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Fundamental Theorem Of Algebra
The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant polynomial, constant single-variable polynomial with Complex number, complex coefficients has at least one complex Zero of a function, root. This includes polynomials with real coefficients, since every real number is a complex number with its imaginary part equal to zero. Equivalently (by definition), the theorem states that the field (mathematics), field of complex numbers is Algebraically closed field, algebraically closed. The theorem is also stated as follows: every non-zero, single-variable, Degree of a polynomial, degree ''n'' polynomial with complex coefficients has, counted with Multiplicity (mathematics)#Multiplicity of a root of a polynomial, multiplicity, exactly ''n'' complex roots. The equivalence of the two statements can be proven through the use of successive polynomial division. Despite its name, it is not fundamental for modern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constant Polynomial
In mathematics, a polynomial is a Expression (mathematics), mathematical expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms. An example of a polynomial of a single indeterminate is . An example with three indeterminates is . Polynomials appear in many areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problem (mathematics education), word problems to complicated scientific problems; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; and they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicolaus I Bernoulli
Nicolaus Bernoulli (also spelled Nicolas or Nikolas; in Basel – 29 November 1759 in Basel) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. Biography Nicolaus Bernoulli was born on in Basel. He was the son of Nicolaus Bernoulli, painter and Alderman of Basel. In 1704 he graduated from the University of Basel under Jakob Bernoulli and obtained his PhD five years later (in 1709) with a work on probability theory in law. His thesis was titled ''Dissertatio Inauguralis Mathematico-Juridica de Usu Artis Conjectandi in Jure''. In 1716 he obtained the Galileo-chair at the University of Padua, where he worked on differential equations and geometry. In 1722 he returned to Switzerland and obtained a chair in Logics at the University of Basel. Nicolaus I Bernoulli was deeply influenced by his family, particularly his uncle Jacob Bernoulli and his cousin Daniel Bernoulli, both of whom were prominent mathematicians. Jacob Bernoulli, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cauchy
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 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 was the son of Loui ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Amateur Mathematicians
This is a list of amateur mathematicians—people whose primary vocation did not involve mathematics (or any similar discipline) yet made notable, and sometimes important, contributions to the field of mathematics. *Ahmes (scribe) *Ashutosh Mukherjee (lawyer) *Robert Ammann (programmer and postal worker) *John Arbuthnot (surgeon and author) *Jean-Robert Argand (shopkeeper) *Leon Bankoff (Beverly Hills dentist) *Thomas Bayes, Rev. Thomas Bayes (Presbyterian minister) *Andrew Beal (businessman) *Isaac Beeckman (candlemaker) *Chester Ittner Bliss (biologist) *Napoléon Bonaparte (general) *Mary Everest Boole (homemaker, librarian) *William Bourne (mathematician), William Bourne (innkeeper) *Nathaniel Bowditch (indentured bookkeeper) *Achille Brocot (clockmaker) *Jost Bürgi (clockmaker) *Marvin Ray Burns (veteran) *Gerolamo Cardano (medical doctor) *D. G. Champernowne (college student) *Thomas Clausen (mathematician), Thomas Clausen (technical assistant) *Cleo (mathematician), Cleo ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean-Robert Argand
Jean-Robert Argand (, , ; July 18, 1768 – August 13, 1822) was a Genevan amateur mathematician. In 1806, while managing a bookstore in Paris, he published the idea of geometrical interpretation of complex numbers known as the Argand diagram and is known for the first rigorous proof of the Fundamental Theorem of Algebra. Life Jean-Robert Argand was born in Geneva, then Republic of Geneva, to Jacques Argand and Eve Carnac. His background and education are mostly unknown. Since his knowledge of mathematics was self-taught and he did not belong to any mathematical organizations, he likely pursued mathematics as a hobby rather than a profession. Argand moved to Paris in 1806 with his family and, when managing a bookshop there, privately published his ''Essai sur une manière de représenter les quantités imaginaires dans les constructions géométriques'' (Essay on a method of representing imaginary quantities). In 1813, it was republished in the French journal ''Annales de Mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexander Ostrowski
