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Joseph Fels Ritt
Joseph Fels Ritt (August 23, 1893 – January 5, 1951) was an American mathematician at Columbia University in the early 20th century. He was born and died in New York. Biography After beginning his undergraduate studies at City College of New York, Ritt received his B.A. from George Washington University in 1913. He then earned a doctorate in mathematics from Columbia University in 1917 under the supervision of Edward Kasner. After doing calculations for the war effort in World War I, he joined the Columbia faculty in 1921. He served as department chair from 1942 to 1945, and in 1945 became the Davies Professor of Mathematics.. In 1932, George Washington University honored him with a Doctorate in Science,. and in 1933 he was elected to join the United States National Academy of Sciences. He has 905 academic descendants listed in the Mathematics Genealogy Project, mostly through his student Ellis Kolchin, as of May 2024. Ritt was an Invited Speaker with talk ''Elementary fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indefinite Integral
In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a continuous function is a differentiable function whose derivative is equal to the original function . This can be stated symbolically as . The process of solving for antiderivatives is called antidifferentiation (or indefinite integration), and its opposite operation is called ''differentiation'', which is the process of finding a derivative. Antiderivatives are often denoted by capital Roman letters such as and . Antiderivatives are related to definite integrals through the second fundamental theorem of calculus: the definite integral of a function over a closed interval where the function is Riemann integrable is equal to the difference between the values of an antiderivative evaluated at the endpoints of the interval. In physics, antiderivatives arise in the context of rectilinear motion (e.g., in explaining the relationship between position, velocity ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Columbia Graduate School Of Arts And Sciences Alumni
Columbia most often refers to: * Columbia (personification), the historical personification of the United States * Columbia University, a private university in New York City * Columbia Pictures, an American film studio owned by Sony Pictures * Columbia Sportswear, an American clothing company * Columbia, South Carolina * Columbia, Missouri Columbia may also refer to: Places North America Natural features * Columbia Plateau, a geologic and geographic region in the U.S. Pacific Northwest * Columbia River, in Canada and the United States ** Columbia Bar, a sandbar in the estuary of the Columbia River ** Columbia Country, the region of British Columbia encompassing the northern portion of that river's upper reaches *** Columbia Valley, a region within the Columbia Country ** Columbia Lake, a lake at the head of the Columbia River *** Columbia Wetlands, a protected area near Columbia Lake ** Columbia Slough, along the Columbia watercourse near Portland, Oregon * Glacial Lake ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Members Of The United States National Academy Of Sciences
Member may refer to: * Military jury, referred to as "Members" in military jargon * Element (mathematics), an object that belongs to a mathematical set * In object-oriented programming, a member of a class ** Field (computer science), entries in a database ** Member variable, a variable that is associated with a specific object * Limb (anatomy), an appendage of the human or animal body ** Euphemism for penis * Structural component of a truss, connected by nodes * User (computing), a person making use of a computing service, especially on the Internet * Member (geology), a component of a geological formation * Member of parliament * The Members, a British punk rock band * Meronymy, a semantic relationship in linguistics * Church membership, belonging to a local Christian congregation, a Christian denomination and the universal Church * Member, a participant in a club or learned society A learned society ( ; also scholarly, intellectual, or academic society) is an organizatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1951 Deaths
Events January * January 4 – Korean War: Third Battle of Seoul – Chinese and North Korean forces capture Seoul for the second time (having lost the Second Battle of Seoul in September 1950). * January 9 – The Government of the United Kingdom announces abandonment of the Tanganyika groundnut scheme for the cultivation of peanuts in the Tanganyika Territory, with the writing off of £36.5M debt. * January 11 – In the U.S., a top secret report is delivered to U.S. President Truman by his National Security Resources Board, urging Truman to expand the Korean War by launching "a global offensive against communism" with sustained bombing of Red China and diplomatic moves to establish "moral justification" for a U.S. nuclear attack on the Soviet Union. The report will not not be declassified until 1978. * January 15 – In a criminal court in West Germany, Ilse Koch, The "Witch of Buchenwald", wife of the commandant of the Buchenwald concentration camp, is sentenced to li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1893 Births
