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Augustus De Morgan
Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorous. Biography Childhood Augustus De Morgan was born in Madurai, in the Carnatic region of India in 1806. His father was Lieut.-Colonel John De Morgan (1772–1816), who held various appointments in the service of the East India Company, and his mother, Elizabeth (née Dodson, 1776–1856), was daughter of John Dodson and granddaughter of James Dodson, who computed a table of anti-logarithms (inverse logarithms). Augustus De Morgan became blind in one eye a month or two after he was born. The family moved to England when Augustus was seven months old. As his father and grandfather had both been born in India, De Morgan used to say that he was neither English, nor Scottish, nor Irish, but a Briton "unattached", using the technical term applied to an undergraduate of Oxford or Cambridge w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Madurai
Madurai ( , also , ) is a major city in the Indian state of Tamil Nadu. It is the cultural capital of Tamil Nadu and the administrative headquarters of Madurai District. As of the 2011 census, it was the third largest Urban agglomeration in Tamil Nadu after Chennai and Coimbatore and the 44th most populated city in India. Located on the banks of River Vaigai, Madurai has been a major settlement for two millennia and has a documented history of more than 2500 years. It is often referred to as "Thoonga Nagaram", meaning "the city that never sleeps". Madurai is closely associated with the Tamil language. The third Tamil Sangam, a major congregation of Tamil scholars said to have been held in the city. The recorded history of the city goes back to the 3rd century BCE, being mentioned by Megasthenes, the Greek ambassador to the Maurya empire, and Kautilya, a minister of the Mauryan emperor Chandragupta Maurya. Signs of human settlements and Roman trade links dating back to 3 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Francis Guthrie
Francis Guthrie (born 22 January 1831 in London; d. 19 October 1899 in Claremont, Cape Town) was a South African mathematician and botanist who first posed the Four Colour Problem in 1852. He studied mathematics under Augustus De Morgan, and botany under John Lindley at University College London. Guthrie obtained his B.A. in 1850, and LL.B. in 1852 with first class honours. While colouring a map of the counties of England, he noticed that at least four colours were required so that no two regions sharing a common border were the same colour. He postulated that four colours would be sufficient to colour any map. This became known as the Four Color Problem, and remained one of the most famous unsolved problems in topology for more than a century until it was eventually proven in 1976 using a lengthy computer-aided proof. Guthrie arrived in South Africa on 10 April 1861 and was met and entertained by Dr Dale (later Sir Langham Dale), who was instrumental in the establishing of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Induction
Mathematical induction is a method for proving that a statement ''P''(''n'') is true for every natural number ''n'', that is, that the infinitely many cases ''P''(0), ''P''(1), ''P''(2), ''P''(3), ... all hold. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: A proof by induction consists of two cases. The first, the base case, proves the statement for ''n'' = 0 without assuming any knowledge of other cases. The second case, the induction step, proves that ''if'' the statement holds for any given case ''n'' = ''k'', ''then'' it must also hold for the next case ''n'' = ''k'' + 1. These two steps establish that the statement holds for every natural number ''n''. The base case does not necessarily begin with ''n'' = 0, but often with ''n'' = 1, and possibly with any fixed natural number ''n'' = ''N'', establishing the truth of the statement for all natu ... [...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, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); 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' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) 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 mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William De Morgan
William Frend De Morgan (16 November 1839 – 15 January 1917) was an English potter, tile designer and novelist. A lifelong friend of William Morris, he designed tiles, stained glass and furniture for Morris & Co. from 1863 to 1872. His tiles often recall medieval or Islamic design patterns. He applied innovative glazes and firing techniques. Galleons and fish were common motifs, as were "fantastical" birds and animals. Many of De Morgan's tiles were designed to create intricate patterns when several were laid together. Life and work Born in Gower Street, London, the son of the distinguished mathematician Augustus De Morgan and his highly educated wife Sophia Elizabeth Frend, De Morgan was supported in his desire to become an artist. At the age of twenty, he entered the Royal Academy schools, but he was swiftly disillusioned with the establishment. Then he met Morris and through him the Pre-Raphaelite circle. Soon De Morgan began experimenting with stained glass, ventured ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lotfi Asker Zadeh
Lotfi Aliasker Zadeh (; az, Lütfi Rəhim oğlu Ələsgərzadə; fa, لطفی علیعسکرزاده; 4 February 1921 – 6 September 2017) was a mathematician, computer scientist, electrical engineer, artificial intelligence researcher, and professor of computer science at the University of California, Berkeley. Zadeh is best known for proposing fuzzy mathematics, consisting of several ''fuzzy''-related concepts: fuzzy sets, fuzzy logic, fuzzy algorithms, fuzzy semantics, fuzzy languages, fuzzy control, fuzzy systems, fuzzy probabilities, fuzzy events, and fuzzy information. Zadeh was a founding member of the Eurasian Academy. Early life and career Azerbaijan Zadeh was born in Baku, Azerbaijan SSR, as Lotfi Aliaskerzadeh. McNeil & Freiberger, p. 17 His father was Rahim Aleskerzade, an Iranian Muslim Azerbaijani journalist from Ardabil on assignment from Iran, and his mother was Fanya (Feyga) Korenman, a Jewish pediatrician from Odessa, Ukraine, who was an Iranian citiz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isaac Todhunter
