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Alexandre-Théophile Vandermonde
Alexandre-Théophile Vandermonde (28 February 1735 – 1 January 1796) was a French mathematician, musician and chemist who worked with Bézout and Lavoisier; his name is now principally associated with determinant theory in mathematics. He was born in Paris, and died there. Biography Vandermonde was a violinist, and became engaged with mathematics only around 1770. In ''Mémoire sur la résolution des équations'' (1771) he reported on symmetric functions and solution of cyclotomic polynomials; this paper anticipated later Galois theory (see also abstract algebra for the role of Vandermonde in the genesis of group theory). In ''Remarques sur des problèmes de situation'' (1771) he studied knight's tours, and presaged the development of knot theory by explicitly noting the importance of topological features when discussing the properties of knots: ''"Whatever the twists and turns of a system of threads in space, one can always obtain an expression for the calculation of its dimen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemist
A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin ''alchemist'') is a scientist trained in the study of chemistry. Chemists study the composition of matter and its properties. Chemists carefully describe the properties they study in terms of quantities, with detail on the level of molecules and their component atoms. Chemists carefully measure substance proportions, chemical reaction rates, and other chemical properties. In Commonwealth English, pharmacists are often called chemists. Chemists use their knowledge to learn the composition and properties of unfamiliar substances, as well as to reproduce and synthesize large quantities of useful naturally occurring substances and create new artificial substances and useful processes. Chemists may specialize in any number of subdisciplines of chemistry. Materials scientists and metallurgists share much of the same education and skills with chemists. The work of chemists is often related to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conservatoire National Des Arts Et Métiers
A music school is an educational institution specialized in the study, training, and research of music. Such an institution can also be known as a school of music, music academy, music faculty, college of music, music department (of a larger institution), conservatory, conservatorium or conservatoire ( , ). Instruction consists of training in the performance of musical instruments, singing, musical composition, conducting, musicianship, as well as academic and research fields such as musicology, music history and music theory. Music instruction can be provided within the compulsory general education system, or within specialized children's music schools such as the Purcell School. Elementary-school children can access music instruction also in after-school institutions such as music academies or music schools. In Venezuela El Sistema of youth orchestras provides free after-school instrumental instruction through music schools called ''núcleos''. The term "music school" can a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Algebraists
Linearity is the property of a mathematical relationship (''function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear relationship of voltage and current in an electrical conductor (Ohm's law), and the relationship of mass and weight. By contrast, more complicated relationships are ''nonlinear''. Generalized for functions in more than one dimension, linearity means the property of a function of being compatible with addition and scaling, also known as the superposition principle. The word linear comes from Latin ''linearis'', "pertaining to or resembling a line". In mathematics In mathematics, a linear map or linear function ''f''(''x'') is a function that satisfies the two properties: * Additivity: . * Homogeneity of degree 1: for all α. These properties are known as the superposition principle. In this definition, ''x'' is not necessarily a real nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
18th-century French Mathematicians
The 18th century lasted from January 1, 1701 ( MDCCI) to December 31, 1800 ( MDCCC). During the 18th century, elements of Enlightenment thinking culminated in the American, French, and Haitian Revolutions. During the century, slave trading and human trafficking expanded across the shores of the Atlantic, while declining in Russia, China, and Korea. Revolutions began to challenge the legitimacy of monarchical and aristocratic power structures, including the structures and beliefs that supported slavery. The Industrial Revolution began during mid-century, leading to radical changes in human society and the environment. Western historians have occasionally defined the 18th century otherwise for the purposes of their work. For example, the "short" 18th century may be defined as 1715–1789, denoting the period of time between the death of Louis XIV of France and the start of the French Revolution, with an emphasis on directly interconnected events. To historians who expand ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientists From Paris
A scientist is a person who conducts scientific research to advance knowledge in an area of the natural sciences. In classical antiquity, there was no real ancient analog of a modern scientist. Instead, philosophers engaged in the philosophical study of nature called natural philosophy, a precursor of natural science. Though Thales (circa 624-545 BC) was arguably the first scientist for describing how cosmic events may be seen as natural, not necessarily caused by gods,Frank N. Magill''The Ancient World: Dictionary of World Biography'', Volume 1 Routledge, 2003 it was not until the 19th century that the term ''scientist'' came into regular use after it was coined by the theologian, philosopher, and historian of science William Whewell in 1833. In modern times, many scientists have advanced degrees in an area of science and pursue careers in various sectors of the economy such as academia, industry, government, and nonprofit environments.'''' History The roles ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1796 Deaths