Events January * January 2 – Webb C. Ball introduces railroad chronometers, which become the general railroad timepiece standards in North America. * January 6 – The Washington National Cathedral is chartered by Congress; the charter is signed by President Benjamin Harrison. * January 13 ** The Independent Labour Party of the United Kingdom has its first meeting. ** U.S. Marines from the ''USS Boston'' land in Honolulu, Hawaii, to prevent the queen from abrogating the Bayonet Constitution. * January 15 – The '' Telefon Hírmondó'' service starts with around 60 subscribers, in Budapest. * January 17 – Overthrow of the Kingdom of Hawaii: Lorrin A. Thurston and the Citizen's Committee of Public Safety in Hawaii, with the intervention of the United States Marine Corps, overthrow the government of Queen Liliuokalani. * January 21 – The Tati Concessions Land, formerly part of Matabeleland, is formally annexed to the Bechuanaland Protec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ritt's Polynomial Decomposition Theorem
In mathematics, a polynomial decomposition expresses a polynomial ''f'' as the functional composition g \circ h of polynomials ''g'' and ''h'', where ''g'' and ''h'' have degree greater than 1; it is an algebraic functional decomposition. Algorithms are known for decomposing univariate polynomials in polynomial time. Polynomials which are decomposable in this way are composite polynomials; those which are not are indecomposable polynomials or sometimes prime polynomials J.F. Ritt, "Prime and Composite Polynomials", ''Transactions of the American Mathematical Society'' 23:1:51–66 (January, 1922) (not to be confused with irreducible polynomials, which cannot be factored into products of polynomials). The degree of a composite polynomial is always a composite number, the product of the degrees of the composed polynomials. The rest of this article discusses only univariate polynomials; algorithms also exist for multivariate polynomials of arbitrary degree. Examples In the simp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ritt Theorem
In mathematics, exponential polynomials are functions on fields, rings, or abelian groups that take the form of polynomials in a variable and an exponential function. Definition In fields An exponential polynomial generally has both a variable ''x'' and some kind of exponential function ''E''(''x''). In the complex numbers there is already a canonical exponential function, the function that maps ''x'' to '' e''''x''. In this setting the term exponential polynomial is often used to mean polynomials of the form ''P''(''x'', ''e''''x'') where ''P'' ∈ C 'x'', ''y''is a polynomial in two variables. There is nothing particularly special about C here; exponential polynomials may also refer to such a polynomial on any exponential field or exponential ring with its exponential function taking the place of ''e''''x'' above. Similarly, there is no reason to have one variable, and an exponential polynomial in ''n'' variables would be of the form ''P''(''x''1, ..., ''x''''n'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bôcher Prize
Bocher is a surname. Notable people with the surname include: *Christiane Bøcher (1798–1874), Norwegian stage actress who was engaged at the Christiania Offentlige Theater * Édouard Bocher (1811–1900), French politician who was one of the founders of the Conférence Molé-Tocqueville * Herbert Böcher (1903–1983), German middle-distance runner who competed in the 1928 Summer Olympics * Joan Bocher (died 1550), English Anabaptist burned at the stake for heresy * Main Bocher (1890–1976), American fashion designer who founded the fashion label Mainbocher * Maxime Bôcher (1867–1918), American mathematician who published about 100 papers on differential equations, series, and algebra * Tyge W. Böcher (1909–1983), Danish botanist, evolutionary biologist, plant ecologist and phytogeographer See also *Bôcher Memorial Prize, founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher *Bôcher's theorem In mathematics, Bôcher's theorem is either of two t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wu's Method Of Characteristic Set
Wenjun Wu's method is an algorithm for solving multivariate polynomial equations introduced in the late 1970s by the Chinese mathematician Wen-Tsun Wu. This method is based on the mathematical concept of characteristic set introduced in the late 1940s by J.F. Ritt. It is fully independent of the Gröbner basis method, introduced by Bruno Buchberger (1965), even if Gröbner bases may be used to compute characteristic sets. Wu's method is powerful for mechanical theorem proving in elementary geometry, and provides a complete decision process for certain classes of problem. It has been used in research in his laboratory (KLMM, Key Laboratory of Mathematics Mechanization in Chinese Academy of Science) and around the world. The main trends of research on Wu's method concern systems of polynomial equations of positive dimension and differential algebra where Ritt's results have been made effective. Wu's method has been applied in various scientific fields, like biology, computer v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Algebraic Group
In mathematics, a differential algebraic group is a differential algebraic variety with a compatible group A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic iden ... structure. Differential algebraic groups were introduced by . References * * Algebraic groups {{group-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
