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Nigel Cutland
Nigel J. Cutland is Professor of Mathematics at the University of York. His main fields of interest are non-standard analysis, Loeb spaces, and applications in probability Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ... and stochastic analysis. He was Editor-in-Chief of '' Logic and Analysis'' and '' Journal of Logic and Analysis''. Books * * * See also * Influence of non-standard analysis References 20th-century British mathematicians 21st-century British mathematicians Living people Academics of the University of York Year of birth missing (living people) {{UK-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of York
The University of York (abbreviated as or ''York'' for Post-nominal letters, post-nominals) is a public Collegiate university, collegiate research university in York, England. Established in 1963, the university has expanded to more than thirty departments and centres, covering a wide range of subjects. South-east of the city of York, the university campus is about in size. The original campus, Campus West, incorporates the York Science Park and the Science Learning Centres, National Science Learning Centre, and its wildlife, campus lakes and greenery are prominent. In May 2007 the university was granted permission to build an extension to its main campus, on arable land just east of the nearby village of Heslington. The second campus, Campus East, opened in 2009 and now hosts five colleges and three departments as well as conference spaces, a sports village and a business startup company, start-up 'incubator'. The institution also leases King's Manor in York city centre. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-standard Analysis
The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using (ε, δ)-definition of limit, limits rather than infinitesimals. Nonstandard analysis instead reformulates the calculus using a logically rigorous notion of infinitesimal numbers. Nonstandard analysis originated in the early 1960s by the mathematician Abraham Robinson. He wrote: ... the idea of infinitely small or ''infinitesimal'' quantities seems to appeal naturally to our intuition. At any rate, the use of infinitesimals was widespread during the formative stages of the Differential and Integral Calculus. As for the objection ... that the distance between two distinct real numbers cannot be infinitely small, Gottfried Wilhelm Leibniz argued that the theory of infinitesimals implies the introduction of ideal numbers which might be infinitely small or inf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loeb Space
In mathematics, a Loeb space is a type of measure space introduced by using nonstandard analysis. Construction Loeb's construction starts with a finitely additive map \nu from an internal algebra \mathcal A of sets to the nonstandard reals. Define \mu to be given by the standard part of \nu, so that \mu is a finitely additive map from \mathcal A to the extended reals \overline\mathbb R. Even if \mathcal A is a nonstandard \sigma -algebra, the algebra \mathcal A need not be an ordinary \sigma-algebra as it is not usually closed under countable unions. Instead the algebra \mathcal A has the property that if a set in it is the union of a countable family of elements of \mathcal A, then the set is the union of a finite number of elements of the family, so in particular any finitely additive map (such as \mu) from \mathcal A to the extended reals is automatically countably additive. Define \mathcal M to be the \sigma-algebra generated by \mathcal A. Then by Carathéodory's extension ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th ed., (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', vol. 1, 3rd ed., (1968), Wiley, . This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These concepts have been given an axiomatic mathematical formaliza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Analysis
Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. This field was created and started by the Japanese mathematician Kiyosi Itô during World War II. The best-known stochastic process to which stochastic calculus is applied is the Wiener process (named in honor of Norbert Wiener), which is used for modeling Brownian motion as described by Louis Bachelier in 1900 and by Albert Einstein in 1905 and other physical diffusion processes in space of particles subject to random forces. Since the 1970s, the Wiener process has been widely applied in financial mathematics and economics to model the evolution in time of stock prices and bond interest rates. The main flavours of stochastic calculus are the Itô calculus and its variational relative the Malliavin calculus. For technical reasons the Itô integral is the mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic And Analysis
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to work." Premise ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Logic And Analysis
The Association for Symbolic Logic (ASL) is an international organization of specialists in mathematical logic and philosophical logic. The ASL was founded in 1936, and its first president was Curt John Ducasse. The current president of the ASL is Phokion Kolaitis. Publications The ASL publishes books and academic journals. Its three official journals are: * ''Journal of Symbolic Logic'' – publishes research in all areas of mathematical logic. Founded in 1936, . * ''Bulletin of Symbolic Logic'' – publishes primarily expository articles and reviews. Founded in 1995, . * ''Review of Symbolic Logic'' – publishes research relating to logic, philosophy, science, and their interactions. Founded in 2008, . In addition, the ASL has a sponsored journal: * ''Journal of Logic and Analysis'' publishes research on the interactions between mathematical logic and pure and applied analysis. Founded in 2009 as an open-access successor to the Springer journal ''Logic and Analysis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 rev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century British Mathematicians
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Living People
Purpose: Because living persons may suffer personal harm from inappropriate information, we should watch their articles carefully. By adding an article to this category, it marks them with a notice about sources whenever someone tries to edit them, to remind them of WP:BLP (biographies of living persons) policy that these articles must maintain a neutral point of view, maintain factual accuracy, and be properly sourced. Recent changes to these articles are listed on Special:RecentChangesLinked/Living people. Organization: This category should not be sub-categorized. Entries are generally sorted by family name In many societies, a surname, family name, or last name is the mostly hereditary portion of one's personal name that indicates one's family. It is typically combined with a given name to form the full name of a person, although several give .... Maintenance: Individuals of advanced age (over 90), for whom there has been no new documentation in the last ten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academics Of The University Of York , a person who is a researcher or has expertise in an academic discipline
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Academic means of or related to an academy, an institution learning. Academic or academics may also refer to: * Academic staff, or faculty, teachers or research staff * school of philosophers associated with the Platonic Academy in ancient Greece * The Academic, Irish indie rock band * "Academic", song by New Order from the 2015 album ''Music Complete'' Other uses *Academia (other) *Academy (other) *Faculty (other) *Scholar A scholar is a person who is a researcher or has expertise in an academic discipline. A scholar can also be an academic, who works as a professor, teacher, or researcher at a university. An academic usually holds an advanced degree or a termina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
