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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. In 2006 he received a Deborah and Franklin Haimo Awards for Distinguished College or University Teaching of Mathematics, Deborah and Franklin Haimo Award for Distinguished College or University Teaching of Mathematics. Publications *Stroyan, K. D.; Wilhelmus Luxemburg, Luxemburg, W. A. J. ''Introduction to the theory of infinitesimals''. Pure and Applied Mathematics, No. 72. Academic Press [Harcourt 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 analysi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Iowa
The University of Iowa (U of I, UIowa, or Iowa) is a public university, public research university in Iowa City, Iowa, United States. Founded in 1847, it is the oldest and largest university in the state. The University of Iowa is organized into 12 colleges offering more than 200 areas of study and 7 professional degrees. On an urban 1,880-acre campus on the banks of the Iowa River, the University of Iowa is Carnegie Classification of Institutions of Higher Education, classified among "R1: Doctoral Universities – Very high research activity". In fiscal year 2021, research expenditures at Iowa totaled $818 million. The university was the original developer of the Master of Fine Arts degree, and it operates the Iowa Writers' Workshop, whose alumni include 17 of the university's 46 Pulitzer Prize winners. Iowa is a member of the Association of American Universities and the Universities Research Association. Among public universities in the United States, UI was the first to beco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analysis
Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 BC), though ''analysis'' as a formal concept is a relatively recent development. The word comes from the Ancient Greek (''analysis'', "a breaking-up" or "an untying" from ''ana-'' "up, throughout" and ''lysis'' "a loosening"). From it also comes the word's plural, ''analyses''. As a formal concept, the method has variously been ascribed to René Descartes ('' Discourse on the Method''), and Galileo Galilei. It has also been ascribed to Isaac Newton, in the form of a practical method of physical discovery (which he did not name). The converse of analysis is synthesis: putting the pieces back together again in a new or different whole. Science and technology Chemistry The field of chemistry uses analysis in three ways: to i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deborah And Franklin Haimo Awards For Distinguished College Or University Teaching Of Mathematics
The Deborah and Franklin Tepper Haimo Awards for Distinguished College or University Teaching of Mathematics are awards given by the Mathematical Association of America to recognize college or university teachers "who have been widely recognized as extraordinarily successful and whose teaching effectiveness has been shown to have had influence beyond their own institutions." The Haimo awards are the highest teaching honor bestowed by the MAA. The awards were established in 1993 by Deborah Tepper Haimo and named after Haimo and her husband Franklin Haimo. After the first year of the award (when seven awards were given) up to three awards are given every year. Winners The winners of the award have been: *1993: Joseph Gallian, Robert V. Hogg, Anne Hudson, Frank Morgan, V. Frederick Rickey, Doris Schattschneider, and Philip D. Straffin Jr. *1994: Paul Halmos, Justin Jesse Price, and Alan Tucker *1995: Robert L. Devaney, Lisa Mantini, and David S. Moore *1996: Thomas Banch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilhelmus Luxemburg
Wilhelmus Anthonius Josephus Luxemburg (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 an assistant professor at Caltech from 1958-60; an associate professor from 1960–62; a professor from 1962–2000; and a 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 Ro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Math Reviews
''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also publishes an associated online bibliographic database called MathSciNet, which contains an electronic version of ''Mathematical Reviews''. Reviews Mathematical Reviews was founded by Otto E. Neugebauer in 1940 as an alternative to the German journal '' Zentralblatt für Mathematik'', which Neugebauer had also founded a decade earlier, but which under the Nazis had begun censoring reviews by and of Jewish mathematicians. The goal of the new journal was to give reviews of every mathematical research publication. As of November 2007, the ''Mathematical Reviews'' database contained information on over 2.2 million articles. The authors of reviews are volunteers, usually chosen by the editors because of some expertise in the area of the article ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, Inner product space#Definition, inner product, Norm (mathematics)#Definition, norm, or Topological space#Definitions, topology) and the linear transformation, linear functions defined on these spaces and suitably respecting these structures. The historical roots of functional analysis lie in the study of function space, spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining, for example, continuous function, continuous or unitary operator, unitary operators between function spaces. This point of view turned out to be particularly useful for the study of differential equations, differential and integral equations. The usage of the word ''functional (mathematics), functional'' as a noun goes back to the calculus of v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as well as in physics, including the branches of hydrodynamics, thermodynamics, quantum mechanics, and twistor theory. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering. As a differentiable function of a complex variable is equal to the sum function given by its Taylor series (that is, it is analytic), complex analysis is particularly concerned with analytic functions of a complex variable, that is, '' holomorphic functions''. The concept can be extended to functions of several complex variables. Complex analysis is contrasted with real analysis, which dea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such as Stretch factor, stretching, Torsion (mechanics), twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a Set (mathematics), set endowed with a structure, called a ''Topology (structure), topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of List of continuity-related mathematical topics, continuity. Euclidean spaces, and, more generally, metric spaces are examples of topological spaces, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and Homotopy, homotopies. A property that is invariant under such deformations is a to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Google Scholar
Google Scholar is a freely accessible web search engine that indexes the full text or metadata of Academic publishing, scholarly literature across an array of publishing formats and disciplines. Released in Beta release, beta in November 2004, the Google Scholar index includes peer-reviewed online academic journals and books, conference papers, theses and dissertations, preprints, Abstract (summary), abstracts, technical reports, and other scholarly literature, including Legal opinion, court opinions and patents. Google Scholar uses a web crawler, or web robot, to identify files for inclusion in the search results. For content to be indexed in Google Scholar, it must meet certain specified criteria. An earlier statistical estimate published in PLOS One using a mark and recapture method estimated approximately 79–90% coverage of all articles published in English with an estimate of 100 million.'' Trend Watch'' (2014) Nature (journal), Nature 509(7501), 405 – discussing Madian K ... [...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] |
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] |
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] |
