Nonstandard Analysis In Practice

Author : Francine Diener,Marc Diener
Publisher : Springer Science & Business Media
Page : 262 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642577581

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Nonstandard Analysis in Practice by Francine Diener,Marc Diener Pdf

This book introduces the graduate mathematician and researcher to the effective use of nonstandard analysis (NSA). It provides a tutorial introduction to this modern theory of infinitesimals, followed by nine examples of applications, including complex analysis, stochastic differential equations, differential geometry, topology, probability, integration, and asymptotics. It ends with remarks on teaching with infinitesimals.

Author : Francine Diener
Publisher : Unknown
Page : 250 pages
File Size : 54,7 Mb
Release : 1995
Category : Nonstandard mathematical analysis
ISBN : 0387602976

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Nonstandard Analysis in Practice by Francine Diener Pdf

Author : Robert Goldblatt
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 53,5 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 : Abraham Robinson
Publisher : Princeton University Press
Page : 308 pages
File Size : 54,5 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 : Vladimir Kanovei,Michael Reeken
Publisher : Springer Science & Business Media
Page : 421 pages
File Size : 51,7 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 : J.E. Rubio
Publisher : CRC Press
Page : 380 pages
File Size : 51,7 Mb
Release : 1994-08-10
Category : Mathematics
ISBN : 0824792815

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Optimization and Nonstandard Analysis by J.E. Rubio Pdf

This text presents an up-to-date overview of optimization and control theory, including existence theory, modelling, approximation and numerical methods. It also provides a self-contained treatment of the theory and practice of non-standard analysis and its applications, illustrated with problems and research material based on optimization theory. A complete set of detailed exercises and a thorough bibliography arranged by topic are included.;College or university bookstores may order five or more copies at a special student price, available upon request.

Author : Albert E. Hurd,Peter A. Loeb
Publisher : Academic Press
Page : 232 pages
File Size : 45,7 Mb
Release : 1985-10-01
Category : Mathematics
ISBN : 0080874371

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An Introduction to Nonstandard Real Analysis by Albert E. Hurd,Peter A. Loeb Pdf

The aim of this book is to make Robinson's discovery, and some of the subsequent research, available to students with a background in undergraduate mathematics. In its various forms, the manuscript was used by the second author in several graduate courses at the University of Illinois at Urbana-Champaign. The first chapter and parts of the rest of the book can be used in an advanced undergraduate course. Research mathematicians who want a quick introduction to nonstandard analysis will also find it useful. The main addition of this book to the contributions of previous textbooks on nonstandard analysis (12,37,42,46) is the first chapter, which eases the reader into the subject with an elementary model suitable for the calculus, and the fourth chapter on measure theory in nonstandard models.

Author : Imme van den Berg,Vitor Neves
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 43,6 Mb
Release : 2007-12-03
Category : Mathematics
ISBN : 9783211499054

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The Strength of Nonstandard Analysis by Imme van den Berg,Vitor Neves Pdf

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.

Author : H. Jerome Keisler
Publisher : Orange Groove Books
Page : 992 pages
File Size : 42,7 Mb
Release : 2009-09-01
Category : Mathematics
ISBN : 1616100311

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Elementary Calculus by H. Jerome Keisler Pdf

Author : Ali Enayat,Roman Kossak
Publisher : American Mathematical Soc.
Page : 167 pages
File Size : 43,9 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 : Mangatiana A. Robdera
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 49,5 Mb
Release : 2011-06-27
Category : Mathematics
ISBN : 9780857293473

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A Concise Approach to Mathematical Analysis by Mangatiana A. Robdera Pdf

This text introduces to undergraduates the more abstract concepts of advanced calculus, smoothing the transition from standard calculus to the more rigorous approach of proof writing and a deeper understanding of mathematical analysis. The first part deals with the basic foundation of analysis on the real line; the second part studies more abstract notions in mathematical analysis. Each topic contains a brief introduction and detailed examples.

Author : R. Lutz,M. Goze
Publisher : Springer
Page : 275 pages
File Size : 51,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540708087

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Nonstandard Analysis. by R. Lutz,M. Goze Pdf

Author : Mauro Di Nasso,Isaac Goldbring,Martino Lupini
Publisher : Springer
Page : 206 pages
File Size : 40,6 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 : Douglas Samuel Jones
Publisher : World Scientific
Page : 184 pages
File Size : 50,7 Mb
Release : 1997
Category : Mathematics
ISBN : 9810229151

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Introduction to Asymptotics by Douglas Samuel Jones Pdf

"A very attractive feature of the book is the numerous examples illustrating the methods. A fine collection of exercises enriches each chapter, challenging the reader to check his progress in understanding the methods".Mathematical Reviews"As an introductory book to asymptotics, with chapters on uniform asymptotics and exponential asymptotics, this book clearly fills a gap it has a friendly size and contains many convincing numerical examples and interesting exercises. Hence, I recommend the book to everyone who works in asymptotics".SIAM, 1998" it is an excellent book that contains interesting results and methods for the researchers. It will be useful for the students interested in analysis and lectures on asymptotic methods The reviewer recommends the book to everyone who is interested in analysis, engineers and specialists in ODE-s"Acta Sci. Math. (Szeged), 1999

Author : Bart van Kerkhove,jean paul van bendegem
Publisher : Springer Science & Business Media
Page : 243 pages
File Size : 49,9 Mb
Release : 2007-06-01
Category : Science
ISBN : 9781402050343

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Perspectives on Mathematical Practices by Bart van Kerkhove,jean paul van bendegem Pdf

In the eyes of the editors, this book will be considered a success if it can convince its readers of the following: that it is warranted to dream of a realistic and full-fledged theory of mathematical practices, in the plural. If such a theory is possible, it would mean that a number of presently existing fierce oppositions between philosophers, sociologists, educators, and other parties involved, are in fact illusory.