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

Author: Catherine Goldstein; Norbert Schappacher; Joachim Schwermer
Publisher: Berlin : Springer, 2007
Edition/Format:   Print book : EnglishView all editions and formats

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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Document Type: Book
All Authors / Contributors: Catherine Goldstein; Norbert Schappacher; Joachim Schwermer
ISBN: 9783540204411 3540204415
OCLC Number: 475842149
Description: xi, 578 s.
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of Mathematics.- D. Fenster, J. Schwermer: Composition of Quadratic Forms: An Algebraic Perspective.- G. Frei: Gauss's Unpublished Section Eight: On the Way to Function Fields over a Finite Field.- III.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, eds.
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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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