Isaac Todhunter FRS (23 November 1820 – 1 March 1884), was an English mathematician who is best known today for the books he wrote on mathematics and its history. Life and work The son of George Todhunter, a Nonconformist minister, and Mary née Hume, he was born at Rye, Sussex. He was educated at Hastings, where his mother had opened a school after the death of his father in 1826. He became an assistant master at a school at Peckham, attending at the same time evening classes at the University College, London where he was influenced by Augustus De Morgan. In 1842 he obtained a mathematical scholarship and graduated as B.A. at London University, where he was awarded the gold medal on the M.A. examination. About this time he became mathematical master at a school at Wimbledon. In 1844 Todhunter entered St John's College, Cambridge, where he was senior wrangler in 1848, and gained the first Smith's Prize and the Burney Prize; and in 1849 he was elected to a fellowship, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas Corwin Mendenhall
Thomas Corwin Mendenhall (October 4, 1841 – March 23, 1924) was an American autodidact physicist and meteorologist. He was the first professor hired at Ohio State University in 1873 and the superintendent of the U.S. Coast and Geodetic Survey (now known as NOAA) from 1889 to 1894. Alongside his work, he was also an advocate for the adoption of the metric system by the United States and is the father of author profiling. Biography Mendenhall was born in Hanoverton, Ohio, to Stephen Mendenhall, a farmer and carriage-maker, and Mary Thomas. In 1852 the family moved to Marlboro, a Quaker community outside of Akron, Ohio. His parents were strong abolitionists and frequently opened their home to escaped slaves heading north along the Underground Railroad. Mendenhall became principal of the local primary school in 1858. He formalized his teaching qualifications at National Normal University in 1861 with an ''Instructor Normalis'' degree.Carey (1999) While living in Columbus, Ohio, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Boole
George Boole (; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher, and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ireland. He worked in the fields of differential equations and algebraic logic, and is best known as the author of ''The Laws of Thought'' (1854) which contains Boolean algebra. Boolean logic is credited with laying the foundations for the Information Age. Early life Boole was born in 1815 in Lincoln, Lincolnshire, England, the son of John Boole senior (1779–1848), a shoemaker and Mary Ann Joyce. He had a primary school education, and received lessons from his father, but due to a serious decline in business, he had little further formal and academic teaching. William Brooke, a bookseller in Lincoln, may have helped him with Latin, which he may also have learned at the school of Thomas Bainbridge. He was self-taught in modern languages.H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universal Algebra
Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of study, in universal algebra one takes the class of groups as an object of study. Basic idea In universal algebra, an algebra (or algebraic structure) is a set ''A'' together with a collection of operations on ''A''. An ''n''- ary operation on ''A'' is a function that takes ''n'' elements of ''A'' and returns a single element of ''A''. Thus, a 0-ary operation (or ''nullary operation'') can be represented simply as an element of ''A'', or a '' constant'', often denoted by a letter like ''a''. A 1-ary operation (or ''unary operation'') is simply a function from ''A'' to ''A'', often denoted by a symbol placed in front of its argument, like ~''x''. A 2-ary operation (or ''binary operation'') is often denoted by a symbol placed between its argum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relation Algebra
In mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation. The motivating example of a relation algebra is the algebra 2''X''² of all binary relations on a set ''X'', that is, subsets of the cartesian square ''X''2, with ''R''•''S'' interpreted as the usual composition of binary relations ''R'' and ''S'', and with the converse of ''R'' as the converse relation. Relation algebra emerged in the 19th-century work of Augustus De Morgan and Charles Peirce, which culminated in the algebraic logic of Ernst Schröder. The equational form of relation algebra treated here was developed by Alfred Tarski and his students, starting in the 1940s. Tarski and Givant (1987) applied relation algebra to a variable-free treatment of axiomatic set theory, with the implication that mathematics founded on set theory could itself be conducted without variables. Definition A relation algebra is an algebr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ratio Test
In mathematics, the ratio test is a test (or "criterion") for the convergence of a series :\sum_^\infty a_n, where each term is a real or complex number and is nonzero when is large. The test was first published by Jean le Rond d'Alembert and is sometimes known as d'Alembert's ratio test or as the Cauchy ratio test. The test The usual form of the test makes use of the limit The ratio test states that: * if ''L'' 1 then the series diverges; * if ''L'' = 1 or the limit fails to exist, then the test is inconclusive, because there exist both convergent and divergent series that satisfy this case. It is possible to make the ratio test applicable to certain cases where the limit ''L'' fails to exist, if limit superior and limit inferior are used. The test criteria can also be refined so that the test is sometimes conclusive even when ''L'' = 1. More specifically, let :R = \lim\sup \left, \frac\ :r = \lim\inf \left, \frac\. Then the ratio test states that: * if ''R'' 1, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