Alexander Markowich Ostrowski (; ; 25 September 1893 – 20 November 1986) was a mathematician. Biography His father Mark having been a merchant, Alexander Ostrowski attended the Kiev College of Commerce, not a high school, and thus had an insufficient qualification to be admitted to university. However, his talent did not remain undetected: Ostrowski's mentor, Dmitry Grave, wrote to Edmund Landau and Kurt Hensel for help. Subsequently, Ostrowski began to study mathematics at Marburg University under Hensel's supervision in 1912. During World War I he was interned, but thanks to the intervention of Hensel, the restrictions on his movements were eased somewhat, and he was allowed to use the university library. After the war ended, Ostrowski moved to Göttingen where he wrote his doctoral dissertation and was influenced by David Hilbert, Felix Klein, and Landau. In 1920, after having obtained his doctorate from the University of Göttingen, Ostrowski moved to Hamburg where he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observatory and professor of astronomy from 1807 until his death in 1855. While studying at the University of Göttingen, he propounded several mathematical theorems. As an independent scholar, he wrote the masterpieces '' Disquisitiones Arithmeticae'' and ''Theoria motus corporum coelestium''. Gauss produced the second and third complete proofs of the fundamental theorem of algebra. In number theory, he made numerous contributions, such as the composition law, the law of quadratic reciprocity and the Fermat polygonal number theorem. He also contributed to the theory of binary and ternary quadratic forms, the construction of the heptadecagon, and the theory of hypergeometric series. Due to Gauss' extensive and fundamental contributions to science ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Wood (mathematician)
James Wood (14 December 1760 – 23 April 1839) was a mathematician, and Master of St John's College, Cambridge. In his later years he was Dean of Ely. Life Wood was born in Holcombe, Greater Manchester, Holcombe, Bury, Greater Manchester, Bury where his father ran an evening school and taught his son the elements of arithmetic and algebra. From Bury Grammar School he proceeded to St John's College, Cambridge in 1778, graduating as senior wrangler in 1782. On graduating he became a fellow of the college and in his long tenure there produced several successful academic textbooks for students of mathematics. Between 1795 and 1799 his ''The principles of mathematics and natural philosophy'', was printed, in four volumes, by J. Burges. Vol.I: 'The elements of algebra', by Wood; Vol.II: 'The principles of fluxions' by Samuel Vince; Vol.III Part I: 'The principles of mechanics" by Wood; and Vol.III Part II: "The principles of hydrostatics" by Samuel Vince; Vol.IV "The principles of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Splitting Field
In abstract algebra, a splitting field of a polynomial with coefficients in a field is the smallest field extension of that field over which the polynomial ''splits'', i.e., decomposes into linear factors. Definition A splitting field of a polynomial ''p''(''X'') over a field ''K'' is a field extension ''L'' of ''K'' over which ''p'' factors into linear factors :p(X) = c \prod_^ (X - a_i) where c \in K and for each i we have X - a_i \in L /math> with ''ai'' not necessarily distinct and such that the roots ''ai'' generate ''L'' over ''K''. The extension ''L'' is then an extension of minimal degree over ''K'' in which ''p'' splits. It can be shown that such splitting fields exist and are unique up to isomorphism. The amount of freedom in that isomorphism is known as the Galois group of ''p'' (if we assume it is separable). A splitting field of a set ''P'' of polynomials is the smallest field over which each of the polynomials in ''P'' splits. Properties An extension ''L'' th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre-Simon Laplace
Pierre-Simon, Marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French polymath, a scholar whose work has been instrumental in the fields of physics, astronomy, mathematics, engineering, statistics, and philosophy. He summarized and extended the work of his predecessors in his five-volume Traité de mécanique céleste, ''Mécanique céleste'' (''Celestial Mechanics'') (1799–1825). This work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. Laplace also popularized and further confirmed Isaac Newton, Sir Isaac Newton's work. In statistics, the Bayesian probability, Bayesian interpretation of probability was developed mainly by Laplace. Laplace formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. The Laplace operator, Laplacian differential operator, widely used in mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Louis Lagrange
Joseph-Louis Lagrange (born Giuseppe Luigi LagrangiaJoseph-Louis Lagrange, comte de l’Empire ''Encyclopædia Britannica'' or Giuseppe Ludovico De la Grange Tournier; 25 January 1736 – 10 April 1813), also reported as Giuseppe Luigi Lagrange or Lagrangia, was an Italian and naturalized French , physicist and astronomer. He made significa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
François Daviet De Foncenex
François Daviet de Foncenex (1734 – 1799) was a Royal Sardinian Army officer and mathematician. Life and work François Daviet de Foncenex was born in Thonon in the Duchy of Savoy in 1734. He studied in the '' Accademia di Torino'' under the professorship of Joseph-Louis Lagrange, who was two years younger than him. In 1759, Daviet was appointed as a member of the ''Accademia delle Scienze di Torino''. He was commissioned as a lieutenant in the Royal Sardinian Army and quickly rose through the ranks. From 1790 to 1792, Daviet served as the governor of Sassari Sassari ( ; ; ; ) is an Italian city and the second-largest of Sardinia in terms of population with 120,497 inhabitants as of 2025, and a functional urban area of about 260,000 inhabitants. One of the oldest cities on the island, it contains ... and Villefranche-sur-Mer. In 1792, he fought against the French Revolutionary Army; he was subsequently convicted of treason and sentenced to imprisonment for one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
