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Tomek Bartoszyński
Tomek Bartoszyński (born May 16, 1957 as ''Tomasz Bartoszyński'' in Warsaw) is a Polish-American mathematician who works in set theory. He is the son of statistician Robert Bartoszyński. Biography Bartoszyński studied mathematics at the University of Warsaw from 1976 to 1981, and worked there from 1981 to 1987. In 1984 he defended his Ph.D. thesis ''Combinatorial aspects of measure and category''; his advisor was Wojciech Guzicki. In 2004 he received his habilitation from the Polish Academy of Sciences. From 1986 onwards he worked in the United States: he taught at the University of California in Berkeley and Davis. From 1990 to 2006 he was a professor (full professor from 1998 on) at Boise State University. In 1990/91 he visited the Hebrew University of Jerusalem as a fellow of the Lady Davis foundation, and in 1996/97 he visited the Free University of Berlin as a Humboldt fellow. Currently he is one of the program directors at the National Science Foundation (NSF), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Będlewo
Będlewo is a village in the administrative district of Gmina Stęszew, within Poznań County, Greater Poland Voivodeship, in west-central Poland. It lies approximately south of Stęszew and south-west of the regional capital Poznań. It is the location of the Mathematical Research and Conference Center of the Institute of Mathematics of the Polish Academy of Sciences The Polish Academy of Sciences ( pl, Polska Akademia Nauk, PAN) is a Polish state-sponsored institution of higher learning. Headquartered in Warsaw, it is responsible for spearheading the development of science across the country by a society of .... References Villages in Poznań County {{Poznań-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hebrew University Of Jerusalem
The Hebrew University of Jerusalem (HUJI; he, הַאוּנִיבֶרְסִיטָה הַעִבְרִית בִּירוּשָׁלַיִם) is a public research university based in Jerusalem, Israel. Co-founded by Albert Einstein and Dr. Chaim Weizmann in July 1918, the public university officially opened in April 1925. It is the second-oldest Israeli university, having been founded 30 years before the establishment of the State of Israel but six years after the older Technion university. The HUJI has three campuses in Jerusalem and one in Rehovot. The world's largest library for Jewish studies—the National Library of Israel—is located on its Edmond J. Safra campus in the Givat Ram neighbourhood of Jerusalem. The university has five affiliated teaching hospitals (including the Hadassah Medical Center), seven faculties, more than 100 research centers, and 315 academic departments. , one-third of all the doctoral candidates in Israel were studying at the HUJI. Among its first ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polish Set Theorists
Polish may refer to: * Anything from or related to Poland, a country in Europe * Polish language * Poles, people from Poland or of Polish descent * Polish chicken *Polish brothers (Mark Polish and Michael Polish, born 1970), American twin screenwriters Polish may refer to: * Polishing, the process of creating a smooth and shiny surface by rubbing or chemical action ** French polishing, polishing wood to a high gloss finish * Nail polish * Shoe polish * Polish (screenwriting), improving a script in smaller ways than in a rewrite See also * * * Polonaise (other) {{Disambiguation, surname Language and nationality disambiguation pages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baire Property
A subset A of a topological space X has the property of Baire (Baire property, named after René-Louis Baire), or is called an almost open set, if it differs from an open set by a meager set; that is, if there is an open set U\subseteq X such that A \bigtriangleup U is meager (where \bigtriangleup denotes the symmetric difference).. Definitions A subset A \subseteq X of a topological space X is called almost open and is said to have the property of Baire or the Baire property if there is an open set U\subseteq X such that A \bigtriangleup U is a meager subset, where \bigtriangleup denotes the symmetric difference. Further, A has the Baire property in the restricted sense if for every subset E of X the intersection A\cap E has the Baire property relative to E. Properties The family of sets with the property of Baire forms a σ-algebra. That is, the complement of an almost open set is almost open, and any countable union or intersection of almost open sets is again almo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cichoń's Diagram
