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Nikolai Luzin
Nikolai Nikolayevich Luzin (also spelled Lusin; rus, Никола́й Никола́евич Лу́зин, p=nʲɪkɐˈlaj nʲɪkɐˈlajɪvʲɪtɕ ˈluzʲɪn, a=Ru-Nikilai Nikilayevich Luzin.ogg; 9 December 1883 – 28 February 1950) was a Soviet and Russian mathematician known for his work in descriptive set theory and aspects of mathematical analysis with strong connections to point-set topology. He was the eponym of Luzitania, a loose group of young Moscow mathematicians of the first half of the 1920s. They adopted his set-theoretic orientation, and went on to apply it in other areas of mathematics. Life He started studying mathematics in 1901 at Moscow State University, where his advisor was Dmitri Egorov. He graduated in 1905. Luzin underwent great personal turmoil in the years 1905 and 1906, when his materialistic worldview had collapsed and he found himself close to suicide. In 1906 he wrote to Pavel Florensky, a former fellow mathematics student who was now studying ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Irkutsk
Irkutsk ( ; rus, Иркутск, p=ɪrˈkutsk; Buryat language, Buryat and , ''Erhüü'', ) is the largest city and administrative center of Irkutsk Oblast, Russia. With a population of 587,891 Irkutsk is the List of cities and towns in Russia by population, 25th-largest city in Russia by population, the fifth-largest in the Siberian Federal District, and one of the largest types of inhabited localities in Russia, cities in Siberia. Located in the south of the eponymous oblast, the city proper lies on the Angara River, a tributary of the Yenisei River, Yenisei, about 850 kilometres (530 mi) to the south-east of Krasnoyarsk and about 520 kilometres (320 mi) north of Ulaanbaatar. The Trans-Siberian Highway (Federal M53 and M55 Highways) and Trans-Siberian Railway connect Irkutsk to other regions in Russia and Mongolia. Many distinguished Russians were sent into exile in Irkutsk for their part in the Decembrist revolt of 1825, and the city became an exile-post for the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pyotr Novikov
Pyotr Sergeyevich Novikov (; 15 August 1901, Moscow – 9 January 1975, Moscow) was a Soviet mathematician known for his work in group theory. His son, Sergei Novikov, was also a mathematician. Early life and education Pyotr Sergeyevich Novikov was born on 15 August 1901 in Moscow, Russia to Sergei Novikov, a merchant, and Alexandra Novikov. He served in the Red Army during the Russian Civil War from 1920 to July 1922. He studied at Moscow University from 1919 to 1920 and again from 1922 until he graduated in 1925. He studied under Nikolai Luzin until he finished his graduate studies in 1929. Career Novikov worked at the Moscow D. Mendeleev Institute of Chemical Technology from 1929 until 1934, when he joined the Department of Real Function Theory at the Steklov Institute of Mathematics. He was awarded his doctorate in 1935 and promoted to full professor in 1939. Novikov became head of the Department of Analysis at the Moscow State Teachers Training Institute in 1944. In 19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor Series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the 18th century. The partial sum formed by the first terms of a Taylor series is a polynomial of degree that is called the th Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally more accurate as increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pavel Florensky
Pavel Alexandrovich Florensky (also P. A. Florenskiĭ, Florenskii, Florenskij; ; ; – December 8, 1937) was a Russian Orthodox theologian, priest, philosopher, mathematician, physicist, electrical engineer, inventor, polymath, neomartyr and folk saint. During the later twentieth century, statements had appeared noting a recognition by the Russian Orthodox Church of him as a saint, though it was later firmly noted that no such decision had been made. Biography Early life Pavel Aleksandrovich Florensky was born on in the town of Yevlakh in Elisabethpol Governorate (in present-day Azerbaijan) into the family of a railroad engineer, Aleksandr Florensky. His father came from a family of Russian Orthodox priests while his mother Olga (Salomia) Saparova (Saparyan, Sapharashvili) was of the Tbilisi Armenian nobility in Georgia.Natalino Valentini, (ed.) Pavel Florenskij, ''La colonna e il fondamento della verità'', San Paolo editore, 2010, p. lxxi. His maternal grandmother Sofia Pa ... [...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] |
Set-theoretic
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory. The non-formalized systems investigated during this early stage go under the name of ''naive set theory''. After the discovery of paradoxes within naive set theory (such as Russell's paradox, Cantor's paradox and the Burali-Forti paradox), various axiomatic systems were proposed in the early twentieth century, of which Zermelo–Fraenkel set theory (with or without the axiom of choice) is still the best-known and most studied. Set theory is commonly employed as a foundationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eponym
