Mathematician); Norbert Schappacher; Joachim Schwermer
Publisher: Berlin : Springer, ©2007.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
The cultural historian, Theodore Merz called it the great book with seven seals, the mathematician Leopold Kronecker, "the book of all books": already one century after their publication, C.F. Gauss's "Disquisitiones Arithmeticae" (1801) had acquired an almost mythical reputation. It had served throughout the XIXth century and beyond as an ideal of exposition in matters of notation, problems and methods; as a model  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Shaping of arithmetic.
Berlin : Springer, c2007
(DLC) 2006932291
(OCoLC)80740189
Named Person: Carl Friedrich Gauss; 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of Mathematics.- D. Fenster, J. Schwermer: Composition of Quadratic Forms: An Algebraic Perspective.- G. Frei: Gauss's Unpublished Section Eight: On the Way to Function Fields over a Finite Field.- III.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:

Since its publication, C F Gauss' "Disquisitiones Arithmeticae" (1801) has acquired an almost mythical reputation, standing as an ideal of exposition in notation, problems and methods; and as a  Read more...

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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 Read more...

 
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