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Cap Set
In affine geometry, a cap set is a subset of \mathbb_3^n (an n-dimensional affine space over a three-element field) with no three elements in a line. The cap set problem is the problem of finding the size of the largest possible cap set, as a function of n.. The first few cap set sizes are 1, 2, 4, 9, 20, 45, 112, ... . Cap sets may be defined more generally as subsets of finite affine or projective spaces with no three in line, where these objects are simply called caps. The "cap set" terminology should be distinguished from other unrelated mathematical objects with the same name, and in particular from sets with the compact absorption property in function spaces as well as from compact convex co-convex subsets of a convex set. Example An example of cap sets comes from the card game Set, a card game in which each card has four features (its number, symbol, shading, and color), each of which can take one of three values. The cards of this game can be interpreted as representing p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cap Set
In affine geometry, a cap set is a subset of \mathbb_3^n (an n-dimensional affine space over a three-element field) with no three elements in a line. The cap set problem is the problem of finding the size of the largest possible cap set, as a function of n.. The first few cap set sizes are 1, 2, 4, 9, 20, 45, 112, ... . Cap sets may be defined more generally as subsets of finite affine or projective spaces with no three in line, where these objects are simply called caps. The "cap set" terminology should be distinguished from other unrelated mathematical objects with the same name, and in particular from sets with the compact absorption property in function spaces as well as from compact convex co-convex subsets of a convex set. Example An example of cap sets comes from the card game Set, a card game in which each card has four features (its number, symbol, shading, and color), each of which can take one of three values. The cards of this game can be interpreted as representing p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramsey Theory
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that focuses on the appearance of order in a substructure given a structure of a known size. Problems in Ramsey theory typically ask a question of the form: "how big must some structure be to guarantee that a particular property holds?" More specifically, Ron Graham described Ramsey theory as a "branch of combinatorics". Examples A typical result in Ramsey theory starts with some mathematical structure that is then cut into pieces. How big must the original structure be in order to ensure that at least one of the pieces has a given interesting property? This idea can be defined as partition regularity. For example, consider a complete graph of order ''n''; that is, there are ''n'' vertices and each vertex is connected to every other vertex by an edge. A complete graph of order 3 is called a triangle. Now colour each edge either red or blue. How large must ''n'' be in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Multiplication
In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices and is denoted as . Matrix multiplication was first described by the French mathematician Jacques Philippe Marie Binet in 1812, to represent the composition of linear maps that are represented by matrices. Matrix multiplication is thus a basic tool of linear algebra, and as such has numerous applications in many areas of mathematics, as well as in applied mathematics, statistics, physics, economics, and engineering. Computing matrix products is a central operation in all computational applications of linear algebra. Notation This article will use the following notati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sunflower (mathematics)
In the mathematical fields of set theory and extremal combinatorics, a sunflower or \Delta-system is a collection of sets whose pairwise intersection is constant. This constant intersection is called the kernel of the sunflower. The main research question arising in relation to sunflowers is: under what conditions does there exist a ''large'' sunflower (a sunflower with many sets) in a given collection of sets? The \Delta-lemma, sunflower lemma, and the Erdős-Rado sunflower conjecture give successively weaker conditions which would imply the existence of a large sunflower in a given collection, with the latter being one of the most famous open problems of extremal combinatorics. Formal definition Suppose W is a set system over U, that is, a collection of subsets of a set U. The collection W is a ''sunflower'' (or ''\Delta-system'') if there is a subset S of U such that for each distinct A and B in W, we have A \cap B = S. In other words, a set system or collection of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Mathematics (journal)
''Discrete Mathematics'' is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications. It was established in 1971 and is published by North-Holland Publishing Company. It publishes both short notes, full length contributions, as well as survey articles. In addition, the journal publishes a number of special issues each year dedicated to a particular topic. Although originally it published articles in French and German, it now allows only English language articles. The editor-in-chief is Douglas West ( University of Illinois, Urbana). History The journal was established in 1971. The very first article it published was written by Paul Erdős, who went on to publish a total of 84 papers in the journal. Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 0.87. Notable publications * The 1972 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lean (proof Assistant)
