|
Gyula Bereznai
Gyula Bereznai (1 May 1921 – 6 September 1990) was a Hungarian mathematician and former head of department at a Teacher Training College in Nyíregyháza. Biography He was born in Sátoraljaújhely on 1 May 1921. He completed his elementary school in Tornyospálca, the secondary school in Kisvárda. His studies at the University of Debrecen were interrupted by the war (captivity). After six years in prison, he received a degree in mathematics from Eötvös Loránd University, Budapest. After the Nyíregyháza Vocational School and the Kölcsey Grammar School, he was admitted to the mathematics department of the Bessenyei György Teacher Training College in 1962. From 1969 to 1983 he was head of the department. For more than two decades he taught the future generation of teachers the basics of mathematical analysis, to whom he tried to pass on his knowledge and experience, and he was always happy to share it with his colleagues. Besides his professional security, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sátoraljaújhely
Sátoraljaújhely (; archaic german: Neustadt am Zeltberg ; sk, Nové Mesto pod Šiatrom; yi, איהעל, Ihel, or ) is a town located in Borsod-Abaúj-Zemplén county in northern Hungary along the Slovak border. It is east from the county capital Miskolc. History ''Sátor-alja'' (meaning "under the tent", referring to the tent-shaped mountain nearby) was a settlement from the Hungarian conquest of the Carpathian Basin until it was destroyed during the First Mongol invasion of Hungary. It was rebuilt in the 13th century, although there was disagreement among the citizens concerning the name: some wanted to keep the original name, and some wanted to rename it ''új hely'' ("new place"). Sátoraljaújhely was granted town status in 1261 by King Stephen V, and a castle was also built around that time. Sátoraljaújhely has often played an important role in the region's history: revolts against Habsburg rule began there in the 17th and 18th centuries. After the Revolution of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean-Marie Duhamel
Jean-Marie Constant Duhamel (; ; 5 February 1797 – 29 April 1872) was a French mathematician and physicist. His studies were affected by the troubles of the Napoleonic era. He went on to form his own school ''École Sainte-Barbe''. Duhamel's principle, a method of obtaining solutions to inhomogeneous linear evolution equations, is named after him. He was primarily a mathematician but did studies on the mathematics of heat, mechanics, and acoustics. He also did work in calculus using infinitesimals. Duhamel's theorem for infinitesimals says that the sum of a series of infinitesimals is unchanged by replacing the infinitesimal with its principal part. In 1843 he published about an early recording device he called a vibroscope. Like other similar devices, the vibroscope was a type of measuring device similar to an oscilloscope, and could not play back the etchings it recorded. Honours * 19617 Duhamel, asteroid An asteroid is a minor planet of the inner Solar System. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Ludwig Raabe
Joseph Ludwig Raabe (15 May 1801 in Brody, Galicia – 22 January 1859 in Zürich, Switzerland) was a Swiss mathematician. Life As his parents were quite poor, Raabe was forced to earn his living from a very early age by giving private lessons. He began to study mathematics in 1820 at the Polytechnicum in Vienna, Austria. In the autumn of 1831, he moved to Zürich, where he became professor of mathematics in 1833. In 1855, he became professor at the newly founded Swiss Polytechnicum. He is best known for Raabe's ratio test, an extension of d'Alembert's ratio test. Raabe's test serves to determine the convergence or divergence of an infinite series, in some cases. He is also known for the Raabe integral of the gamma function In mathematics, the gamma function (represented by , the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except ...:. ... [...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] |
Jean Le Rond D'Alembert
Jean-Baptiste le Rond d'Alembert (; ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the ''Encyclopédie''. D'Alembert's formula for obtaining solutions to the wave equation is named after him. The wave equation is sometimes referred to as d'Alembert's equation, and the fundamental theorem of algebra is named after d'Alembert in French. Early years Born in Paris, d'Alembert was the natural son of the writer Claudine Guérin de Tencin and the chevalier Louis-Camus Destouches, an artillery officer. Destouches was abroad at the time of d'Alembert's birth. Days after birth his mother left him on the steps of the church. According to custom, he was named after the patron saint of the church. D'Alembert was placed in an orphanage for foundling children, but his father found him and placed him with the wife of a glazier, Madame Rousseau, with who ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divergent Series
In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit. If a series converges, the individual terms of the series must approach zero. Thus any series in which the individual terms do not approach zero diverges. However, convergence is a stronger condition: not all series whose terms approach zero converge. A counterexample is the harmonic series :1 + \frac + \frac + \frac + \frac + \cdots =\sum_^\infty\frac. The divergence of the harmonic series was proven by the medieval mathematician Nicole Oresme. In specialized mathematical contexts, values can be objectively assigned to certain series whose sequences of partial sums diverge, in order to make meaning of the divergence of the series. A ''summability method'' or ''summation method'' is a partial function from the set of series to values. For example, Cesàro summation assigns Grandi's divergent ser ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called the ''length'' of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. The notion of a sequence can be generalized to an indexed family, defined as a function from an ''arbitrary'' index set. For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be ''finite'', as in these examples, or ''infi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convergent Series
In mathematics, a series is the sum of the terms of an infinite sequence of numbers. More precisely, an infinite sequence (a_0, a_1, a_2, \ldots) defines a series that is denoted :S=a_0 +a_1+ a_2 + \cdots=\sum_^\infty a_k. The th partial sum is the sum of the first terms of the sequence; that is, :S_n = \sum_^n a_k. A series is convergent (or converges) if the sequence (S_1, S_2, S_3, \dots) of its partial sums tends to a limit; that means that, when adding one a_k after the other ''in the order given by the indices'', one gets partial sums that become closer and closer to a given number. More precisely, a series converges, if there exists a number \ell such that for every arbitrarily small positive number \varepsilon, there is a (sufficiently large) integer N such that for all n \ge N, :\left , S_n - \ell \right , 1 produce a convergent series: *: ++++++\cdots = . * Alternating the signs of reciprocals of powers of 2 also produces a convergent series: *: -+-+-+\cdots = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Series (mathematics)
In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures (such as in combinatorics) through generating functions. In addition to their ubiquity in mathematics, infinite series are also widely used in other quantitative disciplines such as physics, computer science, statistics and finance. For a long time, the idea that such a potentially infinite summation could produce a finite result was considered paradoxical. This paradox was resolved using the concept of a limit during the 17th century. Zeno's paradox of Achilles and the tortoise illustrates this counterintuitive property of infinite sums: Achilles runs after a tortoise, but when he reaches the position of the tortoise at the beginning of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Books
A book is a medium for recording information in the form of writing or images, typically composed of many pages (made of papyrus, parchment, vellum, or paper) bound together and protected by a cover. The technical term for this physical arrangement is '' codex'' (plural, ''codices''). In the history of hand-held physical supports for extended written compositions or records, the codex replaces its predecessor, the scroll. A single sheet in a codex is a leaf and each side of a leaf is a page. As an intellectual object, a book is prototypically a composition of such great length that it takes a considerable investment of time to compose and still considered as an investment of time to read. In a restricted sense, a book is a self-sufficient section or part of a longer composition, a usage reflecting that, in antiquity, long works had to be written on several scrolls and each scroll had to be identified by the book it contained. Each part of Aristotle's ''Physics'' is called ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
