Author: Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Nonstandard analysis. Conference ; 4
Author: Nonstandard analysis. Conference ; 6
Author: Nonstandard analysis. Conference ; 2
Author: Nonstandard analysis. Conference ; 5
Author: Nonstandard Analysis for the Working Mathematician
Author: Peter A. LoebPublisher: Springer
ISBN: 9401773270
Category : Mathematics
Languages : en
Pages : 485
Book Description
Starting with a simple formulation accessible to all mathematicians, this second edition is designed to provide a thorough introduction to nonstandard analysis. Nonstandard analysis is now a well-developed, powerful instrument for solving open problems in almost all disciplines of mathematics; it is often used as a ‘secret weapon’ by those who know the technique. This book illuminates the subject with some of the most striking applications in analysis, topology, functional analysis, probability and stochastic analysis, as well as applications in economics and combinatorial number theory. The first chapter is designed to facilitate the beginner in learning this technique by starting with calculus and basic real analysis. The second chapter provides the reader with the most important tools of nonstandard analysis: the transfer principle, Keisler’s internal definition principle, the spill-over principle, and saturation. The remaining chapters of the book study different fields for applications; each begins with a gentle introduction before then exploring solutions to open problems. All chapters within this second edition have been reworked and updated, with several completely new chapters on compactifications and number theory. Nonstandard Analysis for the Working Mathematician will be accessible to both experts and non-experts, and will ultimately provide many new and helpful insights into the enterprise of mathematics.
Radically Elementary Probability Theory
Author: Edward NelsonPublisher: Princeton University Press
ISBN: 9780691084749
Category : Mathematics
Languages : en
Pages : 112
Book Description
Using only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.
Contemporary Stochastic Analysis - Proceedings Of The Conference
Author: Ekhaguere G O SPublisher: #N/A
ISBN: 981455605X
Category :
Languages : en
Pages : 160
Book Description
The following topical subjects were discussed: quantum stochastic calculus; unbounded quantum dynamical system; the principles of nonstandard analysis that are fundamental to an understanding of a modern approach to stochastic analysis on fractals; Brownian motion on nested fractals; stable processes; stochastic modelling of sexually transmitted diseases.
Proceedings of the Conference on Differential & Difference Equations and Applications
Author: Ravi P. AgarwalPublisher: Hindawi Publishing Corporation
ISBN: 9789775945389
Category : Difference equations
Languages : en
Pages : 1266
Book Description
Nonstandard Analysis and its Applications
Author: Nigel CutlandPublisher: Cambridge University Press
ISBN: 9780521359474
Category : Mathematics
Languages : en
Pages : 364
Book Description
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.
Nonstandard Analysis, Axiomatically
Author: Vladimir KanoveiPublisher: Springer Science & Business Media
ISBN: 366208998X
Category : Mathematics
Languages : en
Pages : 421
Book Description
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.