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The Erdős Distance Problem
''The Erdős Distance Problem'' is a monograph on the Erdős distinct distances problem in discrete geometry: how can one place n points into d-dimensional Euclidean space so that the pairs of points make the smallest possible distance set? It was written by Julia Garibaldi, Alex Iosevich, and Steven Senger, and published in 2011 by the American Mathematical Society as volume 56 of the Student Mathematical Library. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. Topics ''The Erdős Distance Problem'' consists of twelve chapters and three appendices. After an introductory chapter describing the formulation of the problem by Paul Erdős and Erdős's proof that the number of distances is always at least proportional to \sqrt /math>, the next six chapters cover the two-dimensional version of the problem. They build on each other to describe successive improvements to the known results on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metric Space
In mathematics, a metric space is a Set (mathematics), set together with a notion of ''distance'' between its Element (mathematics), elements, usually called point (geometry), points. The distance is measured by a function (mathematics), function called a metric or distance function. Metric spaces are a general setting for studying many of the concepts of mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance. Other well-known examples are a sphere equipped with the angular distance and the hyperbolic plane. A metric may correspond to a Conceptual metaphor , metaphorical, rather than physical, notion of distance: for example, the set of 100-character Unicode strings can be equipped with the Hamming distance, which measures the number of characters that need to be changed to get from one string to another. Since they are very general, metric spaces are a tool used in many different bra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2011 Non-fiction Books
Eleven or 11 may refer to: *11 (number) * One of the years 11 BC, AD 11, 1911, 2011 Literature * ''Eleven'' (novel), a 2006 novel by British author David Llewellyn *''Eleven'', a 1970 collection of short stories by Patricia Highsmith *''Eleven'', a 2004 children's novel in The Winnie Years by Lauren Myracle *''Eleven'', a 2008 children's novel by Patricia Reilly Giff *''Eleven'', a short story by Sandra Cisneros Music * Eleven (band), an American rock band * Eleven: A Music Company, an Australian record label * Up to eleven, an idiom from popular culture, coined in the movie ''This Is Spinal Tap'' Albums * ''11'' (The Smithereens album), 1989 * ''11'' (Ua album), 1996 * ''11'' (Bryan Adams album), 2008 * ''11'' (Sault album), 2022 * ''Eleven'' (Harry Connick, Jr. album), 1992 * ''Eleven'' (22-Pistepirkko album), 1998 * ''Eleven'' (Sugarcult album), 1999 * ''Eleven'' (B'z album), 2000 * ''Eleven'' (Reamonn album), 2010 * ''Eleven'' (Martina McBride album), 2011 * ''Eleven'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Textbooks
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] |
Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ACM SIGACT News
ACM SIGACT or SIGACT is the Association for Computing Machinery Special Interest Group on Algorithms and Computation Theory, whose purpose is support of research in theoretical computer science. It was founded in 1968 by Patrick C. Fischer. Publications SIGACT publishes a quarterly print newsletter, ''SIGACT News''. Its online version, ''SIGACT News Online'', is available since 1996 for SIGACT members, with unrestricted access to some features. Conferences SIGACT sponsors or has sponsored several annual conferences. *COLT: Conference on Learning Theory, until 1999 *PODC: ACM Symposium on Principles of Distributed Computing (jointly sponsored by SIGOPS) *PODS: ACM Symposium on Principles of Database Systems (jointly sponsored by SIGAI and SIGACT) *POPL: ACM Symposium on Principles of Programming Languages *SOCG: ACM Symposium on Computational Geometry (jointly sponsored by SIGGRAPH), until 2014 *SODA: ACM/SIAM Symposium on Discrete Algorithms (jointly sponsored by the Societ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Austrian Mathematical Society
The Austrian Mathematical Society () is the national mathematical society of Austria and a member society of the European Mathematical Society. History The society was founded in 1903 by Ludwig Boltzmann, Gustav von Escherich, and Emil Müller as ''Mathematical Society in Vienna'' (). After the Second World War it resumed operation in May 1946 and was formally reestablished at the 10th of August 1946 by Rudolf Inzinger. In autumn 1948 the name was changed to ''Austrian Mathematical Society''. Publications It publishes the "International Mathematical News" () with three issues per year (not to be confused with ''Mathematische Nachrichten'', an unrelated mathematics journal). It was issued for the first time in 1947. It also publishes the mathematics journal '' Monatshefte für Mathematik'' in cooperation with Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Gasarch
