Abraham Robinson's theory of nonstandard analysis has been applied in a number of fields. "Radically elementary probability theory" of Edward Nelson combines...
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operations of calculus using limits rather than infinitesimals. Nonstandard analysis instead reformulates the calculus using a logically rigorous notion of infinitesimal...
31 KB (3,972 words) - 11:12, 2 September 2024
Nonstandard analysis and its offshoot, nonstandard calculus, have been criticized by several authors, notably Errett Bishop, Paul Halmos, and Alain Connes...
28 KB (3,520 words) - 13:42, 3 July 2024
Hyperreal number (redirect from Nonstandard real numbers)
Constructive nonstandard analysis Hyperinteger – A hyperreal number that is equal to its own integer part Influence of nonstandard analysis Nonstandard calculus –...
33 KB (4,878 words) - 01:13, 16 September 2024
Elementary Calculus: An Infinitesimal Approach (category Nonstandard analysis)
_{10}(xy)=\log _{10}x+\log _{10}y} . Criticism of nonstandard analysis Influence of nonstandard analysis Nonstandard calculus Increment theorem Keisler 2011...
13 KB (1,371 words) - 18:08, 31 March 2024
Peter A. Loeb (category University of Illinois Urbana-Champaign faculty)
Society. Influence of nonstandard analysis Perry Smith Robert Goldblatt, Lectures on the hyperreals. An introduction to nonstandard analysis. Graduate...
3 KB (340 words) - 21:45, 20 December 2022
Abraham Robinson (category Alumni of the University of London)
1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite...
9 KB (751 words) - 03:20, 21 May 2024
Nigel Cutland (category Year of birth missing (living people))
ISBN 9783540413844. Influence of non-standard analysis "Professor Nigel Cutland". Department of Mathematics. The University of York. Retrieved 25 October...
2 KB (127 words) - 12:53, 26 March 2024
Ultraproduct (redirect from The fundamental theorem of ultraproducts)
construct nonstandard models of analysis, leading to the growth of the area of nonstandard analysis, which was pioneered (as an application of the compactness...
18 KB (3,104 words) - 20:35, 16 August 2024
In social sciences, sequence analysis (SA) is concerned with the analysis of sets of categorical sequences that typically describe longitudinal data....
95 KB (10,041 words) - 14:27, 17 September 2024
Robert M. Anderson (mathematician) (category University of California, Berkeley College of Letters and Science faculty)
primarily within General Equilibrium Theory. Some of this work uses nonstandard analysis, but much of it provides simple elementary treatments that generalize...
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Augustin-Louis Cauchy (category Fellows of the American Academy of Arts and Sciences)
one of the first to rigorously state and prove the key theorems of calculus (thereby creating real analysis), pioneered the field complex analysis, and...
42 KB (5,401 words) - 03:03, 16 September 2024
(including chloroplasts). Other amino acids are called nonstandard or non-canonical. Most of the nonstandard amino acids are also non-proteinogenic (i.e. they...
98 KB (10,141 words) - 04:18, 2 September 2024
Leonhard Euler (category Fellows of the American Academy of Arts and Sciences)
attributed to many of them: Pierre-Simon Laplace expressed Euler's influence on mathematics by stating, "Read Euler, read Euler, he is the master of us all." Carl...
102 KB (10,269 words) - 13:32, 13 September 2024
The Analyst (redirect from Ghosts of departed quantities)
"Newton and the notion of limit", Historia Math., 28 (1): 393–30, doi:10.1006/hmat.2000.2301 Robert, Alain (1988), Nonstandard analysis, New York: Wiley,...
18 KB (2,061 words) - 12:54, 16 September 2024
Robert Goldblatt (category Academic staff of Victoria University of Wellington)
an introduction to nonstandard analysis. He has been Coordinating Editor of The Journal of Symbolic Logic and a Managing Editor of Studia Logica. He was...
4 KB (463 words) - 05:20, 18 July 2023
Alain M. Robert (category Year of birth missing (living people))
Bell numbers. Simon Stevin 3 (1996), no. 4, 467–475. Robert, Alain: Nonstandard analysis. Translated from the French by the author. A Wiley-Interscience Publication...
3 KB (288 words) - 14:48, 28 October 2021
Leif Arkeryd (category Academic staff of the Chalmers University of Technology)
supervision of Jaak Peetre. Arkeryd, Leif: On the Boltzmann equation. I. Existence. Arch. Rational Mech. Anal. 45 (1972), 1–16. Nonstandard analysis. Theory...
1 KB (136 words) - 01:13, 4 June 2023
Calculus (redirect from Degree of smallness)
is an abbreviation of both infinitesimal calculus and integral calculus, which denotes courses of elementary mathematical analysis. In Latin, the word...
73 KB (8,584 words) - 06:57, 18 September 2024
Pierre de Fermat (category History of calculus)
much influenced by the work of François Viète. In 1630, he bought the office of a councilor at the Parlement de Toulouse, one of the High Courts of Judicature...
21 KB (2,280 words) - 12:43, 31 August 2024
sociolinguistic prestige than other, nonstandard lects and are generally thought of as "correct" by speakers of the language. Since the selection is an...
14 KB (1,670 words) - 05:29, 17 September 2024
prestige is a type of scenario in which nonstandard languages or dialects are regarded to be of high linguistic prestige by members of a speech community...
38 KB (4,823 words) - 14:49, 15 June 2024
analyzed in terms of both his own historical and economic theories, and in light of their potential applications of nonstandard analysis. Marx left over...
11 KB (1,230 words) - 23:45, 25 June 2024
Number (redirect from History of numbers)
and used to develop the field of nonstandard analysis. The system of hyperreal numbers represents a rigorous method of treating the ideas about infinite...
62 KB (7,747 words) - 11:27, 10 September 2024
Monte Carlo method (redirect from Monte Carlo analysis)
"Monte Carlo Computation of the Fisher Information Matrix in Nonstandard Settings". Journal of Computational and Graphical Statistics. 14 (4): 889–909. CiteSeerX 10...
91 KB (10,526 words) - 18:31, 11 September 2024
Rioplatense Spanish (redirect from Accents of Argentina)
Chile and Colombia, the use of voseo has at times been considered a nonstandard lower speaking style, whereas in Argentina and Uruguay it is standard...
33 KB (3,180 words) - 14:55, 15 September 2024
Epsilon (redirect from 5th letter of the Greek alphabet)
calculus or nonstandard analysis) An infinitesimally small positive quantity is commonly denoted ε. (In analysis) By extension, a quantity thought of as "small...
19 KB (1,915 words) - 01:24, 27 August 2024
Non-standard cosmology (redirect from Nonstandard cosmology)
generally considered unworthy of consideration by cosmologists while many of the historically significant nonstandard cosmologies are considered to have...
35 KB (4,547 words) - 20:38, 14 September 2024
Gottfried Wilhelm Leibniz (redirect from System of Leibniz)
ideology, and the politics of infinitesimals: mathematical logic and nonstandard analysis in modern China". History and Philosophy of Logic. 24 (4): 327–363...
152 KB (18,845 words) - 22:41, 17 September 2024
International Phonetic Alphabet (category Pages displaying short descriptions of redirect targets via Module:Annotated link)
linguists, however, use a mix of IPA with Americanist phonetic notation or Sinological phonetic notation or otherwise use nonstandard symbols for various reasons...
164 KB (15,903 words) - 17:10, 12 September 2024