An eponym is a noun after which or for which someone or something is, or is believed to be, named. Adjectives derived from the word ''eponym'' include ''eponymous'' and ''eponymic''. Eponyms are commonly used for time periods, places, innovations, biological nomenclature, astronomical objects, works of art and media, and tribal names. Various orthographic conventions are used for eponyms. Usage of the word The term ''eponym'' functions in multiple related ways, all based on an explicit relationship between two named things. ''Eponym'' may refer to a person or, less commonly, a place or thing for which someone or something is, or is believed to be, named. ''Eponym'' may also refer to someone or something named after, or believed to be named after, a person or, less commonly, a place or thing. A person, place, or thing named after a particular person share an eponymous relationship. In this way, Elizabeth I of England is the eponym of the Elizabethan era, but the Elizabethan ... [...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, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); 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's theorem. The number of known mathematicians grew when Pythagoras of Samos () 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 math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luzin Set
In mathematics, a Luzin space (or Lusin space), named for N. N. Luzin, is an uncountable topological T1 space without isolated points in which every nowhere-dense subset is countable. There are many minor variations of this definition in use: the T1 condition can be replaced by T2 or T3, and some authors allow a countable or even arbitrary number of isolated points. The existence of a Luzin space is independent of the axioms of ZFC. showed that the continuum hypothesis implies that a Luzin space exists. showed that assuming Martin's axiom and the negation of the continuum hypothesis, there are no Hausdorff Luzin spaces. In real analysis In real analysis and descriptive set theory, a Luzin set (or Lusin set), is defined as an uncountable subset of the reals such that every uncountable subset of is nonmeager; that is, of second Baire category. Equivalently, is an uncountable set of reals that meets every first category set in only countably many points. Luzin proved ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luzin's Theorem
In the mathematical field of mathematical analysis, Lusin's theorem (or Luzin's theorem, named for Nikolai Luzin) or Lusin's criterion states that an almost-everywhere finite function is measurable if and only if it is a continuous function on nearly all its domain. In the informal formulation of J. E. Littlewood, "every measurable function is nearly continuous". Classical statement For an interval 'a'', ''b'' let :f: ,brightarrow \mathbb be a measurable function. Then, for every ''ε'' > 0, there exists a compact ''E'' ⊆ 'a'', ''b''such that ''f'' restricted to ''E'' is continuous and :\mu ( E ) > b - a - \varepsilon. Note that ''E'' inherits the subspace topology from 'a'', ''b'' continuity of ''f'' restricted to ''E'' is defined using this topology. Also for any function ''f'', defined on the interval 'a, b''and almost-everywhere finite, if for any ''ε > 0'' there is a function ''ϕ'', continuous on 'a, b'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point-set Topology
In mathematics, general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. The fundamental concepts in point-set topology are ''continuity'', ''compactness'', and ''connectedness'': * Continuous functions, intuitively, take nearby points to nearby points. * Compact sets are those that can be covered by finitely many sets of arbitrarily small size. * Connected sets are sets that cannot be divided into two pieces that are far apart. The terms 'nearby', 'arbitrarily small', and 'far apart' can all be made precise by using the concept of open sets. If we change the definition of 'open set', we change what continuous functions, compact sets, and connected sets are. Each choice of definition for 'open set' is called a ''topology''. A set with a topology i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (mathematics), series, and analytic functions. These theories are usually studied in the context of Real number, real and Complex number, complex numbers and Function (mathematics), functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any Space (mathematics), space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space). History Ancient Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
