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Book Review: Radically elementary probability theory

Loren D. Pitt
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."  ... 
doi:10.1090/s0273-0979-1989-15779-0 fatcat:hsvp7uj42ng5pelhjo5qqbb5du

Book Review: Foundations of infinitesimal stochastic analysis

D. N. Hoover
1989 Bulletin of the American Mathematical Society  
Consequently, 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.  ... 
doi:10.1090/s0273-0979-1989-15832-1 fatcat:3xc6f7tuqzgitnkcf3yi33jszy

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.  ... 
doi:10.1016/0898-1221(98)90197-3 fatcat:jxuxk4grf5eundgxgarwzyt6u4

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.  ... 
doi:10.1016/0898-1221(98)90195-x fatcat:lvxyocjhkrckje7aov4uvkaysu

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.  ... 
doi:10.1016/0898-1221(98)90194-8 fatcat:wbf2bvcimrarnn35myaxxuiiwe

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.  ... 
doi:10.1016/s0898-1221(98)00135-7 fatcat:x3s3knjy4jhhzhq42e2jzrfbiu

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.  ... 
doi:10.1016/0898-1221(98)90193-6 fatcat:2dzqnynhhneopn4ylddj4euysq

Book Review: Nonstandard methods in stochastic analysis and mathematical physics

A. E. Hurd
1987 Bulletin of the American Mathematical Society  
A large part of the book under review is devoted to applications of 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.  ... 
doi:10.1090/s0273-0979-1987-15607-2 fatcat:f77lhpng4jd5thzptdttwbx3da

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.  ... 
doi:10.1016/0898-1221(98)90196-1 fatcat:kdzy4gzr3ne2hdddmrenhz2vu4

Nonstandard analysis: Its creator and place

S. S. Kutateladze
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 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.  ... 
doi:10.1134/s1990478913030010 fatcat:it3v7eh3uffapjo3gsuppepn2i

Cofinite numbers, nonstandard analysis, and mechanics

A. E. Gutman, S. S. Kutateladze, Yu. G. Reshetnyak
2010 Journal of Applied and Industrial Mathematics  
We demonstrate the mathematical insignificance of the versions of 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.  ... 
doi:10.1134/s1990478910020079 fatcat:zedqqrp2afcixeuciqbp7puvje

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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