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Handbook Of Constructive Mathematics


Handbook Of Constructive Mathematics
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Handbook Of Constructive Mathematics


Handbook Of Constructive Mathematics
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Author : Douglas Bridges
language : en
Publisher: Cambridge University Press
Release Date : 2023-05-11

Handbook Of Constructive Mathematics written by Douglas Bridges and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-11 with Mathematics categories.


Gives a complete overview of modern constructive mathematics and its applications through surveys by leading experts.



A Course In Constructive Algebra


A Course In Constructive Algebra
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Author : Ray Mines
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-10

A Course In Constructive Algebra written by Ray Mines 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 2012-09-10 with Mathematics categories.


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.



Handbook Of Analysis And Its Foundations


Handbook Of Analysis And Its Foundations
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Author : Eric Schechter
language : en
Publisher: Academic Press
Release Date : 1996-10-24

Handbook Of Analysis And Its Foundations written by Eric Schechter and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-10-24 with Mathematics categories.


Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/



Foundations Of Constructive Probability Theory


Foundations Of Constructive Probability Theory
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Author : Yuen-Kwok Chan
language : en
Publisher: Cambridge University Press
Release Date : 2021-05-27

Foundations Of Constructive Probability Theory written by Yuen-Kwok Chan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-27 with Mathematics categories.


This book provides a systematic and general theory of probability within the framework of constructive mathematics.



Foundations Of Constructive Analysis


Foundations Of Constructive Analysis
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Author : Errett Bishop
language : en
Publisher: Ishi Press
Release Date : 2012-07

Foundations Of Constructive Analysis written by Errett Bishop and has been published by Ishi Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07 with Mathematics categories.


This book, Foundations of Constructive Analysis, founded the field of constructive analysis because it proved most of the important theorems in real analysis by constructive methods. The author, Errett Albert Bishop, born July 10, 1928, was an American mathematician known for his work on analysis. In the later part of his life Bishop was seen as the leading mathematician in the area of Constructive mathematics. From 1965 until his death, he was professor at the University of California at San Diego.



Handbook Of Mathematical Logic


Handbook Of Mathematical Logic
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Author : J. Barwise
language : en
Publisher: Elsevier
Release Date : 1982-03-01

Handbook Of Mathematical Logic written by J. Barwise and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-03-01 with Computers categories.


The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own.



Mathematics For Computation M4c


Mathematics For Computation M4c
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Author : Marco Benini
language : en
Publisher: World Scientific
Release Date : 2023-03-21

Mathematics For Computation M4c written by Marco Benini and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-21 with Mathematics categories.


The overall topic of the volume, Mathematics for Computation (M4C), is mathematics taking crucially into account the aspect of computation, investigating the interaction of mathematics with computation, bridging the gap between mathematics and computation wherever desirable and possible, and otherwise explaining why not.Recently, abstract mathematics has proved to have more computational content than ever expected. Indeed, the axiomatic method, originally intended to do away with concrete computations, seems to suit surprisingly well the programs-from-proofs paradigm, with abstraction helping not only clarity but also efficiency.Unlike computational mathematics, which rather focusses on objects of computational nature such as algorithms, the scope of M4C generally encompasses all the mathematics, including abstract concepts such as functions. The purpose of M4C actually is a strongly theory-based and therefore, is a more reliable and sustainable approach to actual computation, up to the systematic development of verified software.While M4C is situated within mathematical logic and the related area of theoretical computer science, in principle it involves all branches of mathematics, especially those which prompt computational considerations. In traditional terms, the topics of M4C include proof theory, constructive mathematics, complexity theory, reverse mathematics, type theory, category theory and domain theory.The aim of this volume is to provide a point of reference by presenting up-to-date contributions by some of the most active scholars in each field. A variety of approaches and techniques are represented to give as wide a view as possible and promote cross-fertilization between different styles and traditions.



Handbook Of Mathematical Logic


Handbook Of Mathematical Logic
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Author : Jon Barwise
language : en
Publisher: North-Holland
Release Date : 1977

Handbook Of Mathematical Logic written by Jon Barwise and has been published by North-Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with MATHEMATICS categories.




Handbook Of Mathematical Geodesy


Handbook Of Mathematical Geodesy
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Author : Willi Freeden
language : en
Publisher: Birkhäuser
Release Date : 2018-06-11

Handbook Of Mathematical Geodesy written by Willi Freeden and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-11 with Mathematics categories.


Written by leading experts, this book provides a clear and comprehensive survey of the “status quo” of the interrelating process and cross-fertilization of structures and methods in mathematical geodesy. Starting with a foundation of functional analysis, potential theory, constructive approximation, special function theory, and inverse problems, readers are subsequently introduced to today’s least squares approximation, spherical harmonics reflected spline and wavelet concepts, boundary value problems, Runge-Walsh framework, geodetic observables, geoidal modeling, ill-posed problems and regularizations, inverse gravimetry, and satellite gravity gradiometry. All chapters are self-contained and can be studied individually, making the book an ideal resource for both graduate students and active researchers who want to acquaint themselves with the mathematical aspects of modern geodesy.



A Guide To Functional Analysis


A Guide To Functional Analysis
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Author : Steven G. Krantz
language : en
Publisher: MAA
Release Date : 2013-06-06

A Guide To Functional Analysis written by Steven G. Krantz and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-06 with Mathematics categories.


This book is a quick but precise and careful introduction to the subject of functional analysis. It covers the basic topics that can be found in a basic graduate analysis text. But it also covers more sophisticated topics such as spectral theory, convexity, and fixed-point theorems. A special feature of the book is that it contains a great many examples and even some applications. It concludes with a statement and proof of Lomonosov's dramatic result about invariant subspaces.