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Influence Of Non-standard Analysis
Abraham Robinson's theory of nonstandard analysis has been applied in a number of fields. Probability theory "Radically elementary probability theory" of Edward Nelson combines the discrete and the continuous theory through the infinitesimal approach. The model-theoretical approach of nonstandard analysis together with Loeb measure theory allows one to define Brownian motion as a hyperfinite random walk, obviating the need for cumbersome measure-theoretic developments. Jerome Keisler used this classical approach of nonstandard analysis to characterize general stochastic processes as hyperfinite ones. Economics Economists have used nonstandard analysis to model markets with large numbers of agents (see Robert M. Anderson (economist)). Education An article by Michèle Artigue concerns the teaching of analysis. Artigue devotes a section, "The non standard analysis and its weak impact on education" on page 172, to non-standard analysis. She writes: :The non-standard analysis re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abraham Robinson
Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorporated into modern mathematics. Nearly half of Robinson's papers were in applied mathematics rather than in pure mathematics. Biography He was born to a Jewish family with strong Zionist beliefs, in Waldenburg, Germany, which is now Wałbrzych, in Poland. In 1933, he emigrated to British Mandate of Palestine, where he earned a first degree from the Hebrew University. Robinson was in France when the Nazis invaded during World War II, and escaped by train and on foot, being alternately questioned by French soldiers suspicious of his German passport and asked by them to share his map, which was more detailed than theirs. While in London, he joined the Free French Air Force and contributed to the war effort by teaching himself aerodynamics a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Goldblatt
__notoc__ Robert Ian Goldblatt (born 1949) is a mathematical logician who is Emeritus Professor in the School of Mathematics and Statistics at Victoria University, Wellington, New Zealand. His most popular books are ''Logics of Time and Computation'' and ''Topoi: the Categorial Analysis of Logic''. He has also written a graduate level textbook on hyperreal numbers which is 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 elected Fellow and Councillor of the Royal Society of New Zealand, President of the New Zealand Mathematical Society, and represented New Zealand to the International Mathematical Union. In 2012 he was awarded theJones Medalfor lifetime achievement in mathematics. Books and handbook chapters * 1979: ''Topoi: The Categorial Analysis of Logic'', North-Holland. Revised edition 1984. Dover Publications edition 2006Internet edition Project Euclid. :: Benja ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Melvin Fitting
Melvin Fitting (born January 24, 1942) is a logician with special interests in philosophical logic and tableau proof systems. He was a professor at City University of New York, Lehman College and the Graduate Center. from 1968 to 2013. At the Graduate Center he was in the departments of Computer Science, Philosophy, and Mathematics, and at Lehman College he was in the department of Mathematics and Computer Science. He is now Professor emeritus. Fitting was born in Troy, New York. His undergraduate degree is from Rensselaer Polytechnic Institute, and his doctorate is from Yeshiva University, both in mathematics. His thesis advisor was Raymond Smullyan. In June 2012 Melvin Fitting was given the Herbrand Award by CADE, for distinguished contributions to automated deduction. A loose motivation for much of Melvin Fitting's work can be formulated succinctly as follows. There are many logics. Our principles of reasoning vary with context and subject matter. Multiplicity is on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Criticism Of Nonstandard Analysis
Nonstandard analysis and its offshoot, nonstandard calculus, have been criticized by several authors, notably Errett Bishop, Paul Halmos, and Alain Connes. These criticisms are analyzed below. Introduction The evaluation of nonstandard analysis in the literature has varied greatly. Paul Halmos described it as a technical special development in mathematical logic. Terence Tao summed up the advantage of the hyperreal framework by noting that it The nature of the criticisms is not directly related to the logical status of the results proved using nonstandard analysis. In terms of conventional mathematical foundations in classical logic, such results are quite acceptable. Abraham Robinson's nonstandard analysis does not need any axioms beyond Zermelo–Fraenkel set theory (ZFC) (as shown explicitly by Wilhelmus Luxemburg's ultrapower construction of the hyperreals), while its variant by Edward Nelson, known as internal set theory, is similarly a conservative extension of ZFC. It ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Terence Tao
Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing and analytic number theory. Tao was born to ethnic Chinese immigrant parents and raised in Adelaide. Tao won the Fields Medal in 2006 and won the Royal Medal and Breakthrough Prize in Mathematics in 2014. He is also a 2006 MacArthur Fellow. Tao has been the author or co-author of over three hundred research papers. He is widely regarded as one of the greatest living mathematicians and has been referred to as the "Mozart of mathematics". Life and career Family Tao's parents are first-generation immigrants from Hong Kong to Australia.''Wen Wei Po'', Page A4, 24 Au ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Keith Stroyan
