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ISBN: 9780387966403
ID: 9780387966403
The constructive approach to mathematics has enjoyed a renaissance, caused in large part by the appearance of Errett Bishop`s book Foundations of constr`uctiue analysis in 1967, and by the subtle influences of the proliferation of powerful computers. Bishop demonstrated that pure mathematics can be developed from a constructive point of view while maintaining a continuity with classical terminology and spirit much more of classical mathematics was preserved than had been thought possible, and no classically false theorems resulted, as had been the case in other constructive schools such as intuitionism and Russian constructivism. The computers created a widespread awareness of the intuitive notion of an effecti ve procedure, and of computation in principle, in addi tion to stimulating the study of constructive algebra for actual implementation, and from the point of view of recursive function theory. In analysis, constructive problems arise instantly because we must start with the real numbers, and there is no finite procedure for deciding whether two given real numbers are equal or not (the real numbers are not discrete) . The main thrust of constructive mathematics was in the direction of analysis, although several mathematicians, including Kronecker and van der waerden, made important contributions to construc tive algebra. Heyting, working in intuitionistic algebra, concentrated on issues raised by considering algebraic structures over the real numbers, and so developed a handmaiden`of analysis rather than a theory of discrete algebraic structures. A Course in Constructive Algebra: The constructive approach to mathematics has enjoyed a renaissance, caused in large part by the appearance of Errett Bishop`s book Foundations of constr`uctiue analysis in 1967, and by the subtle influences of the proliferation of powerful computers. Bishop demonstrated that pure mathematics can be developed from a constructive point of view while maintaining a continuity with classical terminology and spirit much more of classical mathematics was preserved than had been thought possible, and no classically false theorems resulted, as had been the case in other constructive schools such as intuitionism and Russian constructivism. The computers created a widespread awareness of the intuitive notion of an effecti ve procedure, and of computation in principle, in addi tion to stimulating the study of constructive algebra for actual implementation, and from the point of view of recursive function theory. In analysis, constructive problems arise instantly because we must start with the real numbers, and there is no finite procedure for deciding whether two given real numbers are equal or not (the real numbers are not discrete) . The main thrust of constructive mathematics was in the direction of analysis, although several mathematicians, including Kronecker and van der waerden, made important contributions to construc tive algebra. Heyting, working in intuitionistic algebra, concentrated on issues raised by considering algebraic structures over the real numbers, and so developed a handmaiden`of analysis rather than a theory of discrete algebraic structures. Algebra, Springer
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ISBN: 9780387966403
ID: 9780387966403
A Course in Constructive Algebra: Paperback: Springer-Verlag New York Inc. : 9780387966403: 01 Dec 1987: Presents the fundamental structures of modern algebra from a constructive point of view. This book contains basic notions, and also covers PID's, field theory (including Galois theory), factorisation of polynomials, noetherian rings, valuation theory, and Dedekind domains. The constructive approach to mathematics has enjoyed a renaissance, caused in large part by the appearance of Errett Bishop's book Foundations of constr"uctiue analysis in 1967, and by the subtle influences of the proliferation of powerful computers. Bishop demonstrated that pure mathematics can be developed from a constructive point of view while maintaining a continuity with classical terminology and spirit; much more of classical mathematics was preserved than had been thought possible, and no classically false theorems resulted, as had been the case in other constructive schools such as intuitionism and Russian constructivism. The computers created a widespread awareness of the intuitive notion of an effecti ve procedure, and of computation in principle, in addi tion to stimulating the study of constructive algebra for actual implementation, and from the point of view of recursive function theory. In analysis, constructive problems arise instantly because we must start with the real numbers, and there is no finite procedure for deciding whether two given real numbers are equal or not (the real numbers are not discrete) . The main thrust of constructive mathematics was in the direction of analysis, although several mathematicians, including Kronecker and van der waerden, made important contributions to construc- tive algebra. Heyting, working in intuitionistic algebra, concentrated on issues raised by considering algebraic structures over the real numbers, and so developed a handmaiden'of analysis rather than a theory of discrete algebraic structures. Algebra, , , , A Course in Constructive Algebra, Ray Mines, 9780387966403, Springer-Verlag New York Inc., , , , ,, [PU: Springer]
