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Computability: a mathematical sketchbook
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ISBN: 9780387941745 0387941746 Year: 1994 Publisher: Berlin: Springer,

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Book
Constructive analysis
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ISBN: 3540150668 0387150668 9783642649059 364264905X 3642616674 9783540150664 Year: 1985 Volume: 279 Publisher: Berlin: Springer,

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Varieties of constructive mathematics
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Year: 1988 Publisher: Cambridge: Cambridge university press,

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Techniques of Constructive Analysis
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ISBN: 0387381473 Year: 2006 Publisher: New York, NY : Springer New York : Imprint: Springer,

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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.


Book
Representations of preferences orderings
Authors: ---
ISBN: 3540588396 3642514952 0387588396 9783540588399 Year: 1995 Volume: 422 Publisher: Berlin: Springer,

Techniques of constructive analysis
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ISBN: 9780387336466 038733646X Year: 2006 Publisher: New York (N.Y.) : Springer,

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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.


Digital
Techniques of Constructive Analysis
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ISBN: 9780387381473 Year: 2006 Publisher: New York, NY Springer Science+Business Media, LLC

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Digital
Apartness and Uniformity : A Constructive Development
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ISBN: 9783642224157 Year: 2011 Publisher: Berlin, Heidelberg Springer Berlin Heidelberg

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Book
Techniques of Constructive Analysis
Authors: --- ---
ISBN: 9780387381473 Year: 2006 Publisher: New York NY Springer New York

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Abstract

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.

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