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## Filters

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Book Review: Radically elementary probability theory

1989
*
Bulletin of the American Mathematical Society
*

*Nonstandard*

*analysis*was created by Abraham Robinson in 1960 to lay a rigorous

*foundation*

*for*infinitesimals in

*analysis*. ... As a replacement

*for*the conventional measure theoretic

*foundations*of probability, Nelson proposes elementary finite probability spaces and a "tiny bit of

*nonstandard*

*analysis*." ...

##
###
Book Review: Foundations of infinitesimal stochastic analysis

1989
*
Bulletin of the American Mathematical Society
*

Consequently,

doi:10.1090/s0273-0979-1989-15832-1
fatcat:3xc6f7tuqzgitnkcf3yi33jszy
*nonstandard**analysis*has developed as an extension of*standard**analysis*, and has tended to use*standard*concepts as a point of reference and a criterion*for*whether*nonstandard*results are ... The Anderson construction represents half of a common method*for*using*nonstandard**analysis*to solve problems expressed in the language of*standard*mathematics. ...##
###
Codesign for real-time video applications

1998
*
Computers and Mathematics with Applications
*

*Standard*vs.

*nonstandard*distinction: A watershed in the

*foundations*of mathematics. 7.

*Standard*vs.

*nonstandard*logic: Higher-order, modal, and first-order logics. 8. ... New

*foundations*

*for*mathematical theories. Contents: Preface. Part I. Fundamentals of compilation. 1. Introduction. 2. Lexical

*analysis*. 3. Parsing. 4. Abstract syntax. 5. Semantic

*analysis*. 6. ...

##
###
Page 1189 of Mathematical Reviews Vol. , Issue 93c
[page]

1993
*
Mathematical Reviews
*

The editors note that although many historians of mathematics are irritated when

*nonstandard**analysis*is invoked in discussing earlier work, there are ultimately only two possible*foundations**for*calcu ... Dauben, Abraham Robinson: les infinitésimaux, l’analyse non*standard*, et les fondements des mathématiques [Abraham Robinson: infinitesimals,*nonstandard**analysis*and the*foundations*of mathematics] (157 ...##
###
Page 4420 of Mathematical Reviews Vol. , Issue 86j
[page]

1986
*
Mathematical Reviews
*

Whether or not such an

*analysis*of a proof written within the language of*nonstandard**analysis**for*a*standard*theorem shows that the proof is “simpler” and that the proof concepts have special relevance ... Using these concepts the authors analyze some*nonstandard*proofs of various well-known*standard*theorems of classical elementary*analysis*. ...##
###
Page 4842 of Mathematical Reviews Vol. , Issue 81M
[page]

1981
*
Mathematical Reviews
*

*For*persons unfamiliar with

*nonstandard*

*analysis*, it provides a painless way

*for*them to see what

*nonstandard*

*analysis*is all about without having to wade in too far. ...

*For*example, a topological space is Hausdorff provided Vx,y p(x)NuW(y)=2 (compared to the

*standard*definition Vx,y 3AE%,, BEB, such that AM B=, where &, denotes a basis

*for*the topology at p). ...

##
###
Language, truth and logic in mathematics

1998
*
Computers and Mathematics with Applications
*

*Standard*vs.

*nonstandard*distinction: A watershed in the

*foundations*of mathematics. 7.

*Standard*vs.

*nonstandard*logic: Higher-order, modal, and first-order logics. 8. ... New

*foundations*

*for*mathematical theories. Contents: Preface. Part I. Fundamentals of compilation. 1. Introduction. 2. Lexical

*analysis*. 3. Parsing. 4. Abstract syntax. 5. Semantic

*analysis*. 6. ...

##
###
Bioinformatics: The machine learning approach

1998
*
Computers and Mathematics with Applications
*

*Standard*vs.

*nonstandard*distinction: A watershed in the

*foundations*of mathematics. 7.

*Standard*vs.

*nonstandard*logic: Higher-order, modal, and first-order logics. 8. ... New

*foundations*

*for*mathematical theories. Contents: Preface. Part I. Fundamentals of compilation. 1. Introduction. 2. Lexical

*analysis*. 3. Parsing. 4. Abstract syntax. 5. Semantic

*analysis*. 6. ...