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ISBN: 9780387966403
ID: 9780387966403
A Course in Constructive Algebra: Paperback: Springer-Verlag New York Inc. : 9780387966403: 01 Dec 1987: Presents the fundamental structures of modern algebra from a constructive point of view. This book contains basic notions, and also covers PID's, field theory (including Galois theory), factorisation of polynomials, noetherian rings, valuation theory, and Dedekind domains. The constructive approach to mathematics has enjoyed a renaissance, caused in large part by the appearance of Errett Bishop's book Foundations of constr"uctiue analysis in 1967, and by the subtle influences of the proliferation of powerful computers. Bishop demonstrated that pure mathematics can be developed from a constructive point of view while maintaining a continuity with classical terminology and spirit; much more of classical mathematics was preserved than had been thought possible, and no classically false theorems resulted, as had been the case in other constructive schools such as intuitionism and Russian constructivism. The computers created a widespread awareness of the intuitive notion of an effecti ve procedure, and of computation in principle, in addi tion to stimulating the study of constructive algebra for actual implementation, and from the point of view of recursive function theory. In analysis, constructive problems arise instantly because we must start with the real numbers, and there is no finite procedure for deciding whether two given real numbers are equal or not (the real numbers are not discrete) . The main thrust of constructive mathematics was in the direction of analysis, although several mathematicians, including Kronecker and van der waerden, made important contributions to construc- tive algebra. Heyting, working in intuitionistic algebra, concentrated on issues raised by considering algebraic structures over the real numbers, and so developed a handmaiden'of analysis rather than a theory of discrete algebraic structures. Algebra, , , , , , , , , , , ,, [PU: Springer]
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ISBN: 9780387966403
[ED: Softcover], [PU: Springer, Berlin], The constructive approach to mathematics has enjoyed a renaissance, caused in large part by the appearance of Errett Bishop's book Foundations of constr"uctiue analysis in 1967, and by the subtle influences of the proliferation of powerful computers. Bishop demonstrated that pure mathematics can be developed from a constructive point of view while maintaining a continuity with classical terminology and spirit much more of classical mathematics was preserved than had been thought possible, and no classically false theorems resulted, as had been the case in other constructive schools such as intuitionism and Russian constructivism. The computers created a widespread awareness of the intuitive notion of an effecti ve procedure, and of computation in principle, in addi tion to stimulating the study of constructive algebra for actual implementation, and from the point of view of recursive function theory. In analysis, constructive problems arise instantly because we must start with the real numbers, and there is no finite procedure for deciding whether two given real numbers are equal or not (the real numbers are not discrete) . The main thrust of constructive mathematics was in the direction of analysis, although several mathematicians, including Kronecker and van der waerden, made important contributions to construc tive algebra. Heyting, working in intuitionistic algebra, concentrated on issues raised by considering algebraic structures over the real numbers, and so developed a handmaiden'of analysis rather than a theory of discrete algebraic structures. xi, 344 S. 1 SW-Abb. Versandfertig in 3-5 Tagen, [SC: 0.00], Neuware, gewerbliches Angebot
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ISBN: 9780387966403
ID: 978038796640
The constructive approach to mathematics has recently enjoyed a renaissance. This was caused largely by the appearance of Bishop''s Foundations of Constructive Analysis, but also by the proliferation of powerful computers, which stimulated the development of constructive algebra for implementation purposes. In this book, the authors present the fundamental structures of modern algebra from a constructive point of view. Beginning with basic notions, the authors proceed to treat PID''s, field theory (including Galois theory), factorisation of polynomials, noetherian rings, valuation theory, and Dedekind domains. Ray Mines, Wim Ruitenburg, Books, Science and Nature, A Course in Constructive Algebra Books>Science and Nature, Springer
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Titel: | A Course in Constructive Algebra |
ISBN-Nummer: | 9780387966403 |
Detailangaben zum Buch - A Course in Constructive Algebra
EAN (ISBN-13): 9780387966403
ISBN (ISBN-10): 0387966404
Taschenbuch
Erscheinungsjahr: 2007
Herausgeber: Springer-Verlag GmbH
360 Seiten
Gewicht: 0,533 kg
Sprache: eng/Englisch
Buch in der Datenbank seit 18.04.2007 11:55:15
Buch zuletzt gefunden am 09.02.2017 14:26:48
ISBN/EAN: 9780387966403
ISBN - alternative Schreibweisen:
0-387-96640-4, 978-0-387-96640-3
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