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- catalog abstract ""The notion of a mathematical structure is among the most pervasive ones in twentieth-century mathematics. Modern Algebra and the Rise of Mathematical Structures describes two stages in the historical development of this notion: first, it traces its rise in the context of algebra from the mid-nineteenth century to its consolidation by 1930, and then it considers several attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea. Part one dicusses the process whereby the aims and scope of the discipline of algebra were deeply transformed, turning it into that branch of mathematics dealing with a new kind of mathematical entities: the "algebraic structures". The transition from the classical, nineteenth-century, image of the discipline to the thear of ideals, from Richard Dedekind to Emmy Noether, and culminating with the publication in 1930 of Bartel L. van der Waerden's Moderne Algebra. Following its enormous success in algebra, the structural approach has been widely adopted in other mathematical domains since 1930s. But what is a mathematical structure and what is the place of this notion within the whole fabric of mathematics? Part Two describes the historical roots, the early stages and the interconnections between three attempts to address these questions from a purely formal, mathematical perspective: Oystein Ore's lattice-theoretical theory of structures, Nicolas Bourbaki's theory of structures, and the theory of categories and functors."--BOOK JACKET.".
- catalog contributor b13302690.
- catalog created "c2004.".
- catalog date "2004".
- catalog date "c2004.".
- catalog dateCopyrighted "c2004.".
- catalog description ""The notion of a mathematical structure is among the most pervasive ones in twentieth-century mathematics. Modern Algebra and the Rise of Mathematical Structures describes two stages in the historical development of this notion: first, it traces its rise in the context of algebra from the mid-nineteenth century to its consolidation by 1930, and then it considers several attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea. Part one dicusses the process whereby the aims and scope of the discipline of algebra were deeply transformed, turning it into that branch of mathematics dealing with a new kind of mathematical entities: the "algebraic structures". The transition from the classical, nineteenth-century, image of the discipline to the thear of ideals, from Richard Dedekind to Emmy Noether, and culminating with the publication in 1930 of Bartel L. van der Waerden's Moderne Algebra. Following its enormous success in algebra, the structural approach has been widely adopted in other mathematical domains since 1930s. But what is a mathematical structure and what is the place of this notion within the whole fabric of mathematics? Part Two describes the historical roots, the early stages and the interconnections between three attempts to address these questions from a purely formal, mathematical perspective: Oystein Ore's lattice-theoretical theory of structures, Nicolas Bourbaki's theory of structures, and the theory of categories and functors."--BOOK JACKET.".
- catalog description "Includes bibliographical references (p. [399]-431) and indexes.".
- catalog description "Introduction: Structures in Mathematics -- Structures in Algebra: Changing Images -- Richard Dedekind: Number and Ideals -- David Hilbert: Algebra and Axiomatics -- Concrete and Abstracts: Numbers, Polynomials, Rings -- Emmy Noether: Ideals and Structures -- Oystein Ore: Algebraic Structures -- Nicolas Bourbaki: Theory of Structures -- Category Theory: Early Stages -- Categories and Images of Mathematics.".
- catalog extent "451 p. :".
- catalog identifier "3764370025".
- catalog issued "2004".
- catalog issued "c2004.".
- catalog language "eng".
- catalog publisher "Basel ; Boston : Birkhäuser,".
- catalog subject "512.009 21".
- catalog subject "Algebra History.".
- catalog subject "Algebra.".
- catalog subject "Categories (Mathematics)".
- catalog subject "Mathematics.".
- catalog subject "QA151 .C67 2004".
- catalog tableOfContents "Introduction: Structures in Mathematics -- Structures in Algebra: Changing Images -- Richard Dedekind: Number and Ideals -- David Hilbert: Algebra and Axiomatics -- Concrete and Abstracts: Numbers, Polynomials, Rings -- Emmy Noether: Ideals and Structures -- Oystein Ore: Algebraic Structures -- Nicolas Bourbaki: Theory of Structures -- Category Theory: Early Stages -- Categories and Images of Mathematics.".
- catalog title "Modern algebra and the rise of mathematical structures / Leo Corry.".
- catalog type "History. fast".
- catalog type "text".