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Cauchy Sequence Illustration2
Baron Augustin-Louis Cauchy ( , , ; ; 21 August 1789 – 23 May 1857) was a French mathematician, engineer, and physicist. He was one of the first to rigorously state and prove the key theorems of calculus (thereby creating real analysis), pioneered the field complex analysis, and the study of permutation groups in abstract algebra. Cauchy also contributed to a number of topics in mathematical physics, notably continuum mechanics. A profound mathematician, Cauchy had a great influence over his contemporaries and successors; Hans Freudenthal stated: : "More concepts and theorems have been named for Cauchy than for any other mathematician (in Elasticity (physics), elasticity alone there are sixteen concepts and theorems named for Cauchy)." Cauchy was a prolific worker; he wrote approximately eight hundred research articles and five complete textbooks on a variety of topics in the fields of mathematics and mathematical physics. Biography Youth and education Cauchy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kingdom Of France
The Kingdom of France is the historiographical name or umbrella term given to various political entities of France in the Middle Ages, medieval and Early modern France, early modern period. It was one of the most powerful states in Europe from the High Middle Ages to 1848 during its dissolution. It was also an early French colonial empire, colonial power, with colonies in Asia and Africa, and the largest being New France in North America geographically centred around the Great Lakes. The Kingdom of France was descended directly from the West Francia, western Frankish realm of the Carolingian Empire, which was ceded to Charles the Bald with the Treaty of Verdun (843). A branch of the Carolingian dynasty continued to rule until 987, when Hugh Capet was elected king and founded the Capetian dynasty. The territory remained known as ''Francia'' and its ruler as ('king of the Franks') well into the High Middle Ages. The first king calling himself ('King of France') was Philip II of Fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
École Centrale Du Panthéon
École or Ecole may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoie, a French commune * École-Valentin, a French commune in the Doubs département * Grandes écoles, higher education establishments in France * The École The École, formerly Ecole Internationale de New York, is an intimate and independent French-American school, which cultivates an internationally minded community of students from 2 to 14 years old in New York City’s vibrant Flatiron Distric ..., a French-American bilingual school in New York City * Ecole Software, a Japanese video-games developer/publisher {{disambiguation, geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum Mechanics
Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a ''continuous medium'' (also called a ''continuum'') rather than as discrete particles. Continuum mechanics deals with ''deformable bodies'', as opposed to rigid bodies. A continuum model assumes that the substance of the object completely fills the space it occupies. While ignoring the fact that matter is made of atoms, this provides a sufficiently accurate description of matter on length scales much greater than that of inter-atomic distances. The concept of a continuous medium allows for intuitive analysis of bulk matter by using differential equations that describe the behavior of such matter according to physical laws, such as mass conservation, momentum conservation, and energy conservation. Information about the specific material is expressed in constitutive relationships. Continuum mechanics treats the physical properties of ... [...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, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structures include group (mathematics), groups, ring (mathematics), rings, field (mathematics), fields, module (mathematics), modules, vector spaces, lattice (order), lattices, and algebra over a field, algebras over a field. The term ''abstract algebra'' was coined in the early 20th century to distinguish it from older parts of algebra, and more specifically from elementary algebra, the use of variable (mathematics), variables to represent numbers in computation and reasoning. The abstract perspective on algebra has become so fundamental to advanced mathematics that it is simply called "algebra", while the term "abstract algebra" is seldom used except in mathematical education, pedagogy. Algebraic structures, with their associated homomorphisms, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation Group
In mathematics, a permutation group is a group ''G'' whose elements are permutations of a given set ''M'' and whose group operation is the composition of permutations in ''G'' (which are thought of as bijective functions from the set ''M'' to itself). The group of ''all'' permutations of a set ''M'' is the symmetric group of ''M'', often written as Sym(''M''). The term ''permutation group'' thus means a subgroup of the symmetric group. If then Sym(''M'') is usually denoted by S''n'', and may be called the ''symmetric group on n letters''. By Cayley's theorem, every group is isomorphic to some permutation group. The way in which the elements of a permutation group permute the elements of the set is called its group action. Group actions have applications in the study of symmetries, combinatorics and many other branches of mathematics, physics and chemistry. Basic properties and terminology A ''permutation group'' is a subgroup of a symmetric group; that is, its elements ... [...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] |
Real Analysis
In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include convergence, limits, continuity, smoothness, differentiability and integrability. Real analysis is distinguished from complex analysis, which deals with the study of complex numbers and their functions. Scope Construction of the real numbers The theorems of real analysis rely on the properties of the (established) real number system. The real number system consists of an uncountable set (\mathbb), together with two binary operations denoted and \cdot, and a total order denoted . The operations make the real numbers a field, and, along with the order, an ordered field. The real number system is the unique '' complete ordered field'', in the sense that any other complete ordered field is isomorphic to it. Intuitively, completenes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus
Calculus is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus. The former concerns instantaneous Rate of change (mathematics), rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus. They make use of the fundamental notions of convergence (mathematics), convergence of infinite sequences and Series (mathematics), infinite series to a well-defined limit (mathematics), limit. It is the "mathematical backbone" for dealing with problems where variables change with time or another reference variable. Infinitesimal calculus was formulated separately ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physicist
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate causes of Phenomenon, phenomena, and usually frame their understanding in mathematical terms. They work across a wide range of Physics#Research fields, research fields, spanning all length scales: from atom, sub-atomic and particle physics, through biological physics, to physical cosmology, cosmological length scales encompassing the universe as a whole. The field generally includes two types of physicists: Experimental physics, experimental physicists who specialize in the observation of natural phenomena and the development and analysis of experiments, and Theoretical physics, theoretical physicists who specialize in mathematical modeling of physical systems to rationalize, explain and predict natural phenomena. Physicists can apply their k ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random House Webster's Unabridged Dictionary
''Random House Webster's Unabridged Dictionary'' is a large American dictionary, first published in 1966 as ''The Random House Dictionary of the English Language: The Unabridged Edition''. Edited by Editor-in-chief Jess Stein, it contained 315,000 entries in 2256 pages, as well as 2400 illustrations. The CD-ROM version in 1994 also included 120,000 spoken pronunciations. History The Random House publishing company entered the reference book market after World War II. They acquired rights to the ''Century Dictionary'' and the ''Dictionary of American English'', both out of print. Their first dictionary was Clarence Barnhart's ''American College Dictionary'', published in 1947, and based primarily on ''The New Century Dictionary'', an abridgment of the ''Century''. In the late 1950s, it was decided to publish an expansion of the ''American College Dictionary'', which had been modestly updated with each reprinting since its publication. Under editors Jess Stein and Laurence Urdan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HarperCollins
HarperCollins Publishers LLC is a British–American publishing company that is considered to be one of the "Big Five (publishers), Big Five" English-language publishers, along with Penguin Random House, Hachette Book Group USA, Hachette, Macmillan Publishers, Macmillan, and Simon & Schuster. HarperCollins is headquartered in New York City and London and is a subsidiary of News Corp. The company's name is derived from a combination of the firm's predecessors. Harper & Brothers, founded in 1817 in New York, merged with Row, Peterson & Company in 1962 to form Harper & Row, which was acquired by News Corp in 1987. The Scotland, Scottish publishing company William Collins, Sons, founded in 1819 in Glasgow, was acquired by News Corp in 1987 and merged with Harper & Row to form HarperCollins. The logo for the firm combines the fire from Harper's torch and the water from Collins' fountain. HarperCollins operates publishing groups in the United States, Canada, the United Kingdom, Austr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
