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Timeline Of Scientific Computing
The following is a timeline of scientific computing, also known as computational science. Before modern computers 18th century * Simpson rediscovers Simpson's rule, a century after Johannes Kepler (who derived it in 1615 after seeing it used for wine barrels). * 1733 – The French naturalist Comte de Buffon poses his needle problem. * Euler comes up with a simple numerical method for integrands. 19th century * First formulation of Gram-Schmidt orthogonalisation by Laplace, to be further improved decades later. * Babbage in 1822, began work on a machine made to compute/calculate values of polynomial functions automatically by using the method of finite differences. This was eventually called the Difference engine. * Lovelace's note G on the Analytical Engine (1842) describes an algorithm for generating Bernoulli numbers. It is considered the first algorithm ever specifically tailored for implementation on a computer, and thus the first-ever computer programme. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simpson's Rule
In numerical integration, Simpson's rules are several approximations for definite integrals, named after Thomas Simpson (1710–1761). The most basic of these rules, called Simpson's 1/3 rule, or just Simpson's rule, reads \int_a^b f(x) \, dx \approx \frac \left (a) + 4f\left(\frac\right) + f(b)\right In German and some other languages, it is named after Johannes Kepler, who derived it in 1615 after seeing it used for wine barrels (barrel rule, ). The approximate equality in the rule becomes exact if is a polynomial up to and including 3rd degree. If the 1/3 rule is applied to ''n'' equal subdivisions of the integration range 'a'', ''b'' one obtains the composite Simpson's 1/3 rule. Points inside the integration range are given alternating weights 4/3 and 2/3. Simpson's 3/8 rule, also called Simpson's second rule, requires one more function evaluation inside the integration range and gives lower error bounds, but does not improve on order of the error. If the 3/8 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Munich
The Ludwig Maximilian University of Munich (simply University of Munich or LMU; german: Ludwig-Maximilians-Universität München) is a public research university in Munich, Germany. It is Germany's List of universities in Germany, sixth-oldest university in continuous operation. Originally University of Ingolstadt, established in Ingolstadt in 1472 by Louis IX, Duke of Bavaria, Duke Ludwig IX of Bavaria-Landshut, the university was moved in 1800 to Landshut by Maximilian I Joseph of Bavaria, King Maximilian I of Bavaria when the city was threatened by the French, before being relocated to its present-day location in Munich in 1826 by Ludwig I of Bavaria, King Ludwig I of Bavaria. In 1802, the university was officially named Ludwig-Maximilians-Universität by King Maximilian I of Bavaria in honor of himself and Ludwig IX. LMU is currently the second-largest university in Germany in terms of student population; in the 2018/19 winter semester, the university had a total of 51,606 m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal (ring Theory)
In ring theory, a branch of abstract algebra, an ideal of a ring is a special subset of its elements. Ideals generalize certain subsets of the integers, such as the even numbers or the multiples of 3. Addition and subtraction of even numbers preserves evenness, and multiplying an even number by any integer (even or odd) results in an even number; these closure and absorption properties are the defining properties of an ideal. An ideal can be used to construct a quotient ring in a way similar to how, in group theory, a normal subgroup can be used to construct a quotient group. Among the integers, the ideals correspond one-for-one with the non-negative integers: in this ring, every ideal is a principal ideal consisting of the multiples of a single non-negative number. However, in other rings, the ideals may not correspond directly to the ring elements, and certain properties of integers, when generalized to rings, attach more naturally to the ideals than to the elements of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ''abstract algebra'' was coined in the early 20th century to distinguish this area of study from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning. Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory is a formalism that allows a unified way for expressing properties and constructions that are similar for various structures. Universal algebra is a related subject that studies types of algebraic structures as single objects. For example, the structure of groups is a single object in universal algebra, which is called the ''variety of groups''. History Before the nineteenth century, algebra meant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithms
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm can be expressed within a finite amount of space and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Algebra
In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects. Although computer algebra could be considered a subfield of scientific computing, they are generally considered as distinct fields because scientific computing is usually based on numerical computation with approximate floating point numbers, while symbolic computation emphasizes ''exact'' computation with expressions containing variables that have no given value and are manipulated as symbols. Software applications that perform symbolic calculations are called ''computer algebra systems'', with the term ''system'' alluding to the complexity of the main applications that include, at least, a method to represent mathematical data in a computer, a user programming language (usually different from the languag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grete Hermann