In set theory, Cichoń's diagram or Cichon's diagram is a table of 10 infinite cardinal numbers related to the set theory of the reals displaying the provable relations between these Cardinal characteristic of the continuum, cardinal characteristics of the continuum. All these cardinals are greater than or equal to \aleph_1, the smallest uncountable cardinal, and they are bounded above by 2^, the cardinality of the continuum. Four cardinals describe properties of the ideal (order theory), ideal of sets of Lebesgue measure, measure zero; four more describe the corresponding properties of the ideal of meagre set, meager sets (first category sets). Definitions Let ''I'' be an ideal (set theory), ideal of a fixed infinite set ''X'', containing all finite subsets of ''X''. We define the following "Cardinal function, cardinal coefficients" of ''I'': *\operatorname(I)=\min\. ::The "additivity" of ''I'' is the smallest number of sets from ''I'' whose union is not in ''I'' any more. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haim Judah
The name ''Haim'' can be a first name or surname originating in the Hebrew language, or deriving from the Old German name ''Haimo''. Hebrew etymology Chayyim ( he, חַיִּים ', Classical Hebrew: , Israeli Hebrew: ), also transcribed ''Haim, Hayim, Chayim'', or ''Chaim'' (English pronunciations: , , ), is a Hebrew name meaning "life". Its first usage can be traced to the Middle Ages. It is a popular name among Jewish people. The feminine form for this name is Chaya ( he, חַיָּה ', Classical Hebrew: , Israeli Hebrew: ; English pronunciations: , ). '' Chai'' is the Hebrew word for "alive". According to Kabbalah, the name Hayim helps the person to remain healthy, and people were known to add Hayim as their second name to improve their health. In the United States, Chaim is a common spelling; however, since the phonemic pattern is unusual for English words, Hayim is often used as an alternative spelling. The "ch" spelling comes from transliteration of the Hebrew let ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Analysis
Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of linear elliptic PDEs dates at least as far back as Hodge theory. More recently, it refers largely to the use of nonlinear partial differential equations to study geometric and topological properties of spaces, such as submanifolds of Euclidean space, Riemannian manifolds, and symplectic manifolds. This approach dates back to the work by Tibor Radó and Jesse Douglas on minimal surfaces, John Forbes Nash Jr. on isometric embeddings of Riemannian manifolds into Euclidean space, work by Louis Nirenberg on the Minkowski problem and the Weyl problem, and work by Aleksandr Danilovich Aleksandrov and Aleksei Pogorelov on convex hypersurfaces. In the 1980s fundamental contributions by Karen Uhlenbeck,Jackson, Allyn. (2019)Founder of geometric anal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such as Stretch factor, stretching, Twist (mathematics), twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set (mathematics), set endowed with a structure, called a ''Topology (structure), topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity (mathematics), continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopy, homotopies. A property that is invariant under such deformations is a topological property. Basic exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joanna Kania-Bartoszyńska
Joanna is a feminine given name deriving from from he, יוֹחָנָה, translit=Yôḥānāh, lit=God is gracious. Variants in English include Joan, Joann, Joanne, and Johanna. Other forms of the name in English are Jan, Jane, Janet, Janice, Jean, and Jeanne. The earliest recorded occurrence of the name Joanna, in Luke 8:3, refers to the disciple "Joanna the wife of Chuza," who was an associate of Mary Magdalene. Her name as given is Greek in form, although it ultimately originated from the Hebrew masculine name יְהוֹחָנָן ''Yəhôḥānān'' or יוֹחָנָן ''Yôḥānān'' meaning 'God is gracious'. In Greek this name became Ιωαννης ''Iōannēs'', from which ''Iōanna'' was derived by giving it a feminine ending. The name Joanna, like Yehohanan, was associated with Hasmonean families. Saint Joanna was culturally Hellenized, thus bearing the Grecian adaptation of a Jewish name, as was commonly done in her milieu. At the beginning of the Christian era, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foundations Of Mathematics
Foundations of mathematics is the study of the philosophy, philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be quite vague. Foundations of mathematics can be conceived as the study of the basic mathematical concepts (set, function, geometrical figure, number, etc.) and how they form hierarchies of more complex structures and concepts, especially the fundamentally important structures that form the language of mathematics (formulas, theories and their model theory, models giving a meaning to formulas, definitions, proofs, algorithms, etc.) also called metamathematics, metamathematical concepts, with an eye to the philosophical aspects and the unity of mathematics. The search for foundations of mathematics is a cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ''ad hoc'' solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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