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Endre Szemerédi
Endre Szemerédi (; born August 21, 1940) is a Hungarian-American mathematician and computer scientist, working in the field of combinatorics and theoretical computer science. He has been the State of New Jersey Professor of computer science at Rutgers University since 1986. He also holds a professor emeritus status at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences. Szemerédi has won prizes in mathematics and science, including the Abel Prize in 2012. He has made a number of discoveries in combinatorics and computer science, including Szemerédi's theorem, the Szemerédi regularity lemma, the Erdős–Szemerédi theorem, the Hajnal–Szemerédi theorem and the Szemerédi–Trotter theorem. Early life Szemerédi was born in Budapest. Since his parents wished him to become a doctor, Szemerédi enrolled at a college of medicine, but he dropped out after six months (in an interview he explained it: "I was not sure I could do work bearing su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Budapest
Budapest is the Capital city, capital and List of cities and towns of Hungary, most populous city of Hungary. It is the List of cities in the European Union by population within city limits, tenth-largest city in the European Union by population within city limits and the List of cities and towns on the river Danube, second-largest city on the river Danube. The estimated population of the city in 2025 is 1,782,240. This includes the city's population and surrounding suburban areas, over a land area of about . Budapest, which is both a List of cities and towns of Hungary, city and Counties of Hungary, municipality, forms the centre of the Budapest metropolitan area, which has an area of and a population of 3,019,479. It is a primate city, constituting 33% of the population of Hungary. The history of Budapest began when an early Celts, Celtic settlement transformed into the Ancient Rome, Roman town of Aquincum, the capital of Pannonia Inferior, Lower Pannonia. The Hungarian p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfréd Rényi Prize
The Alfréd Rényi Prize is awarded biennially by the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Science in honor of founder Alfréd Rényi. By the current rules it is given to one or two fellows of the Institute in recognition of their outstanding performance in 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 ar ... research of the previous five-year period. Members of the Hungarian Academy of Sciences and the director are not eligible. Laureates See also * List of mathematics awards * List of prizes named after people References External links Official Website {{DEFAULTSORT:Alfred Renyi Prize Awards of the Hungarian Academy of Sciences Awards established in 1972 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hajnal–Szemerédi Theorem
In graph theory, an area of mathematics, an equitable coloring is an assignment of colors to the vertices of an undirected graph, in such a way that *No two adjacent vertices have the same color, and *The numbers of vertices in any two color classes differ by at most one. That is, the partition of vertices among the different colors is as uniform as possible. For instance, giving each vertex a distinct color would be equitable, but would typically use many more colors than are necessary in an optimal equitable coloring. An equivalent way of defining an equitable coloring is that it is an embedding of the given graph as a subgraph of a Turán graph with the same set of vertices. There are two kinds of chromatic number associated with equitable coloring.. The equitable chromatic number of a graph ''G'' is the smallest number ''k'' such that ''G'' has an equitable coloring with ''k'' colors. But ''G'' might not have equitable colorings for some larger numbers of colors; the equitable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős–Szemerédi Theorem
In arithmetic combinatorics, the Erdős–Szemerédi theorem states that for every finite set of integers, at least one of the sets and (the sets of pairwise sums and pairwise products, respectively) form a significantly larger set. More precisely, the Erdős–Szemerédi theorem states that there exist positive constants and such that, for any non-empty set , :\max( , A+A, , , A \cdot A, ) \geq c , A, ^ . It was proved by Paul Erdős and Endre Szemerédi in 1983.. The notation denotes the cardinality of the set . The set of pairwise sums is and is called the sumset of . The set of pairwise products is and is called the product set of ; it is also written . The theorem is a version of the maxim that additive structure and multiplicative structure cannot coexist. It can also be viewed as an assertion that the real line does not contain any set resembling a finite subring or finite subfield; it is the first example of what is now known as the sum-product phenomenon, whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Szemerédi Regularity Lemma
In extremal graph theory, Szemerédi’s regularity lemma states that a graph can be partitioned into a bounded number of parts so that the edges between parts are regular (in the sense defined below). The lemma shows that certain properties of random graphs can be applied to dense graphs like counting the copies of a given subgraph within graphs. Endre Szemerédi proved the lemma over bipartite graphs for his theorem on arithmetic progressions in 1975 and for general graphs in 1978. Variants of the lemma use different notions of regularity and apply to other mathematical objects like hypergraphs. Statement To state Szemerédi's regularity lemma formally, we must formalize what the edge distribution between parts behaving 'almost randomly' really means. By 'almost random', we're referring to a notion called -regularity. To understand what this means, we first state some definitions. In what follows is a graph with vertex set . Definition 1. Let be disjoint subsets of . The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Szemerédi's Theorem
