Developments In Nonstandard Mathematics

Author : Nigel J Cutland,Vitor Neves,A F Oliveira,Jose Sousa-Pinto
Publisher : CRC Press
Page : 278 pages
File Size : 44,6 Mb
Release : 2020-01-30
Category : Mathematics
ISBN : 9781000724646

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Developments in Nonstandard Mathematics by Nigel J Cutland,Vitor Neves,A F Oliveira,Jose Sousa-Pinto Pdf

This book contains expository papers and articles reporting on recent research by leading world experts in nonstandard mathematics, arising from the International Colloquium on Nonstandard Mathematics held at the University of Aveiro, Portugal in July 1994. Nonstandard mathematics originated with Abraham Robinson, and the body of ideas that have developed from this theory of nonstandard analysis now vastly extends Robinson's work with infinitesimals. The range of applications includes measure and probability theory, stochastic analysis, differential equations, generalised functions, mathematical physics and differential geometry, moreover, the theory has implicaitons for the teaching of calculus and analysis. This volume contains papers touching on all of the abovbe topics, as well as a biographical note about Abraham Robinson based on the opening address given by W.A>J> Luxemburg - who knew Robinson - to the Aveiro conference which marked the 20th anniversary of Robinson's death. This book will be of particular interest to students and researchers in nonstandard analysis, measure theory, generalised functions and mathematical physics.

Author : A. E. Hurd
Publisher : Unknown
Page : 228 pages
File Size : 50,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662165449

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Nonstandard Analysis - Recent Developments by A. E. Hurd Pdf

Author : Albert Emerson Hurd
Publisher : Springer Verlag
Page : 213 pages
File Size : 52,5 Mb
Release : 1983-01-01
Category : Mathematics
ISBN : 0387122796

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Nonstandard Analysis--recent Developments by Albert Emerson Hurd Pdf

Author : Abraham Robinson
Publisher : Princeton University Press
Page : 308 pages
File Size : 46,8 Mb
Release : 2016-08-11
Category : Mathematics
ISBN : 9781400884223

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Non-standard Analysis by Abraham Robinson Pdf

Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.

Author : Martin Davis
Publisher : Courier Corporation
Page : 208 pages
File Size : 45,6 Mb
Release : 2014-06-10
Category : Mathematics
ISBN : 9780486152349

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Applied Nonstandard Analysis by Martin Davis Pdf

This applications-oriented text assumes no knowledge of mathematical logic in its development of nonstandard analysis techniques and their applications to elementary real analysis and topological and Hilbert space. 1977 edition.

Author : Ali Enayat,Roman Kossak
Publisher : American Mathematical Soc.
Page : 184 pages
File Size : 53,5 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821835357

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Nonstandard Models of Arithmetic and Set Theory by Ali Enayat,Roman Kossak Pdf

This is the proceedings of the AMS special session on nonstandard models of arithmetic and set theory held at the Joint Mathematics Meetings in Baltimore (MD). The volume opens with an essay from Haim Gaifman that probes the concept of non-standardness in mathematics and provides a fascinating mix of historical and philosophical insights into the nature of nonstandard mathematical structures. In particular, Gaifman compares and contrasts the discovery of nonstandard models with other key mathematical innovations, such as the introduction of various number systems, the modern concept of function, and non-Euclidean geometries. Other articles in the book present results related to nonstandard models in arithmetic and set theory, including a survey of known results on the Turing upper bounds of arithmetic sets and functions. The volume is suitable for graduate students and research mathematicians interested in logic, especially model theory.

Author : Nigel J. Cutland,Mauro Di Nasso,David A. Ross
Publisher : Cambridge University Press
Page : 248 pages
File Size : 52,8 Mb
Release : 2017-03-30
Category : Mathematics
ISBN : 9781108621298

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Nonstandard Methods and Applications in Mathematics by Nigel J. Cutland,Mauro Di Nasso,David A. Ross Pdf

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twenty-fifth publication in the Lecture Notes in Logic series, grew from a conference on Nonstandard Methods and Applications in Mathematics held in Pisa, Italy from 12–16 June, 2002. It contains ten peer-reviewed papers that aim to provide something more timely than a textbook, but less ephemeral than a conventional proceedings. Nonstandard analysis is one of the great achievements of modern applied mathematical logic. These articles consider the foundations of the subject, as well as its applications to pure and applied mathematics and mathematics education.

Author : Robert Goldblatt
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206156

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Lectures on the Hyperreals by Robert Goldblatt Pdf

An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers, but as a radically different way of viewing many standard mathematical concepts and constructions. It is a source of new ideas, objects and proofs, and a wealth of powerful new principles of reasoning. The book begins with the ultrapower construction of hyperreal number systems, and proceeds to develop one-variable calculus, analysis and topology from the nonstandard perspective. It then sets out the theory of enlargements of fragments of the mathematical universe, providing a foundation for the full-scale development of the nonstandard methodology. The final chapters apply this to a number of topics, including Loeb measure theory and its relation to Lebesgue measure on the real line. Highlights include an early introduction of the ideas of internal, external and hyperfinite sets, and a more axiomatic set-theoretic approach to enlargements than is usual.