Keith D. Stroyan is Professor of Mathematics at the University of Iowa. His main research interests are in analysis and visual depth perception. Publications *Stroyan, K. D.; Luxemburg, W. A. J. ''Introduction to the theory of infinitesimals''. Pure and Applied Mathematics, No. 72. Academic Press arcourt Brace Jovanovich, Publishers New York-London, 1976. ::Reviewer Frank Wattenberg for Math Reviews wrote that "mathematicians whose principal interest is in functional analysis, complex analysis, or topology will find here some very valuable contributions to our understanding of these subjectshere :The book was cited over 365 times at Google Scholar in 2011. *Stroyan, K. D.; Bayod, José Manuel: Foundations of infinitesimal stochastic analysis. Studies in Logic and the Foundations of Mathematics, 119. North-Holland Publishing Co., Amsterdam, 1986. ::Reviewer Tom L. Lindström for Math Reviews wrote that "the authors have written a very comprehensive and readable monograph whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alain M
Alain may refer to: People * Alain (given name), common given name, including list of persons and fictional characters with the name * Alain (surname) * "Alain", a pseudonym for cartoonist Daniel Brustlein * Alain, a standard author abbreviation used to indicate Henri Alain Liogier, also known as Brother Alain, as the author when citing a botanical name * Émile Chartier (1868–1951), French philosopher and antimilitarist commonly known as Alain Places * Alain, Iran, a village in Tehran Province, Iran * Al Ain, a city in Abu Dhabi, United Arab Emirates ** Al Ain International Airport in the United Arab Emirates * Val-Alain, Quebec, village of 950 people in Quebec, Canada Other uses * 1969 Alain (1935 CG), a Main-belt Asteroid discovered in 1935 * ''Alain'' (crab), a genus of crabs in the family Pinnotheridae * Prix Alain-Grandbois or Alain Grandbois Prize is awarded each year to an author for a book of poetry * Rosa 'Alain' ''Rosa'' 'Alain' is a red Floribunda rose variety, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilhelmus Luxemburg
Wilhelmus Anthonius Josephus Luxemburg ( Delft, 11 April 1929 – 2 October 2018) was a Dutch American mathematician who was a professor of mathematics at the California Institute of Technology. He received his B.A. from the University of Leiden in 1950; his M.A., in 1953; his Ph.D., from the Delft Institute of Technology, in 1955. He was assistant professor at Caltech during 1958–60; Associate Professor, during 1960–62; Professor, during 1962–2000; Professor Emeritus, from 2000. He was the Executive Officer for Mathematics during 1970–85. In 2012 he became a fellow of the American Mathematical Society. Luxemburg became a corresponding member of the Royal Netherlands Academy of Arts and Sciences in 1974. Luxemburg contributed to the development of non-standard analysis by popularizing the construction of hyperreal numbers in the 1960s. Though Edwin Hewitt had shown the construction in 1948, the formalization of non-standard analysis is generally associated with Abraham ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Loeb
Peter Albert Loeb (born July 3, 1937) is a mathematician at the University of Illinois at Urbana–Champaign. He co-authored a basic reference text on nonstandard analysis (Hurd–Loeb 1985). Reviewer Perry Smith for MathSciNet wrote: :This book is a welcome addition to the literature on nonstandard analysis. The notion of Loeb measure named after him has become a standard tool in the field. In 2012 he became a fellow of the American Mathematical Society. retrieved 2013-02-02. See also * Influence of nonstandard analysisNotes Publications *Hurd, Albert E.; Loeb, Peter A. ' ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semen Samsonovich Kutateladze
Semen, also known as seminal fluid, is an organic bodily fluid created to contain spermatozoon, spermatozoa. It is secreted by the gonads (sexual glands) and other sexual organs of male or hermaphrodite, hermaphroditic animals and can fertilization, fertilize the female ovum. Semen is produced and originates from the seminal vesicle, which is located in the pelvis. The process that results in the discharge of semen from the Ureteral orifice, urethral orifice is called ejaculation. In humans, seminal fluid contains several components besides spermatozoa: Proteolytic enzyme, proteolytic and other enzymes as well as fructose are elements of seminal fluid which promote the survival of spermatozoa, and provide a medium through which they can move or "swim". The fluid is designed to be discharged deep into the vagina, so the spermatozoa can pass into the uterus and form a zygote with an egg. Semen is also a form of genetic material. In animals, semen has been collected for cryoconse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir Kanovei
Vladimir G. Kanovei (born 1951) is a Russian mathematician working at the Institute for Information Transmission Problems in Moscow, Russia. His interests include mathematical logic and foundations, as well as mathematical history. Selected publications *. *Kanovei, Vladimir; Reeken, Michael; Nonstandard analysis, axiomatically. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2004. xvi+408 pp. *Kanovei, Vladimir; Borel equivalence relations. Structure and classification. University Lecture Series, 44. American Mathematical Society, Providence, RI, 2008. x+240 pp. *Kanoveĭ, V.; Reeken, M.; On Ulam's problem concerning the stability of approximate homomorphisms. (Russian) Tr. Mat. Inst. Steklova 231 (2000), Din. Sist., Avtom. i Beskon. Gruppy, 249–283; translation in Proc. Steklov Inst. Math. 2000, no. 4 (231), 238–270 *Kanoveĭ, V. G.; Lyubetskiĭ, V. A.; On some classical problems in descriptive set theory. (Russian) Uspekhi Mat. Nauk 58 (2003), no. 5(353), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
