operations of calculus using limits rather than infinitesimals. Nonstandard analysis instead reformulates the calculus using a logically rigorous notion of infinitesimal...
31 KB (3,978 words) - 00:54, 22 April 2025
Abraham Robinson's theory of nonstandard analysis has been applied in a number of fields. "Radically elementary probability theory" of Edward Nelson combines...
5 KB (653 words) - 09:54, 2 April 2025
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 (4,924 words) - 08:45, 23 June 2025
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 (756 words) - 01:22, 11 May 2025
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 (1,370 words) - 19:27, 16 June 2025
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) - 01:53, 9 June 2025
Peter A. Loeb (category University of Illinois Urbana-Champaign faculty)
20, 2024. He was survived by his wife of 66 years and their three children. Influence of nonstandard analysis Peter A. Loeb (2019-10-26). "Biographical...
5 KB (597 words) - 22:27, 10 February 2025
Nigel Cutland (category Academics of the University of York)
ISBN 9783540413844. Influence of non-standard analysis "Professor Nigel Cutland". Department of Mathematics. The University of York. Retrieved 25 October...
2 KB (127 words) - 07:05, 8 January 2025
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 (3,108 words) - 20:35, 16 August 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 (2,065 words) - 07:32, 9 June 2025
Calculus (redirect from Degree of smallness)
which denotes courses of elementary mathematical analysis. In Latin, the word calculus means “small pebble”, (the diminutive of calx, meaning "stone")...
76 KB (8,805 words) - 00:02, 20 June 2025
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...
22 KB (2,376 words) - 19:34, 18 June 2025
In social sciences, sequence analysis (SA) is concerned with the analysis of sets of categorical sequences that typically describe longitudinal data....
98 KB (10,207 words) - 21:19, 11 June 2025
Leonhard Euler (category Fellows of the American Academy of Arts and Sciences)
of graph theory and topology and made influential discoveries in many other branches of mathematics, such as analytic number theory, complex analysis...
99 KB (10,444 words) - 14:22, 25 June 2025
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
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...
10 KB (966 words) - 05:27, 6 June 2025
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and...
58 KB (9,530 words) - 08:36, 5 June 2025
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 (1,247 words) - 08:15, 30 January 2025
patterns that establish her rural, Southern-influenced character. These included 121 instances of nonstandard grammar (such as auxiliary verb deletion,...
16 KB (1,562 words) - 01:40, 26 June 2025
Robert Goldblatt (category Academic staff of Victoria University of Wellington)
introduction to nonstandard analysis. In 1987 he took "a trip on Einstein's train" to develop hyperbolic orthogonality, the geometry of relativity of simultaneity...
5 KB (503 words) - 14:35, 19 December 2024
(terminology that is nonstandard), which reinforced the KLM captain's misinterpretation that they had takeoff clearance. The controller's response of "OK" to the...
70 KB (7,180 words) - 19:28, 24 June 2025
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) - 20:59, 3 April 2025
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 (10,690 words) - 23:18, 29 April 2025
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 (4,535 words) - 02:19, 8 April 2025
(including chloroplasts). Other amino acids are called nonstandard or non-canonical. Most of the nonstandard amino acids are also non-proteinogenic (i.e. they...
94 KB (10,037 words) - 18:20, 18 June 2025
Noether's theorem (redirect from Conservation of symmetry)
\right]\approx 0.} Looking at the specific case of a Newtonian particle of mass m, coordinate x, moving under the influence of a potential V, coordinatized by time...
71 KB (11,807 words) - 22:12, 19 June 2025
Wilhelmus Luxemburg (category Members of the Royal Netherlands Academy of Arts and Sciences)
Robinson: The Creation of Nonstandard Analysis: A Personal and Mathematical Odyssey, Princeton University Press "Caltech Mourns the Passing of Wilhelmus A. J...
5 KB (428 words) - 08:48, 6 March 2025
Semyon Kutateladze (category Academic staff of Novosibirsk State University)
Journal of Applied and Industrial Mathematics, 2011, Vol. 5, No. 3, 365–373. Kutateladze S.S. Nonstandard analysis: its creator and place. Journal of Applied...
10 KB (747 words) - 21:23, 24 May 2025
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