Grete Hermann (2 March 1901 – 15 April 1984) was a Germans, German mathematician and philosopher noted for her work in mathematics, physics, philosophy and education. She is noted for her early philosophical work on the foundations of quantum mechanics, and is now known most of all for an early, but long-ignored critique of a "Hidden variable theory, no hidden-variables theorem" by John von Neumann. It has been suggested that, had her critique not remained nearly unknown for decades, the historical development of quantum mechanics might have been very different. Mathematics Hermann studied mathematics at Göttingen under Emmy Noether and Edmund Landau, where she achieved her PhD in 1926. Her doctoral thesis, "Die Frage der endlich vielen Schritte in der Theorie der Polynomideale" (in English "The Question of Finitely Many Steps in Polynomial Ideal Theory"), published in ''Mathematische Annalen'', is the foundational paper for computer algebra. It first established the existe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Miami
The University of Miami (UM, UMiami, Miami, U of M, and The U) is a private research university in Coral Gables, Florida. , the university enrolled 19,096 students in 12 colleges and schools across nearly 350 academic majors and programs, including the Leonard M. Miller School of Medicine in Miami's Health District, the law school on the main campus, and the Rosenstiel School of Marine and Atmospheric Science on Virginia Key with research facilities in southern Miami-Dade County. The University of Miami offers 138 undergraduate, 140 master's, and 67 doctoral degree programs. Since its founding in 1925, the university has attracted students from all 50 states and 173 foreign countries. With 16,954 faculty and staff as of 2021, the University of Miami is the second largest employer in Miami-Dade County. The university's main campus in Coral Gables spans , has over of buildings, and is located south of Downtown Miami, the heart of the nation's ninth largest and world's 65th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Computational Physics
The ''Journal of Computational Physics'' is a bimonthly scientific journal covering computational physics that was established in 1966 and is published by Elsevier. As of 2015, its editor-in-chief is Rémi Abgrall (University of Zurich). According to the ''Journal Citation Reports'', ''Journal of Computational Physics'' has a 2021 impact factor of 4.645, ranking it third out of 56 in the category ''Physics, Mathematical''. See also *List of fluid mechanics journals This is a list of scientific journals related to the field of fluid mechanics. {{columns-list, colwidth=30em, *''AIAA Journal'' *''Annual Review of Fluid Mechanics'' *''Experiments in Fluids'' *'' Fluid Dynamics Research'' *''Flow, Turbulence and ... References External links * English-language journals Physics journals Elsevier academic journals Publications established in 1966 Biweekly journals {{physics-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing house specializing in monographs and scholarly journals. Most are nonprofit organizations and an integral component of a large research university. They publish work that has been reviewed by schola ... in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 Country, countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vilhelm Bjerknes
Vilhelm Friman Koren Bjerknes ( , ; 14 March 1862 – 9 April 1951) was a Norwegian physicist and meteorologist who did much to found the modern practice of weather forecasting. He formulated the primitive equations that are still in use in numerical weather prediction and climate modeling, and he developed the so-called Bergen School of Meteorology, which was successful in advancing weather prediction and meteorology in the early 20th century. Life and career Born in Christiania (later renamed Oslo), Bjerknes enjoyed an early exposure to fluid dynamics, as assistant to his father, Carl Anton Bjerknes, who had discovered by mathematical analysis the apparent actions at a distance between pulsating and oscillating bodies in a fluid, and their analogy with the electric and magnetic actions at a distance. Apparently no attempt had been made to demonstrate experimentally the theories arrived at by the older professor until Vilhelm Bjerknes, then about 17 or 18 years of age, tur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Weather Forecasting
Numerical weather prediction (NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in the 1950s that numerical weather predictions produced realistic results. A number of global and regional forecast models are run in different countries worldwide, using current weather observations relayed from radiosondes, weather satellites and other observing systems as inputs. Mathematical models based on the same physical principles can be used to generate either short-term weather forecasts or longer-term climate predictions; the latter are widely applied for understanding and projecting climate change. The improvements made to regional models have allowed for significant improvements in tropical cyclone track and air quality forecasts; however, atmospheric models perform poorly at handling processes that occur in a relatively con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
