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Andrew Odlyzko
Andrew Michael Odlyzko (Andrzej Odłyżko) (born 23 July 1949) is a Polish- American mathematician and a former head of the University of Minnesota's Digital Technology Center and of the Minnesota Supercomputing Institute. He began his career in 1975 at Bell Telephone Laboratories, where he stayed for 26 years before joining the University of Minnesota in 2001. Work in mathematics Odlyzko received his B.S. and M.S. in mathematics from the California Institute of Technology and his Ph.D. from the Massachusetts Institute of Technology in 1975. In the field of mathematics he has published extensively on analytic number theory, computational number theory, cryptography, algorithms and computational complexity, combinatorics, probability, and error-correcting codes. In the early 1970s, he was a co-author (with D. Kahaner and Gian-Carlo Rota) of one of the founding papers of the modern umbral calculus. In 1985 he and Herman te Riele disproved the Mertens conjecture. In mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Research Institute Of Oberwolfach
The Oberwolfach Research Institute for Mathematics () is a center for mathematical research in Oberwolfach, Germany. It was founded by mathematician Wilhelm Süss in 1944. It organizes weekly workshops on diverse topics where mathematicians and scientists from all over the world come to do interdisciplinary, collaborative research. The Institute is a member of the Leibniz Association, funded mainly by the Federal Ministry of Education and Research (Germany), German Federal Ministry of Education and Research and by the state of Baden-Württemberg. It also receives substantial funding from the ''Friends of Oberwolfach'' foundation, from the ''Oberwolfach Foundation'' and from numerous donors. History The Oberwolfach Research Institute for Mathematics (MFO) was founded as the ''Reich Institute of Mathematics'' (German: ''Reichsinstitut für Mathematik'') on 1 September 1944. It was one of several research institutes founded by the Nazism, Nazis in order to further the German war ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analysis Of Algorithms
In computer science, the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other resources needed to execute them. Usually, this involves determining a function that relates the size of an algorithm's input to the number of steps it takes (its time complexity) or the number of storage locations it uses (its space complexity). An algorithm is said to be efficient when this function's values are small, or grow slowly compared to a growth in the size of the input. Different inputs of the same size may cause the algorithm to have different behavior, so best, worst and average case descriptions might all be of practical interest. When not otherwise specified, the function describing the performance of an algorithm is usually an upper bound, determined from the worst case inputs to the algorithm. The term "analysis of algorithms" was coined by Donald Knuth. Algorithm analysis is an important part of a broa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Publishing
Electronic publishing (also referred to as e-publishing, digital publishing, or online publishing) includes the digital publication of e-books, digital magazines, and the development of digital libraries and catalogues. It also includes the editing of books, journals, and magazines to be posted on a screen (computer, e-reader, tablet, or smartphone). About Electronic publishing has become common in scientific publishing where it has been argued that peer-reviewed scientific journals are in the process of being replaced by electronic publishing. It is also becoming common to distribute books, magazines, and newspapers to consumers through tablet reading devices, a market that is growing by millions each year, generated by online vendors such as Apple's iTunes bookstore, Amazon's bookstore for Kindle, and books in the Google Play Bookstore. Market research suggested that half of all magazine and newspaper circulation would be via digital delivery by the end of 2015 and that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Communication Network
A telecommunications network is a group of nodes interconnected by telecommunications links that are used to exchange messages between the nodes. The links may use a variety of technologies based on the methodologies of circuit switching, message switching, or packet switching, to pass messages and signals. Multiple nodes may cooperate to pass the message from an originating node to the destination node, via multiple network hops. For this routing function, each node in the network is assigned a network address for identification and locating it on the network. The collection of addresses in the network is called the address space of the network. Examples of telecommunications networks include computer networks, the Internet, the public switched telephone network (PSTN), the global Telex network, the aeronautical ACARS network, and the wireless radio networks of cell phone telecommunication providers. Network structure this is the structure of network general, every teleco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős Number
The Erdős number () describes the "collaborative distance" between mathematician Paul Erdős and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a particular individual has collaborated with a large and broad number of peers. Overview Paul Erdős (1913–1996) was an influential Hungarian mathematician who, in the latter part of his life, spent a great deal of time writing papers with a large number of colleagues — more than 500 — working on solutions to outstanding mathematical problems. He published more papers during his lifetime (at least 1,525) than any other mathematician in history. (Leonhard Euler published more total pages of mathematics but fewer separate papers: about 800.) Erdős spent most of his career with no permanent home or job. He traveled with everything he owned in two suitcases, and would visit mathematicians with whom he wanted to collaborate, often unexpectedly, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Erdős