Author : Vladimir Kanovei,Michael Reeken
Publisher : Springer Science & Business Media
Page : 421 pages
File Size : 48,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662089989

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Nonstandard Analysis, Axiomatically by Vladimir Kanovei,Michael Reeken Pdf

In the aftermath of the discoveries in foundations of mathematiC's there was surprisingly little effect on mathematics as a whole. If one looks at stan dard textbooks in different mathematical disciplines, especially those closer to what is referred to as applied mathematics, there is little trace of those developments outside of mathematical logic and model theory. But it seems fair to say that there is a widespread conviction that the principles embodied in the Zermelo - Fraenkel theory with Choice (ZFC) are a correct description of the set theoretic underpinnings of mathematics. In most textbooks of the kind referred to above, there is, of course, no discussion of these matters, and set theory is assumed informally, although more advanced principles like Choice or sometimes Replacement are often mentioned explicitly. This implicitly fixes a point of view of the mathemat ical universe which is at odds with the results in foundations. For example most mathematicians still take it for granted that the real number system is uniquely determined up to isomorphism, which is a correct point of view as long as one does not accept to look at "unnatural" interpretations of the membership relation.

Author : Sergio Albeverio,Wilhelm A. J. Luxemburg,Manfred P. H. Wolff
Publisher : Unknown
Page : 264 pages
File Size : 43,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401584524

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Advances in Analysis, Probability and Mathematical Physics by Sergio Albeverio,Wilhelm A. J. Luxemburg,Manfred P. H. Wolff Pdf

Author : Semën Samsonovich Kutateladze
Publisher : Unknown
Page : 324 pages
File Size : 53,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401143064

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Nonstandard Analysis and Vector Lattices by Semën Samsonovich Kutateladze Pdf

Author : Mauro Di Nasso,Isaac Goldbring,Martino Lupini
Publisher : Springer
Page : 206 pages
File Size : 42,6 Mb
Release : 2019-05-23
Category : Mathematics
ISBN : 9783030179564

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Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory by Mauro Di Nasso,Isaac Goldbring,Martino Lupini Pdf

The goal of this monograph is to give an accessible introduction to nonstandard methods and their applications, with an emphasis on combinatorics and Ramsey theory. It includes both new nonstandard proofs of classical results and recent developments initially obtained in the nonstandard setting. This makes it the first combinatorics-focused account of nonstandard methods to be aimed at a general (graduate-level) mathematical audience. This book will provide a natural starting point for researchers interested in approaching the rapidly growing literature on combinatorial results obtained via nonstandard methods. The primary audience consists of graduate students and specialists in logic and combinatorics who wish to pursue research at the interface between these areas.

Author : Peter Schuster,Ulrich Berger,Horst Osswald
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 43,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401597579

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Reuniting the Antipodes - Constructive and Nonstandard Views of the Continuum by Peter Schuster,Ulrich Berger,Horst Osswald Pdf

At first glance, Robinson's original form of nonstandard analysis appears nonconstructive in essence, because it makes a rather unrestricted use of classical logic and set theory and, in particular, of the axiom of choice. Recent developments, however, have given rise to the hope that the distance between constructive and nonstandard mathematics is actually much smaller than it appears. So the time was ripe for the first meeting dedicated simultaneously to both ways of doing mathematics – and to the current and future reunion of these seeming opposites. Consisting of peer-reviewed research and survey articles written on the occasion of such an event, this volume offers views of the continuum from various standpoints. Including historical and philosophical issues, the topics of the contributions range from the foundations, the practice, and the applications of constructive and nonstandard mathematics, to the interplay of these areas and the development of a unified theory.

Author : Abraham Robinson
Publisher : Princeton University Press
Page : 318 pages
File Size : 50,8 Mb
Release : 1974
Category : Mathematics
ISBN : 0691044902

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Non-standard Analysis by Abraham Robinson Pdf

Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.

Author : Sergio Albeverio,Jens Erik Fenstad,Raphael Høegh-Krohn,Tom Lindstrøm
Publisher : Courier Dover Publications
Page : 529 pages
File Size : 45,8 Mb
Release : 2009-02-26
Category : Mathematics
ISBN : 9780486468990

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Nonstandard Methods in Stochastic Analysis and Mathematical Physics by Sergio Albeverio,Jens Erik Fenstad,Raphael Høegh-Krohn,Tom Lindstrøm Pdf

Two-part treatment begins with a self-contained introduction to the subject, followed by applications to stochastic analysis and mathematical physics. "A welcome addition." — Bulletin of the American Mathematical Society. 1986 edition.