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" The shaping of arithmetic : "
Catherine Goldstein, Norbert Schappacher, Joachim Schwermer, editors.
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BL
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| Record Number
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1029850
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b784220
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| Title & Author
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The shaping of arithmetic : : after C.F. Gauss's Disquisitiones Arithmeticae /\ Catherine Goldstein, Norbert Schappacher, Joachim Schwermer, editors.
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| Publication Statement
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Berlin :: Springer,, ©2007.
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| Page. NO
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1 online resource (x, 578 pages) :: 36 illustrations
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| ISBN
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1280804068
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: 3540204415
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: 3540347208
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: 6610804060
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: 9781280804069
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: 9783540204411
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: 9783540347200
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: 9786610804061
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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A Book's History -- A Book in Search of a Discipline (1801-1860) -- Several Disciplines and a Book (1860-1901) -- Algebraic Equations, Quadratic Forms, Higher Congruences: Key Mathematical Techniques of the Disquisitiones Arithmeticae -- The Disquisitiones Arithmeticae and the Theory of Equations -- Composition of Binary Quadratic Forms and the Foundations of Mathematics -- Composition of Quadratic Forms: An Algebraic Perspective -- The Unpublished Section Eight: On the Way to Function Fields over a Finite Field -- The German Reception of the Disquisitiones Arithmeticae: Institutions and Ideas -- A Network of Scientific Philanthropy: Humboldt's Relations with Number Theorists -- 'O??ò?' A??????í???: The Rise of Pure Mathematics as Arithmetic with Gauss -- Complex Numbers and Complex Functions in Arithmetic -- From Reciprocity Laws to Ideal Numbers: An (Un)Known Manuscript by E.E. Kummer -- Elliptic Functions and Arithmetic -- Numbers as Model Objects of Mathematics -- The Concept of Number from Gauss to Kronecker -- On Arithmetization -- Number Theory and the Disquisitiones in France after 1850 -- The Hermitian Form of Reading the Disquisitiones -- Number Theory at the Association française pour l'avancement des sciences -- Spotlighting Some Later Reactions -- An Overview on Italian Arithmetic after the Disquisitiones Arithmeticae -- Zolotarev's Theory of Algebraic Numbers -- Gauss Goes West: The Reception of the Disquisitiones Arithmeticae in the USA -- Gauss's Theorems in the Long Run: Three Case Studies -- Reduction Theory of Quadratic Forms: Towards Räumliche Anschauung in Minkowski's Early Work -- Gauss Sums -- The Development of the Principal Genus Theorem.
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| Abstract
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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 of organisation and theory building; and of course as a source of mathematical inspiration. Various readings of the "Disquisitiones Arithmeticae" have left their mark on developments as different as Galois's theory of algebraic equations, Lucas's primality tests, and Dedekind's theory of ideals. The present volume revisits successive periods in the reception of the Disquisitiones: it studies which parts were taken up and when, which themes were further explored. It also focuses on how specific mathematicians reacted to Gauss's book: Dirichlet and Hermite, Kummer and Genocchi, Dedekind and Zolotarev, Dickson and Emmy Noether, among others. An astounding variety of research programmes in the theory of numbers can be traced back to it.; The 19 authors - mathematicians, historians, philosophers - who have collaborated on this volume contribute in-depth studies on the various aspects of the bicentennial voyage of this mathematical text through history, and the way that the number theory we know today came into being.
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| Subject
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Gauss, Carl Friedrich,1777-1855., Disquisitiones arithmeticae.
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Gauss, Carl Friedrich.,1777-1855.
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| Subject
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Number theory.
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MATHEMATICS-- Number Theory.
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Number theory.
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Number theory.
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Disquisitiones arithmeticae (Gauss, Carl Friedrich)
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| Dewey Classification
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512.7
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| LC Classification
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QA241.S443 2007
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| NLM classification
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31.01bcl
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31.14bcl
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O156clc
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| Added Entry
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Goldstein, Catherine, (Mathematician)
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Schappacher, Norbert.
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Schwermer, Joachim.
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