Events January–March * January 16 – The first Dutch (and general) elections are held for the National Assembly of the Batavian Republic. (The next Dutch general elections are held in 1888.) * February 1 – The capital of Upper Canada is moved from Newark to York. * February 9 – The Qianlong Emperor of China abdicates at age 84 to make way for his son, the Jiaqing Emperor. * February 15 – French Revolutionary Wars: The Invasion of Ceylon (1795) ends when Johan van Angelbeek, the Batavian governor of Ceylon, surrenders Colombo peacefully to British forces. * February 16 – The Kingdom of Great Britain is granted control of Ceylon by the Dutch. * February 29 – Ratifications of the Jay Treaty between Great Britain and the United States are officially exchanged, bringing it into effect.''Harper's Encyclopaedia of United States History from 458 A. D. to 1909'', ed. by Benson John Lossing and, Woodrow Wilson (Harper & Brothers, 1910) p17 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1735 Births
Events January–March * January 2 – Alexander Pope's poem ''Epistle to Dr Arbuthnot'' is published in London. * January 8 – George Frideric Handel's opera ''Ariodante'' is premièred at the Royal Opera House in Covent Garden, London. * February 3 – All 256 people on board the Dutch East India Company ships '' Vliegenthart'' and ''Anna Catherina'' die when the two ships sink in a gale off of the Netherlands coast. The wreckage of ''Vliegenthart'' remains undiscovered until 1981. * February 14 – The ''Order of St. Anna'' is established in Russia, in honor of the daughter of Peter the Great. * March 10 – The Russian Empire and Persia sign the Treaty of Ganja, with Russia ceding territories in the Caucasus mountains to Persia, and the two rivals forming a defensive alliance against the Ottoman Empire. * March 11 – Abraham Patras becomes the Governor-General of the Dutch East Indies (now Indonesia) upon the death of Dirck van Cloon. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vandermonde Polynomial
In algebra, the Vandermonde polynomial of an ordered set of ''n'' variables X_1,\dots, X_n, named after Alexandre-Théophile Vandermonde, is the polynomial: :V_n = \prod_ (X_j-X_i). (Some sources use the opposite order (X_i-X_j), which changes the sign \binom times: thus in some dimensions the two formulas agree in sign, while in others they have opposite signs.) It is also called the Vandermonde determinant, as it is the determinant of the Vandermonde matrix. The value depends on the order of the terms: it is an alternating polynomial, not a symmetric polynomial. Alternating The defining property of the Vandermonde polynomial is that it is ''alternating'' in the entries, meaning that permuting the X_i by an odd permutation changes the sign, while permuting them by an even permutation does not change the value of the polynomial – in fact, it is the basic alternating polynomial, as will be made precise below. It thus depends on the order, and is zero if two entries are equal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knot Theory
In the mathematical field of topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, Unknot, the simplest knot being a ring (or "unknot"). In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, \mathbb^3 (in topology, a circle is not bound to the classical geometric concept, but to all of its homeomorphisms). Two mathematical knots are equivalent if one can be transformed into the other via a deformation of \mathbb^3 upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing through itself. Knots can be described in various ways. Using different description methods, there may be more than one description of the same knot. For example, a common method of descr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knight's Tour
A knight's tour is a sequence of moves of a knight on a chessboard such that the knight visits every square exactly once. If the knight ends on a square that is one knight's move from the beginning square (so that it could tour the board again immediately, following the same path), the tour is closed (or re-entrant); otherwise, it is open. The knight's tour problem is the mathematical problem of finding a knight's tour. Creating a program to find a knight's tour is a common problem given to computer science students. Variations of the knight's tour problem involve chessboards of different sizes than the usual , as well as irregular (non-rectangular) boards. Theory The knight's tour problem is an instance of the more general Hamiltonian path problem in graph theory. The problem of finding a closed knight's tour is similarly an instance of the Hamiltonian cycle problem. Unlike the general Hamiltonian path problem, the knight's tour problem can be solved in linear time. Histor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conservatoire National Des Arts Et Métiers
A music school is an educational institution specialized in the study, training, and research of music. Such an institution can also be known as a school of music, music academy, music faculty, college of music, music department (of a larger institution), conservatory, conservatorium or conservatoire ( , ). Instruction consists of training in the performance of musical instruments, singing, musical composition, conducting, musicianship, as well as academic and research fields such as musicology, music history and music theory. Music instruction can be provided within the compulsory general education system, or within specialized children's music schools such as the Purcell School. Elementary-school children can access music instruction also in after-school institutions such as music academies or music schools. In Venezuela El Sistema of youth orchestras provides free after-school instrumental instruction through music schools called ''núcleos''. The term "music school" can a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vandermonde's Identity
In combinatorics, Vandermonde's identity (or Vandermonde's convolution) is the following identity for binomial coefficients: :=\sum_^r for any nonnegative integers ''r'', ''m'', ''n''. The identity is named after Alexandre-Théophile Vandermonde (1772), although it was already known in 1303 by the Chinese mathematician Zhu Shijie.See for the history. There is a ''q''-analog to this theorem called the ''q''-Vandermonde identity. Vandermonde's identity can be generalized in numerous ways, including to the identity : = \sum_ \cdots . Proofs Algebraic proof In general, the product of two polynomials with degrees ''m'' and ''n'', respectively, is given by :\biggl(\sum_^m a_ix^i\biggr) \biggl(\sum_^n b_jx^j\biggr) = \sum_^\biggl(\sum_^r a_k b_\biggr) x^r, where we use the convention that ''ai'' = 0 for all integers ''i'' > ''m'' and ''bj'' = 0 for all integers ''j'' > ''n''. By the binomial theorem, :(1+x)^ = \sum_^ x^r. U ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
