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Noga Alon
Noga Alon (; born 1956) is an Israeli mathematician and a professor of mathematics at Princeton University noted for his contributions to combinatorics and theoretical computer science, having authored hundreds of papers. Education and career Alon was born in 1956 in Haifa, where he graduated from the Hebrew Reali School in 1974. He graduated summa cum laude from the Technion – Israel Institute of Technology in 1979, earned a master's degree in mathematics in 1980 from Tel Aviv University, and received his Ph.D. in Mathematics at the Hebrew University of Jerusalem in 1983 with the dissertation ''Extremal Problems in Combinatorics'' supervised by Micha Perles. After postdoctoral research at the Massachusetts Institute of Technology he returned to Tel Aviv University as a senior lecturer in 1985, obtained a permanent position as an associate professor there in 1986, and was promoted to full professor in 1988. He was head of the School of Mathematical Science from 1999 to 2001, ... [...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] |
Israel Prize
The Israel Prize (; ''pras israél'') is an award bestowed by the State of Israel, and regarded as the state's highest cultural honor. History Prior to the Israel Prize, the most significant award in the arts was the Dizengoff Prize and in Israeli literature, literature the Bialik Prize, awarded by the Tel Aviv municipality annually since 1930s. The Israel Prize is awarded annually, on Yom Ha'atzmaut, Israeli Independence Day, in a state ceremony in Jerusalem, in the presence of the President of Israel, President, the Prime Minister of Israel, Prime Minister, the List of Knesset speakers, Speaker of the Knesset (Israel's legislature), and the Supreme Court of Israel, Supreme Court President. The prize was established in 1953 at the initiative of the Education Minister of Israel, Minister of Education Ben-Zion Dinor, who himself went on to win the prize in 1958 and 1973. Awarding the prize The prize is awarded in the following four areas, with the precise subfields changing from y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parameterized Complexity
In computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according to their inherent difficulty with respect to ''multiple'' parameters of the input or output. The complexity of a problem is then measured as a function of those parameters. This allows the classification of NP-hard problems on a finer scale than in the classical setting, where the complexity of a problem is only measured as a function of the number of bits in the input. This appears to have been first demonstrated in . The first systematic work on parameterized complexity was done by . Under the assumption that P ≠ NP, there exist many natural problems that require super-polynomial running time when complexity is measured in terms of the input size only but that are computable in a time that is polynomial in the input size and exponential or worse in a parameter . Hence, if is fixed at a small value and the growth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Color-coding
In computer science and graph theory, the term color-coding refers to an algorithmic technique which is useful in the discovery of network motifs. For example, it can be used to detect a simple path of length in a given graph. The traditional color-coding algorithm is probabilistic, but it can be derandomized without much overhead in the running time. Color-coding also applies to the detection of cycles of a given length, and more generally it applies to the subgraph isomorphism problem (an NP-complete problem), where it yields polynomial time algorithms when the subgraph pattern that it is trying to detect has bounded treewidth. The color-coding method was proposed and analyzed in 1994 by Noga Alon, Raphael Yuster, and Uri Zwick.Alon, N., Yuster, R., and Zwick, U. 1995. Color-coding. J. ACM 42, 4 (Jul. 1995), 844–856. DOI= http://doi.acm.org/10.1145/210332.210337 Results The following results can be obtained through the method of color-coding: * For every fixed cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistic Method
In mathematics, the probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object. It works by showing that if one randomly chooses objects from a specified class, the probability that the result is of the prescribed kind is strictly greater than zero. Although the proof uses probability, the final conclusion is determined for ''certain'', without any possible error. This method has now been applied to other areas of mathematics such as number theory, linear algebra, and real analysis, as well as in computer science (e.g. randomized rounding), and information theory. Introduction If every object in a collection of objects fails to have a certain property, then the probability that a random object chosen from the collection has that property is zero. Thus, by contraposition, if the probability that a random object chosen from the collection has that property is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Massachusetts Institute Of Technology
The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of modern technology and science. In response to the increasing Technological and industrial history of the United States, industrialization of the United States, William Barton Rogers organized a school in Boston to create "useful knowledge." Initially funded by a land-grant universities, federal land grant, the institute adopted a Polytechnic, polytechnic model that stressed laboratory instruction in applied science and engineering. MIT moved from Boston to Cambridge in 1916 and grew rapidly through collaboration with private industry, military branches, and new federal basic research agencies, the formation of which was influenced by MIT faculty like Vannevar Bush. In the late twentieth century, MIT became a leading center for research in compu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Technion – Israel Institute Of Technology
The Technion – Israel Institute of Technology is a public university, public research university located in Haifa, Israel. Established in 1912 by Jews under the dominion of the Ottoman Empire, the Technion is the oldest university in the country. The university offers degrees in science and engineering, and related fields such as architecture, medicine, industrial management, and education. It has 19 academic departments, 60 research centers, and 12 affiliated teaching hospitals. Since its founding, it has awarded more than 123,000 degrees and its graduates are cited for providing the skills and education behind the creation and protection of the State of Israel. Technion's 565 faculty members include three Nobel laureates in Chemistry, Nobel Laureates in chemistry. Four Nobel Laureates, Nobel laureates have been associated with the university. The current List of presidents of the Technion, president of the Technion is Uri Sivan. The selection of Modern Hebrew, Hebrew as th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Summa Cum Laude
Latin honors are a system of Latin phrases used in some colleges and universities to indicate the level of distinction with which an academic degree has been earned. The system is primarily used in the United States. It is also used in some Southeastern Asian countries with European colonial history, such as Indonesia and the Philippines, and African countries such as Zambia and South Africa, although sometimes translations of these phrases are used instead of the Latin originals. The honors distinction should not be confused with the honors degree, honors degrees offered in some countries, or with honorary degree, honorary degrees. The system usually has three levels of honor (listed in order of increasing merit): ''cum laude'', ''magna cum laude'', and ''summa cum laude''. Generally, a college or university's regulations set out definite criteria a student must meet to obtain a given honor. For example, the student might be required to achieve a specific grade point average, su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hebrew Reali School
The Hebrew Reali School of Haifa (), located in Haifa, Israel, is one of the country's oldest private schools.The Hebrew Reali School, Haifa History The Reali school was established by on behalf of EZRA, a German Jewish organization, and in close connection with the Technion in 1913, before the outbreak of .[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haifa
Haifa ( ; , ; ) is the List of cities in Israel, third-largest city in Israel—after Jerusalem and Tel Aviv—with a population of in . The city of Haifa forms part of the Haifa metropolitan area, the third-most populous metropolitan area in Israel. It is home to the Baháʼí Faith's Baháʼí World Centre, and is a UNESCO World Heritage Site and a destination for Baháʼí pilgrimage. Built on the slopes of Mount Carmel, the settlement has a history spanning more than 3,000 years. The earliest known settlement in the vicinity was Tell Abu Hawam, a small port city established in the Late Bronze Age (14th century BCE).Encyclopaedia Judaica, Encyclopedia Judaica, ''Haifa'', Keter Publishing, Jerusalem, 1972, vol. 7, pp. 1134–1139 In the 3rd century CE, Haifa was known as a Tool and die maker, dye-making center. Over the millennia, the Haifa area has changed hands: being conquered and ruled by the Canaanites, History of ancient Israel and Judah, Israelites, Phoenicians, Assy ... [...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] |
