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Cap Set
In affine geometry, a cap set is a subset of the affine space \mathbb_3^n (the n-dimensional affine space over the three-element field) where no three elements sum to the zero vector. 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, ... . Caps are defined more generally as subsets of a finite affine or projective space with no three in a line. 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 points of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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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] [Amazon] |
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Central Binomial Coefficient
In mathematics the ''n''th central binomial coefficient is the particular binomial coefficient : = \frac \textn \geq 0. They are called central since they show up exactly in the middle of the even-numbered rows in Pascal's triangle. The first few central binomial coefficients starting at ''n'' = 0 are: :, , , , , , 924, 3432, 12870, 48620, ...; Combinatorial interpretations and other properties The central binomial coefficient \binom is the number of arrangements where there are an equal number of two types of objects. For example, when n=2, the binomial coefficient \binom is equal to 6, and there are six arrangements of two copies of ''A'' and two copies of ''B'': ''AABB'', ''ABAB'', ''ABBA'', ''BAAB'', ''BABA'', ''BBAA''. The same central binomial coefficient \binom is also the number of words of length 2''n'' made up of ''A'' and ''B'' within which, as one reads from left to right, there are never more ''B'' than ''A'' at any point. For example, when n=2, there are six ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Lean (proof Assistant)
Lean is a proof assistant and a Functional programming, functional programming language. It is based on the calculus of constructions with inductive types. It is an open-source project hosted on GitHub. Development is currently supported by the Nonprofit organization, non-profit Lean Focused Research Organization, Focused Research Organization (FRO). History Lean was developed primarily by Leonardo de Moura while employed by Microsoft Research and now Amazon Web Services, and has had significant contributions from other coauthors and collaborators during its history. It was launched by Leonardo de Moura at Microsoft Research in 2013. The initial versions of the language, later known as Lean 1 and 2, were experimental and contained features such as support for homotopy type theory – based foundations that were later dropped. Lean 3 (first released Jan 20, 2017) was the first moderately stable version of Lean. It was implemented primarily in C++ with some features written in L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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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] [Amazon] |
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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 Mathematical analysis journals Academic journals est ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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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 (1892–1924) , 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 and televisi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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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 per ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Ernest S
Ernest is a given name derived from the Germanic word ''ernst'', meaning "serious", often shortened to Ernie. 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 Hano ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Terence Tao
Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician, Fields medalist, and professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins Chair in the College of Letters and Sciences. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing and analytic number theory. Tao was born to Chinese immigrant parents and raised in Adelaide. Tao won the Fields Medal in 2006 and won the Royal Medal and Breakthrough Prize in Mathematics in 2014, and is a 2006 MacArthur Fellow. Tao has been the author or co-author of over three hundred research papers, and is widely regarded as one of the greatest living mathematicians. Life and career Family Tao's parents are first generation immigrants from Hong Kong to Australia.'' Wen Wei Po'', Page A4, 24 August ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Timothy Gowers
Sir William Timothy Gowers, (; born 20 November 1963) is a British mathematician. He is the holder of the Combinatorics chair at the Collège de France, a director of research at the University of Cambridge and a Fellow of Trinity College, Cambridge. In 1998, he received the Fields Medal for research connecting the fields of functional analysis and combinatorics. Education Gowers attended King's College School, Cambridge, as a choirboy in the choir of King's College, Cambridge, King's College choir, and then Eton College as a King's Scholar, where he was taught mathematics by Norman Routledge. In 1981, Gowers won a gold medal at the International Mathematical Olympiad with a perfect score. He completed his PhD, with a dissertation on ''Symmetric Structures in Banach Spaces'' at Trinity College, Cambridge in 1990, supervised by Béla Bollobás. Career and research After his PhD, Gowers was elected to a Junior Research Fellowship at Trinity College. From 1991 until his return to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award honours the Canadian mathematician John Charles Fields. The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been list of prizes known as the Nobel or the highest honors of a field, described as the Nobel Prize of Mathematics, although there are several major differences, including frequency of award, number of awards, age limits, monetary value, and award criteria. According to the annual Academic Excellence Survey by Academic Ranking of World Universities, ARWU, the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide, and in another reputation survey conducted by IREG Observatory on Academic Ranking and Excellence, IR ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |