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Functional analysis --- Constructive mathematics --- 517.98 --- Mathematics, Constructive --- Logic, Symbolic and mathematical --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Functional analysis and operator theory --- Constructive mathematics. --- Functional analysis. --- 517.98 Functional analysis and operator theory --- Logique mathématique --- Mathématiques constructives --- Logique mathématique --- Mathématiques constructives --- Analyse fonctionnelle --- Logique mathématique. --- Mathématiques constructives. --- Logique mathématique. --- Mathématiques constructives.
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This text provides a rigorous, wide-ranging introduction to modern constructive analysis for anyone with a strong mathematical background who is interested in the challenge of developing mathematics algorithmically. The authors begin by outlining the history of constructive mathematics, and the logic and set theory that are used throughout the book. They then present a new construction of the real numbers, followed by the fundamentals of the constructive theory of metric and normed spaces; the lambda-technique (a special method that enables one to prove many results that appear, at first sight, to be nonconstructive); finite- dimensional and Hilbert spaces; and convexity, separation, and Hahn-Banach theorems. The book ends with a long chapter in which the work of the preceding ones is applied to operator theory and other aspects of functional analysis. Many results and proofs, especially in the later chapters, are of relatively recent origin. The intended readership includes advanced undergraduates, postgraduates, and professional researchers in mathematics and theoretical computer science. With this book, the authors hope to spread the message that doing mathematics constructively is interesting and challenging, and produces new, deep computational information.
Calculus. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal --- Logic, Symbolic and mathematical. --- Global analysis (Mathematics). --- Mathematics. --- Functional analysis. --- Operator theory. --- Mathematical Logic and Foundations. --- Analysis. --- Real Functions. --- Functional Analysis. --- Operator Theory. --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Mathematical logic. --- Analysis (Mathematics). --- Functions of real variables. --- Real variables
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Consumers' preferences --- Mathematical models --- Management --- Business & Economics --- Management Theory --- Mathematical models. --- Operations research --- Recherche opérationnelle --- Decision making --- Prise de décision --- Modèles mathématiques --- Ensembles ordonnés --- Mathématiques économiques --- Consumers' preferences - Mathematical models --- Ensembles ordonnés --- Mathématiques économiques --- Prise de décision --- Recherche opérationnelle --- Modèles mathématiques
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This book is an introduction to constructive mathematics with an emphasis on techniques and results that have been obtained in the last twenty years. The text covers fundamental theory of the real line and metric spaces, focusing on locatedness in normed spaces and with associated results about operators and their adjoints on a Hilbert space. Some of the other areas that are discussed in this book are the Ishihara's tricks, Separation theorems, and Locally convex spaces. There are two appendices to the book. The first gathers together some basic notions about sets and orders, the second gives the axioms for intuitionistic logic. The intended readership of the book consists of postgraduate or senior undergraduate students, and professional research mathematicians. No background in intuitionistic logic or constructive analysis is needed in order to read the book, but some familiarity with the classical theories of metric, normed and Hilbert spaces is recommended.
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Mathematical logic --- Operator theory --- Functional analysis --- Mathematical analysis --- analyse (wiskunde) --- functies (wiskunde) --- wiskunde --- logica
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Mathematical logic --- Topology --- Mathematical analysis --- Computer science --- Computer. Automation --- analyse (wiskunde) --- toegepaste informatica --- informatica --- wiskunde --- topologie
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This text provides a rigorous, wide-ranging introduction to modern constructive analysis for anyone with a strong mathematical background who is interested in the challenge of developing mathematics algorithmically. The authors begin by outlining the history of constructive mathematics, and the logic and set theory that are used throughout the book. They then present a new construction of the real numbers, followed by the fundamentals of the constructive theory of metric and normed spaces; the lambda-technique (a special method that enables one to prove many results that appear, at first sight, to be nonconstructive); finite- dimensional and Hilbert spaces; and convexity, separation, and Hahn-Banach theorems. The book ends with a long chapter in which the work of the preceding ones is applied to operator theory and other aspects of functional analysis. Many results and proofs, especially in the later chapters, are of relatively recent origin. The intended readership includes advanced undergraduates, postgraduates, and professional researchers in mathematics and theoretical computer science. With this book, the authors hope to spread the message that doing mathematics constructively is interesting and challenging, and produces new, deep computational information.
Mathematical logic --- Operator theory --- Functional analysis --- Mathematical analysis --- analyse (wiskunde) --- functies (wiskunde) --- wiskunde --- logica
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