Lean is a theorem prover and programming language. It is based on the calculus of constructions with inductive types. The Lean project is an open source project, hosted on GitHub. It was launched by Leonardo de Moura at Microsoft Research in 2013. Lean has an interface that differentiates it from other interactive theorem provers. Lean can be compiled to JavaScript and accessed in a web browser. It has native support for Unicode symbols. (These can be typed using LaTeX-like sequences, such as "\times" for "×".) Lean also has an extensive support for meta-programming. Lean has gotten attention from mathematicians Thomas Hales and Kevin Buzzard. Hales is using it for his project, Formal Abstracts. Buzzard uses it for the Xena project. One of the Xena Project's goals is to rewrite every theorem and proof in the undergraduate math curriculum of Imperial College London in Lean. Examples Here is how the natural numbers are defined in Lean. inductive nat : Type , zero : nat , s ... [...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''. The n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Analysis
''Discrete Analysis'' is a mathematics journal covering the applications of analysis to discrete structures. ''Discrete Analysis'' is an arXiv overlay journal, meaning the journal's content is hosted on the arXiv. History ''Discrete Analysis'' was created by Timothy Gowers to demonstrate that a high-quality mathematics journal could be inexpensively produced outside of the traditional academic publishing industry. The journal is open access, and submissions are free for authors. The journal's 2018 MCQ is 1.21.''Discrete Analysis'', MathSciNet MathSciNet is a searchable online bibliographic database created by the American Mathematical Society in 1996. It contains all of the contents of the journal ''Mathematical Reviews'' (MR) since 1940 along with an extensive author database, links ..., 2019. Accessed 2019-09-02. References * * External links *{{Official, https://discreteanalysisjournal.com/ Open access journals Mathematics journals Publications established in 2016 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dion Gijswijt
Dion may refer to: People Ancient *Dion (mythology), a king in Laconia and husband of Iphitea, the daughter of Prognaus * Dion of Syracuse (408–354 BC), ancient Greek politician *Dio of Alexandria, first century BC, ancient Greek philosopher *Dion of Naples, an ancient Greek mathematician cited by Augustine of Hippo along with Adrastus of Cyzicus *Dio Chrysostom, also known as Dion Chrysostomos (c. 40 – c. 115), a Greek orator, writer, philosopher and historian *Cassius Dio, also known as Dion Kassios (c. AD 155 – 235), a Roman consul Modern Given name *Dion Bakker (born 1981), Dutch Youtuber and artist *Dion O'Banion, American mobster *Dion Boucicault (1820–1890), Irish actor and playwright *Dion Boucicault Jr. (1859–1929), American actor and stage director *Dion Dawkins (born 1994), American football player *Dion DiMucci (born 1939), American singer/songwriter known professionally as "Dion" *Dion Dublin (born 1969), English footballer *Dion Fortune (1890–1946), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jordan Ellenberg
Jordan Stuart Ellenberg (born October 30, 1971) is an American mathematician who is a professor of mathematics at the University of Wisconsin–Madison. His research involves arithmetic geometry. He is also an author of both fiction and non-fiction writing. Early life Ellenberg was born in Potomac, Maryland. He was a child prodigy who taught himself to read at the age of two by watching ''Sesame Street''. His mother discovered his ability one day while she was driving on the Capital Beltway when her toddler informed her: "The sign says ' Bethesda is to the right.'" In second grade, he helped his teenage babysitter with her math homework. By fourth grade, he was participating in high school competitions (such as the American Regions Mathematics League) as a member of the Montgomery County math team. And by eighth grade, he had started college-level work. He was part of the Johns Hopkins University Study of Mathematically Precocious Youth longitudinal cohort. He scored a perfec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ernest S
Ernest is a given name derived from Germanic word ''ernst'', meaning "serious". Notable people and fictional characters with the name include: People * Archduke Ernest of Austria (1553–1595), son of Maximilian II, Holy Roman Emperor * Ernest, Margrave of Austria (1027–1075) *Ernest, Duke of Bavaria (1373–1438) * Ernest, Duke of Opava (c. 1415–1464) *Ernest, Margrave of Baden-Durlach (1482–1553) *Ernest, Landgrave of Hesse-Rheinfels (1623–1693) *Ernest Augustus, Elector of Brunswick-Lüneburg (1629–1698) *Ernest, Count of Stolberg-Ilsenburg (1650–1710) * Ernest Augustus, King of Hanover (1771–1851), son of King George III of Great Britain *Ernest II, Duke of Saxe-Coburg and Gotha (1818–1893), sovereign duke of the Duchy of Saxe-Coburg and Gotha *Ernest Augustus, Crown Prince of Hanover (1845–1923) *Ernest, Landgrave of Hesse-Philippsthal (1846–1925) *Ernest Augustus, Prince of Hanover (1914–1987) *Prince Ernst August of Hanover (born 1954) * Prince Erns ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nets Katz
Nets Hawk Katz is the IBM Professor of Mathematics at the California Institute of Technology. He was a professor of Mathematics at Indiana University Bloomington until March 2013. 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 C is a constant that depends on A. This result was followed by the subsequent work of Bourgain, Sergei Konyagin and Glibichuk, establishing that every ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