In arithmetic combinatorics, Szemerédi's theorem is a result concerning arithmetic progressions in subsets of the integers. In 1936, Erdős and Turán conjectured that every set of integers ''A'' with positive natural density contains a ''k''-term arithmetic progression for every ''k''. Endre Szemerédi proved the conjecture in 1975. Statement A subset ''A'' of the natural numbers is said to have positive upper density if :\limsup_\frac > 0. Szemerédi's theorem asserts that a subset of the natural numbers with positive upper density contains an arithmetic progression of length ''k'' for all positive integers ''k''. An often-used equivalent finitary version of the theorem states that for every positive integer ''k'' and real number \delta \in (0, 1], there exists a positive integer :N = N(k,\delta) such that every subset of of size at least \delta N contains an arithmetic progression of length ''k''. Another formulation uses the function ''r''''k''(''N''), the size of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hungarian Academy Of Sciences
The Hungarian Academy of Sciences ( , MTA) is Hungary’s foremost and most prestigious learned society. Its headquarters are located along the banks of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. The Academy's primary functions include the advancement of scientific knowledge, the dissemination of research findings, the support of research and development, and the representation of science in Hungary both domestically and around the world. History The origins of the Hungarian Academy of Sciences date back to 1825, when Count István Széchenyi offered one year's income from his estate to establish a ''Learned Society''. He made this offer during a session of the Diet in Pressburg (Pozsony, now Bratislava), then the seat of the Hungarian Parliament. Inspired by his gesture, other delegates soon followed suit. The Society’s mission was defined as the development of the Hungarian language and the promotion of sciences and the arts in the Hungarian l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfréd Rényi Institute Of Mathematics
The Alfréd Rényi Institute of Mathematics () is the research institute in mathematics of the Hungarian Academy of Sciences. It was created in 1950 by Alfréd Rényi, who directed it until his death. Since its creation, the institute has been the center of mathematical research in Hungary. It received the title ''Centre of Excellence of the European Union'' (2001). The current director is András Stipsicz. The institute publishes the research journal Studia Scientiarum Mathematicarum Hungarica. Research divisions and research groups * Algebra (head: Mátyás Domokos) * Algebraic geometry and differential topology (head: András Némethi) * Algebraic Logic (head: Hajnal Andréka) * Analysis (head: András Kroó) * Combinatorics and discrete mathematics (head: Ervin Győri) * Geometry (head: Gábor Fejes Tóth) * Number theory (head: János Pintz) * Probability & statistics (head: Péter Major) * Set theory and general topology (head: Lajos Soukup) * Cryptology (head: Gábo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Computer Science
Theoretical computer science is a subfield of computer science and mathematics that focuses on the Abstraction, abstract and mathematical foundations of computation. It is difficult to circumscribe the theoretical areas precisely. The Association for Computing Machinery, ACM's Special Interest Group on Algorithms and Computation Theory (SIGACT) provides the following description: History While logical inference and mathematical proof had existed previously, in 1931 Kurt Gödel proved with his incompleteness theorem that there are fundamental limitations on what statements could be proved or disproved. Information theory was added to the field with A Mathematical Theory of Communication, a 1948 mathematical theory of communication by Claude Shannon. In the same decade, Donald Hebb introduced a mathematical model of Hebbian learning, learning in the brain. With mounting biological data supporting this hypothesis with some modification, the fields of neural networks and para ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Scientist
A computer scientist is a scientist who specializes in the academic study of computer science. Computer scientists typically work on the theoretical side of computation. Although computer scientists can also focus their work and research on specific areas (such as algorithm and data structure development and design, software engineering, information theory, database theory, theoretical computer science, numerical analysis, programming language theory, compiler, computer graphics, computer vision, robotics, computer architecture, operating system), their foundation is the theoretical study of computing from which these other fields derive. A primary goal of computer scientists is to develop or validate models, often mathematical, to describe the properties of computational systems (Processor (computing), processors, programs, computers interacting with people, computers interacting with other computers, etc.) with an overall objective of discovering designs that yield useful ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Népszava
''Népszava'' (, meaning "People's Voice" in English) is a social-democratic Hungarian language newspaper published in Hungary. History and profile ''Népszava'' is Hungary's eldest continuous print publication and as of October 2019 the last and only remaining liberal, social democratic political daily in the country. ''Népszava'' was established in 1873 in Budapest by Viktor Külföldi. It was the official newspaper of the Hungarian Social Democratic Party until 1948 when Hungary became a communist state. During this period two of ''Népszava'''s editors in chief were murdered: :hu:Somogyi Béla, Béla Somogyi (along with reporter Béla Bacsó) in 1920 by right wing officers and :hu:Mónus Illés, Illés Mónus in 1944 by members of the Hungarian Nazi Arrow Cross Party militia. During the period of the Hungarian People's Republic between 1948 and 1989, it was the official newspaper of Hungarian trade unions. In 1990 it was privatized. Its publisher, the entrepreneur :hu:Fe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