##
###
Web board 3.0

1998
*
Computers and Mathematics with Applications
*

*Standard*vs.

*nonstandard*distinction: A watershed in the

*foundations*of mathematics. 7.

*Standard*vs.

*nonstandard*logic: Higher-order, modal, and first-order logics. 8. ... New

*foundations*

*for*mathematical theories. Contents: Preface. Part I. Fundamentals of compilation. 1. Introduction. 2. Lexical

*analysis*. 3. Parsing. 4. Abstract syntax. 5. Semantic

*analysis*. 6. ...

##
###
Modern compiler implementation in Java: Revised and expanded edition

1998
*
Computers and Mathematics with Applications
*

*Standard*vs.

*nonstandard*distinction: A watershed in the

*foundations*of mathematics. 7.

*Standard*vs.

*nonstandard*logic: Higher-order, modal, and first-order logics. 8. ... New

*foundations*

*for*mathematical theories. Contents: Preface. Part I. Fundamentals of compilation. 1. Introduction. 2. Lexical

*analysis*. 3. Parsing. 4. Abstract syntax. 5. Semantic

*analysis*. 6. ...

##
###
Book Review: Nonstandard methods in stochastic analysis and mathematical physics

1987
*
Bulletin of the American Mathematical Society
*

A large part of the book under review is devoted to applications of

doi:10.1090/s0273-0979-1987-15607-2
fatcat:f77lhpng4jd5thzptdttwbx3da
*nonstandard**analysis*to various aspects of probability theory, and the*foundations*are presented in Chapter three. ... These models are finite from the*nonstandard*, but infinite from the*standard*point of view. Their use makes*for*an intuitive clarity and ease of calculation which can simplify difficult problems. ...##
###
The netscape programmer's guide: Using OLE to build componentware apps

1998
*
Computers and Mathematics with Applications
*

*Standard*vs.

*nonstandard*distinction: A watershed in the

*foundations*of mathematics. 7.

*Standard*vs.

*nonstandard*logic: Higher-order, modal, and first-order logics. 8. ... New

*foundations*

*for*mathematical theories. Contents: Preface. Part I. Fundamentals of compilation. 1. Introduction. 2. Lexical

*analysis*. 3. Parsing. 4. Abstract syntax. 5. Semantic

*analysis*. 6. ...

##
###
Nonstandard analysis: Its creator and place

2013
*
Journal of Applied and Industrial Mathematics
*

This is a biographical sketch and tribute to Abraham Robinson (1918-1974) on the 95th anniversary of his birth with a short discussion of the place of

doi:10.1134/s1990478913030010
fatcat:it3v7eh3uffapjo3gsuppepn2i
*nonstandard**analysis*in the present-day mathematics ...*Nonstandard**analysis*postulates that each infinite collection of objects has at least one*nonstandard*element, and every collection of*standard*elements is itself*standard*. ... All in all,*nonstandard**analysis*opens up some new opportunities that are unavailable in "*standard*" mathematics. ...##
###
Cofinite numbers, nonstandard analysis, and mechanics

2010
*
Journal of Applied and Industrial Mathematics
*

We demonstrate the mathematical insignificance of the versions of

doi:10.1134/s1990478910020079
fatcat:zedqqrp2afcixeuciqbp7puvje
*nonstandard**analysis*proposed in the articles by A. F. Revuzhenko. ... and*foundations*of*nonstandard**analysis*. ... According to this principle, every statement of usual mathematics valid*for*all*standard*elements of an infinite set holds*for*its*nonstandard*elements as well. ...##
###
Page 2542 of Mathematical Reviews Vol. , Issue 84g
[page]

1984
*
Mathematical Reviews
*

Robinson gave an exact

*foundation*of the calculus of infinitesimals and showed that*nonstandard**analysis*is a general method with applications in many mathematical theories. ... The author constructs an interesting normal form*for*formulas of*nonstandard*arithmetic. Let N* be a*nonstandard*model of arithmetic, and let N be its*standard*submodel. ...
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