Constructive Analysis
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Constructive Analysis
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Author : E. Bishop
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Constructive Analysis written by E. Bishop and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This work grew out of Errett Bishop's fundamental treatise 'Founda tions of Constructive Analysis' (FCA), which appeared in 1967 and which contained the bountiful harvest of a remarkably short period of research by its author. Truly, FCA was an exceptional book, not only because of the quantity of original material it contained, but also as a demonstration of the practicability of a program which most ma thematicians believed impossible to carry out. Errett's book went out of print shortly after its publication, and no second edition was produced by its publishers. Some years later, 'by a set of curious chances', it was agreed that a new edition of FCA would be published by Springer Verlag, the revision being carried out by me under Errett's supervision; at the same time, Errett gener ously insisted that I become a joint author. The revision turned out to be much more substantial than we had anticipated, and took longer than we would have wished. Indeed, tragically, Errett died before the work was completed. The present book is the result of our efforts. Although substantially based on FCA, it contains so much new material, and such full revision and expansion of the old, that it is essentially a new book. For this reason, and also to preserve the integrity of the original, I decided to give our joint work a title of its own. Most of the new material outside Chapter 5 originated with Errett.
Foundations Of Constructive Analysis
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Author : Errett Bishop
language : en
Publisher:
Release Date : 1967
Foundations Of Constructive Analysis written by Errett Bishop and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Constructive mathematics categories.
Techniques Of Constructive Analysis
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Author : Douglas S. Bridges
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-30
Techniques Of Constructive Analysis written by Douglas S. Bridges and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-30 with Mathematics categories.
This book is an introduction to constructive mathematics with an emphasis on techniques and results 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. The first appendix gathers together some basic notions about sets and orders, the second gives the axioms for intuitionistic logic. 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 necessary.
Real Analysis
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Author : Mark Bridger
language : en
Publisher: John Wiley & Sons
Release Date : 2011-10-14
Real Analysis written by Mark Bridger and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-14 with Mathematics categories.
A unique approach to analysis that lets you apply mathematics across a range of subjects This innovative text sets forth a thoroughly rigorous modern account of the theoretical underpinnings of calculus: continuity, differentiability, and convergence. Using a constructive approach, every proof of every result is direct and ultimately computationally verifiable. In particular, existence is never established by showing that the assumption of non-existence leads to a contradiction. The ultimate consequence of this method is that it makes sense—not just to math majors but also to students from all branches of the sciences. The text begins with a construction of the real numbers beginning with the rationals, using interval arithmetic. This introduces readers to the reasoning and proof-writing skills necessary for doing and communicating mathematics, and it sets the foundation for the rest of the text, which includes: Early use of the Completeness Theorem to prove a helpful Inverse Function Theorem Sequences, limits and series, and the careful derivation of formulas and estimates for important functions Emphasis on uniform continuity and its consequences, such as boundedness and the extension of uniformly continuous functions from dense subsets Construction of the Riemann integral for functions uniformly continuous on an interval, and its extension to improper integrals Differentiation, emphasizing the derivative as a function rather than a pointwise limit Properties of sequences and series of continuous and differentiable functions Fourier series and an introduction to more advanced ideas in functional analysis Examples throughout the text demonstrate the application of new concepts. Readers can test their own skills with problems and projects ranging in difficulty from basic to challenging. This book is designed mainly for an undergraduate course, and the author understands that many readers will not go on to more advanced pure mathematics. He therefore emphasizes an approach to mathematical analysis that can be applied across a range of subjects in engineering and the sciences.
Constructive Analysis
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Author : Kristoffer Ahlström
language : en
Publisher:
Release Date : 2007
Constructive Analysis written by Kristoffer Ahlström and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Inquiry (Theory of knowledge) categories.
Ethnomethodology Conversation Analysis And Constructive Analysis
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Author : Graham Button
language : en
Publisher: Taylor & Francis
Release Date : 2022-09-23
Ethnomethodology Conversation Analysis And Constructive Analysis written by Graham Button and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-23 with Social Science categories.
This book revisits the arguments by which Harvey Sacks and Harold Garfinkel opposed the widespread attempt in the social sciences to construct disciplinary theories and methods in place of common-sense knowledge of human action, and proposed instead an alternative that would investigate the organised methods of natural language use and common-sense reasoning that constitute social orders – arguments that led to the establishment and proliferation of ethnomethodology and conversation analysis. As the very "constructive analysis" that they opposed has begun to be incorporated into influential lines of research in ethnomethodology and conversation analysis, the authors return to the founding insights of the field and reiterate the importance of Garfinkel and Sacks’ original and controversial proposals for an "alternate" sociology of practical action and practical reasoning. Showing how constructive analysis has become entrenched in ethnomethodology and conversation analysis and arguing for a need to "re-boot" these approaches, this volume constitutes a call for a renewal of the radical alternative proposed by Garfinkel and Sacks.
Constructive Analysis
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Author : E. Bishop
language : en
Publisher: Springer
Release Date : 1985-08-01
Constructive Analysis written by E. Bishop and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-08-01 with Mathematics categories.
This work grew out of Errett Bishop's fundamental treatise 'Founda tions of Constructive Analysis' (FCA), which appeared in 1967 and which contained the bountiful harvest of a remarkably short period of research by its author. Truly, FCA was an exceptional book, not only because of the quantity of original material it contained, but also as a demonstration of the practicability of a program which most ma thematicians believed impossible to carry out. Errett's book went out of print shortly after its publication, and no second edition was produced by its publishers. Some years later, 'by a set of curious chances', it was agreed that a new edition of FCA would be published by Springer Verlag, the revision being carried out by me under Errett's supervision; at the same time, Errett gener ously insisted that I become a joint author. The revision turned out to be much more substantial than we had anticipated, and took longer than we would have wished. Indeed, tragically, Errett died before the work was completed. The present book is the result of our efforts. Although substantially based on FCA, it contains so much new material, and such full revision and expansion of the old, that it is essentially a new book. For this reason, and also to preserve the integrity of the original, I decided to give our joint work a title of its own. Most of the new material outside Chapter 5 originated with Errett.
Constructive Analysis Of Semicircular Elements
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Author : Ilwoo Cho
language : en
Publisher: CRC Press
Release Date : 2023-05-12
Constructive Analysis Of Semicircular Elements written by Ilwoo Cho and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-12 with Mathematics categories.
Suitable for graduate students and professional researchers in operator theory and/or analysis Numerous applications in related scientific fields and areas.
Lectures On Constructive Mathematical Analysis
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Author : Boris Abramovich Kushner
language : en
Publisher: American Mathematical Soc.
Release Date : 1984-12-31
Lectures On Constructive Mathematical Analysis written by Boris Abramovich Kushner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-12-31 with Mathematics categories.
The basis of this book was a special course given by the author at the Mechanics-Mathematics Faculty of Moscow University. The material presumes almost no previous knowledge and is completely understandable to a reader who is in command of a standard course of mathematical analysis. There are an extensive bibliography and indexes which will be helpful to students.
Constructive Real Analysis
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Author : Allen A. Goldstein
language : en
Publisher: Courier Corporation
Release Date : 2013-05-20
Constructive Real Analysis written by Allen A. Goldstein and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-20 with Mathematics categories.
This text introduces students of mathematics, science, and technology to the methods of applied functional analysis and applied convexity. Topics include iterations and fixed points, metric spaces, nonlinear programming, applications to integral equations, and more. 1967 edition.