William Ian Gasarch ( ; born 1959) is an American computer scientist known for his work in computational complexity theory, computability theory, computational learning theory, and Ramsey theory. He is currently a professor at the University of Maryland Department of Computer Science with an affiliate appointment in Mathematics. Gasarch is a frequent mentor of high school student research projects; one of these, with Jacob Lurie, won the 1996 Westinghouse Science Talent Search for Lurie. He has co-blogged on computational complexity with Lance Fortnow since 2007. He was book review editor for ACM SIGACT NEWS from 1997 to 2015. Education Gasarch received his doctorate in computer science from Harvard in 1985, advised by Harry R. Lewis. His thesis was titled ''Recursion-Theoretic Techniques in Complexity Theory and Combinatorics''. He was hired into a tenure track professorial job at the University of Maryland in the Fall of 1985. He was promoted to associate professor with tenu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nets Katz
Nets Hawk Katz is the W.L. Moody Professor of Mathematics at Rice University. He was a professor of mathematics at Indiana University Bloomington until March 2013 and the IBM Professor of Mathematics at the California Institute of Technology until 2023. He is currently the W. L. Moody Professor of Mathematics at Rice University. Katz earned a B.A. in mathematics from Rice University in 1990 at the age of 17. He received his Ph.D. in 1993 under Dennis DeTurck at the University of Pennsylvania, with a dissertation titled "Noncommutative Determinants and Applications". He is the author of several important results in combinatorics (especially additive combinatorics), harmonic analysis and other areas. In 2003, jointly with Jean Bourgain and Terence Tao, he proved that any subset of \Z/p\Z grows substantially under either addition or multiplication. More precisely, if A is a set such that \max(, A \cdot A, , , A+A, ) \leq K, A, , then A has size at most K^C or at least p/K^C where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Larry Guth
Lawrence David Guth (; born 1977) is a professor of mathematics at the Massachusetts Institute of Technology. Education and career Guth graduated from Yale University in 2000 with a BS in mathematics. In 2005, he received his PhD in mathematics from the Massachusetts Institute of Technology (MIT), where he studied geometry of objects with random shapes under the supervision of Tomasz Mrowka. After MIT, Guth went to Stanford as a postdoc and later to the University of Toronto as an assistant professor on a tenure track In 2011, New York University's Courant Institute of Mathematical Sciences hired Guth as a professor, listing his areas of interest as "metric geometry, harmonic analysis, and geometric combinatorics." In 2012, Guth moved to MIT, where he is Claude Shannon Professor of Mathematics. Research In his research, Guth has strengthened Gromov's systolic inequality for essential manifolds and, along with Nets Katz, found a solution to the Erdős distinct distances ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Number
In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and in many other branches of mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. The set of real numbers, sometimes called "the reals", is traditionally denoted by a bold , often using blackboard bold, . The adjective ''real'', used in the 17th century by René Descartes, distinguishes real numbers from imaginary numbers such as the square roots of . The real numbers include the rational numbers, such as the integer and the fraction . The rest of the real numbers are called irrational numbers. Some irrational numbers (as well as all the rationals) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field (mathematics), field that contains a finite number of Element (mathematics), elements. As with any field, a finite field is a Set (mathematics), set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are the integers mod n, integers mod p when p is a prime number. The ''order'' of a finite field is its number of elements, which is either a prime number or a prime power. For every prime number p and every positive integer k there are fields of order p^k. All finite fields of a given order are isomorphism, isomorphic. Finite fields are fundamental in a number of areas of mathematics and computer science, including number theory, algebraic geometry, Galois theory, finite geometry, cryptography and coding theory. Properties A finite field is a finite set that is a fiel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
