The Strength Of Nonstandard Analysis

The Strength of Nonstandard Analysis PDF
Author: Imme van den Berg
Publisher: Springer Science & Business Media
ISBN: 3211499059
Size: 50.47 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 401
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This book reflects the progress made in the forty years since the appearance of Abraham Robinson’s revolutionary book Nonstandard Analysis in the foundations of mathematics and logic, number theory, statistics and probability, in ordinary, partial and stochastic differential equations and in education. The contributions are clear and essentially self-contained.

Nonstandard Analysis

Nonstandard Analysis PDF
Author: Leif O. Arkeryd
Publisher: Springer Science & Business Media
ISBN: 9401155445
Size: 45.18 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 366
View: 6383

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1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im portant field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual ap proach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) invention - providing new, rich structures that are useful in modelling and representation, as well as being of interest in their own right. The aim of the present volume is to make the power and range of appli cability of NSA more widely known and available to research mathemati cians.

Nonstandard Analysis And Its Applications

Nonstandard Analysis and Its Applications PDF
Author: Nigel Cutland
Publisher: Cambridge University Press
ISBN: 052135109X
Size: 43.58 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 346
View: 3339

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This textbook is an introduction to non-standard analysis and to its many applications. Non standard analysis (NSA) is a subject of great research interest both in its own right and as a tool for answering questions in subjects such as functional analysis, probability, mathematical physics and topology. The book arises from a conference held in July 1986 at the University of Hull which was designed to provide both an introduction to the subject through introductory lectures, and surveys of the state of research. The first part of the book is devoted to the introductory lectures and the second part consists of presentations of applications of NSA to dynamical systems, topology, automata and orderings on words, the non- linear Boltzmann equation and integration on non-standard hulls of vector lattices. One of the book's attractions is that a standard notation is used throughout so the underlying theory is easily applied in a number of different settings. Consequently this book will be ideal for graduate students and research mathematicians coming to the subject for the first time and it will provide an attractive and stimulating account of the subject.

The Axiom Of Choice

The Axiom of Choice PDF
Author: Thomas J. Jech
Publisher: Courier Corporation
ISBN: 0486466248
Size: 19.95 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 202
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Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.

A Companion To Relativism

A Companion to Relativism PDF
Author: Steven D. Hales
Publisher: John Wiley & Sons
ISBN: 9781444392487
Size: 77.49 MB
Format: PDF
Category : Philosophy
Languages : en
Pages : 648
View: 1695

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A Companion to Relativism presents original contributions from leading scholars that address the latest thinking on the role of relativism in the philosophy of language, epistemology, ethics, philosophy of science, logic, and metaphysics. Features original contributions from many of the leading figures working on various aspects of relativism Presents a substantial, broad range of current thinking about relativism Addresses relativism from many of the major subfields of philosophy, including philosophy of language, epistemology, ethics, philosophy of science, logic, and metaphysics

Provability Computability And Reflection

Provability  Computability and Reflection PDF
Author: Lev D. Beklemishev
Publisher: Elsevier
ISBN: 9780080954851
Size: 40.31 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 201
View: 1905

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Provability, Computability and Reflection

Philosophy Of Mathematics

Philosophy of Mathematics PDF
Author: Vincent F. Hendricks
Publisher: Automatic Press / VIP
ISBN:
Size: 74.89 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 342
View: 7114

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Interviews of more than two dozen scholars about the philosophy of mathematics, their interests in the field, and their ideas about future developments.

Mathematica Japonicae

Mathematica Japonicae PDF
Author:
Publisher:
ISBN:
Size: 39.26 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages :
View: 3638

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Numerical Methods For Ordinary Differential Equations

Numerical Methods for Ordinary Differential Equations PDF
Author: Alfredo Bellen
Publisher: Springer
ISBN: 9783540514787
Size: 78.72 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 140
View: 985

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Developments in numerical initial value ode methods were the focal topic of the meeting at L'Aquila which explord the connections between the classical background and new research areas such as differental-algebraic equations, delay integral and integro-differential equations, stability properties, continuous extensions (interpolants for Runge-Kutta methods and their applications, effective stepsize control, parallel algorithms for small- and large-scale parallel architectures). The resulting proceedings address many of these topics in both research and survey papers.

Encyclopedia Of Philosophy

Encyclopedia of Philosophy PDF
Author: Donald M. Borchert
Publisher: Thomson Gale/MacMillan Reference USA
ISBN: 9780028657820
Size: 50.86 MB
Format: PDF, ePub, Docs
Category : Electronic books
Languages : en
Pages : 6200
View: 4609

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This volume, covering entries from "Cabanis, Pierre-Jean Georges" to "Destutt de Tracy, Antoine Louis Claude, Comte," presents articles on Eastern and Western philosophies, medical and scientific ethics, the Holocaust, terrorism, censorship, biographical entries, and much more.

Mathematical Reviews

Mathematical Reviews PDF
Author:
Publisher:
ISBN:
Size: 48.56 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages :
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