Paul Erdős ( ; 26March 191320September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, graph theory, number theory, mathematical analysis, approximation theory, set theory, and probability theory. Much of his work centered on discrete mathematics, cracking many previously unsolved problems in the field. He championed and contributed to Ramsey theory, which studies the conditions in which order necessarily appears. Overall, his work leaned towards solving previously open problems, rather than developing or exploring new areas of mathematics. Erdős published around 1,500 mathematical papers during his lifetime, a figure that remains unsurpassed. He was known both for his social practice of mathematics, working with more than 500 collaborators, and for his eccentric lifestyle; ''Time'' magazine called him "The Oddball's Oddba ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Matrix
In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled randomly from a probability distribution. Random matrix theory (RMT) is the study of properties of random matrices, often as they become large. RMT provides techniques like mean-field theory, diagrammatic methods, the cavity method, or the replica method to compute quantities like traces, spectral densities, or scalar products between eigenvectors. Many physical phenomena, such as the spectrum of nuclei of heavy atoms, the thermal conductivity of a lattice, or the emergence of quantum chaos, can be modeled mathematically as problems concerning large, random matrices. Applications Physics In nuclear physics, random matrices were introduced by Eugene Wigner to model the nuclei of heavy atoms. Wigner postulated that the spacings between the lines in the spectrum of a heavy atom nucleus should resemble the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann Zeta Function
The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots for and its analytic continuation elsewhere. The Riemann zeta function plays a pivotal role in analytic number theory and has applications in physics, probability theory, and applied statistics. Leonhard Euler first introduced and studied the function over the reals in the first half of the eighteenth century. Bernhard Riemann's 1859 article "On the Number of Primes Less Than a Given Magnitude" extended the Euler definition to a complex variable, proved its meromorphic continuation and functional equation, and established a relation between its zeros and the distribution of prime numbers. This paper also contained the Riemann hypothesis, a conjecture about the distribution of complex zeros of the Riemann zeta function that many mathematicians consider th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mertens Conjecture
In mathematics, the Mertens conjecture is the statement that the Mertens function M(n) is bounded by \pm\sqrt. Although now disproven, it had been shown to imply the Riemann hypothesis. It was conjectured by Thomas Joannes Stieltjes, in an 1885 letter to Charles Hermite (reprinted in ), and again in print by , and disproved by . It is a striking example of a mathematical conjecture proven false despite a large amount of computational evidence in its favor. Definition In number theory, the Mertens function is defined as : M(n) = \sum_ \mu(k), where μ(k) is the Möbius function; the Mertens conjecture is that for all ''n'' > 1, : , M(n), < \sqrt. Disproof of the conjecture Stieltjes claimed in 1885 to have proven a weaker result, namely that was[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Herman Te Riele
Hermanus Johannes Joseph te Riele (born 5 January 1947) is a Dutch mathematician at CWI in Amsterdam with a specialization in computational number theory. He is known for proving the correctness of the Riemann hypothesis for the first 1.5 billion non-trivial zeros of the Riemann zeta function with Jan van de Lune and Dik Winter, for disproving the Mertens conjecture with Andrew Odlyzko, and for factoring large numbers of world record size. In 1987, he found a new upper bound for π(''x'') − Li(''x''). In 1970, Te Riele received an engineer's degree in mathematical engineering from Delft University of Technology and, in 1976, a PhD degree in mathematics and physics from University of Amsterdam The University of Amsterdam (abbreviated as UvA, ) is a public university, public research university located in Amsterdam, Netherlands. Established in 1632 by municipal authorities, it is the fourth-oldest academic institution in the Netherlan ... (1976). References * * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Umbral Calculus
The term umbral calculus has two related but distinct meanings. In mathematics, before the 1970s, umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain shadowy techniques used to prove them. These techniques were introduced in 1861 by John Blissard and are sometimes called Blissard's symbolic method. They are often attributed to Édouard Lucas (or James Joseph Sylvester), who used the technique extensively. The use of shadowy techniques was put on a solid mathematical footing starting in the 1970s, and the resulting mathematical theory is also referred to as "umbral calculus". History In the 1930s and 1940s, Eric Temple Bell attempted to set the umbral calculus on a rigorous footing, however his attempt in making this kind of argument logically rigorous was unsuccessful. The combinatorialist John Riordan in his book ''Combinatorial Identities'' published in the 1960s, used techniques of this sort extensively. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gian-Carlo Rota
Gian-Carlo Rota (April 27, 1932 – April 18, 1999) was an Italian-American mathematician and philosopher. He spent most of his career at the Massachusetts Institute of Technology, where he worked in combinatorics, functional analysis, probability theory, and phenomenology. Early life and education Rota was born in Vigevano, Italy. His father, Giovanni, an architect and prominent antifascist, was the brother of the mathematician Rosetta, who was the wife of the writer Ennio Flaiano. Gian-Carlo's family left Italy when he was 13 years old, initially going to Switzerland. Rota attended the Colegio Americano de Quito in Ecuador, and graduated with an A.B. in mathematics from Princeton University in 1953 after completing a senior thesis, titled "On the solubility of linear equations in topological vector spaces", under the supervision of William Feller. He then pursued graduate studies at Yale University, where he received a Ph.D. in mathematics in 1956 after completing a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
