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Thue Equation
In mathematics, a Thue equation is a Diophantine equation of the form :''ƒ''(''x'',''y'') = ''r'', where ''Æ’'' is an irreducible bivariate form of degree at least 3 over the rational numbers, and ''r'' is a nonzero rational number. It is named after Axel Thue who in 1909 proved a theorem, now called Thue's theorem, that a Thue equation has finitely many solutions in integers ''x'' and ''y''. The Thue equation is solvable effectively: there is an explicit bound on the solutions ''x'', ''y'' of the form (C_1 r)^ where constants ''C''1 and ''C''2 depend only on the form ''Æ’''. A stronger result holds, that if ''K'' is the field generated by the roots of ''Æ’'' then the equation has only finitely many solutions with ''x'' and ''y'' integers of ''K'' and again these may be effectively determined. Finiteness of solutions and diophantine approximation Thue's original proof that the equation named in his honour has finitely many solutions is through the proof of what is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magma Computer Algebra System
Magma is a computer algebra system designed to solve problems in algebra, number theory, geometry and combinatorics. It is named after the algebraic structure magma. It runs on Unix-like operating systems, as well as Windows. Introduction Magma is produced and distributed by thComputational Algebra Groupwithin the School of Mathematics and Statistics at the University of Sydney. In late 2006, the booDiscovering Mathematics with Magmawas published by Springer as volume 19 of the Algorithms and Computations in Mathematics series. The Magma system is used extensively within pure mathematics. The Computational Algebra Group maintain a list of publications that cite Magma, and as of 2010 there are about 2600 citations, mostly in pure mathematics, but also including papers from areas as diverse as economics and geophysics. History The predecessor of the Magma system was named Cayley (1982–1993), after Arthur Cayley. Magma was officially released in August 1993 (version 1.0). Vers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematische Annalen
''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück, and Nigel Hitchin. Currently, the managing editor of Mathematische Annalen is Thomas Schick. Volumes 1–80 (1869–1919) were published by Teubner. Since 1920 (vol. 81), the journal has been published by Springer. In the late 1920s, under the editorship of Hilbert, the journal became embroiled in controversy over the participation of L. E. J. Brouwer on its editorial board, a spillover from the foundational Brouwer–Hilbert controversy. Between 1945 and 1947 the journal briefly ceased publication. References External links''Mathematische Annalen''homepage at Springer''Mathematische Annalen''archive (1869†... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanley Yao Xiao
Stanley may refer to: Arts and entertainment Film and television * ''Stanley'' (1972 film), an American horror film * ''Stanley'' (1984 film), an Australian comedy * ''Stanley'' (1999 film), an animated short * ''Stanley'' (1956 TV series), an American situation comedy * ''Stanley'' (2001 TV series), an American animated series Other uses in arts and entertainment * ''Stanley'' (play), by Pam Gems, 1996 * Stanley Award, an Australian Cartoonists' Association award * '' Stanley: The Search for Dr. Livingston'', a video game * Stanley (Cars), a character in ''Cars Toons: Mater's Tall Tales'' * ''The Stanley Parable'', a 2011 video game developed by Galactic Cafe, and its titular character, Stanley Businesses and organisations * Stanley, Inc., American information technology company * Stanley Aviation, American aerospace company * Stanley Black & Decker, formerly The Stanley Works, American hardware manufacturer ** Stanley knife, a utility knife * Stanley bottle, a brand of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shabnam Akhtari
Shabnam Akhtari is a Canadian-Iranian mathematician specializing in number theory, and in particular in Diophantine equations, Thue equations, and the geometry of numbers. She is an associate professor of mathematics at the University of Oregon. Education and career Akhtari graduated from the Sharif University of Technology in 2002 with a bachelor's degree in mathematics. She went to the University of British Columbia for graduate study in mathematics, completing her Ph.D. there in 2008. Her dissertation, ''Thue Equations and Related Topics'', was supervised by Mike Bennett. She was a postdoctoral researcher at Queen's University at Kingston in Canada, the Max Planck Institute for Mathematics in Germany and the Centre de Recherches Mathématiques in Canada before joining the University of Oregon faculty as an assistant professor of mathematics in 2012. She was tenured as an associate professor there in 2018. Recognition Akhtari is the 2021–2022 winner of the Ruth I. Michler M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discriminant
In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them. More precisely, it is a polynomial function of the coefficients of the original polynomial. The discriminant is widely used in polynomial factoring, number theory, and algebraic geometry. The discriminant of the quadratic polynomial ax^2+bx+c is :b^2-4ac, the quantity which appears under the square root in the quadratic formula. If a\ne 0, this discriminant is zero if and only if the polynomial has a double root. In the case of real coefficients, it is positive if the polynomial has two distinct real roots, and negative if it has two distinct complex conjugate roots. Similarly, the discriminant of a cubic polynomial is zero if and only if the polynomial has a multiple root. In the case of a cubic with real coefficients, the discriminant is positive if the polynomial has three distinct real roots, and negative i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Boundedness Conjecture For Rational Points
In arithmetic geometry, the uniform boundedness conjecture for rational points asserts that for a given number field K and a positive integer g \geq 2 that there exists a number N(K,g) depending only on K and g such that for any algebraic curve C defined over K having genus equal to g has at most N(K,g) K-rational points. This is a refinement of Faltings's theorem, which asserts that the set of K-rational points C(K) is necessarily finite. Progress The first significant progress towards the conjecture was due to Caporaso, Harris, and Mazur. They proved that the conjecture holds if one assumes the Bombieri–Lang conjecture. Mazur's Conjecture B A variant of the conjecture, due to Mazur, asserts that there should be a number N(K,g,r) such that for any algebraic curve C defined over K having genus g and whose Jacobian variety J_C has Mordell–Weil rank over K equal to r, the number of K-rational points of C is at most N(K,g,r). This variant of the conjecture is known as Mazur's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The American Mathematical Society
The ''Journal of the American Mathematical Society'' (''JAMS''), is a quarterly peer-reviewed mathematical journal published by the American Mathematical Society. It was established in January 1988. Abstracting and indexing This journal is abstracted and indexed in: 2011. American Mathematical Society. * * * * ISI Ale ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cameron Leigh Stewart
Cameron Leigh Stewart Royal Society of Canada, FRSC is a Canadian mathematician. He is a professor of pure mathematics at the University of Waterloo. Contributions He has made numerous contributions to number theory, in particular to work on the abc conjecture, ''abc'' conjecture. In 1976 he obtained, with Alan Baker (mathematician), Alan Baker, an effective improvement to Liouville's theorem on diophantine approximation, Liouville's Theorem. In 1991 he proved that the number of solutions to a Thue equation f(x,y) = h is at most 2800(1 + 1/4\epsilon \deg f)(\deg f)^, where \epsilon is a pre-determined positive real number and \omega(g) is the number of distinct primes dividing a large divisor g of h. This improves on an earlier result of Enrico Bombieri and Wolfgang M. Schmidt and is close to the best possible result. In 1995 he obtained, along with Jaap Top, the existence of infinitely many quadratic, cubic, and sextic twists of elliptic curves of large rank. In 1991 and 2001 re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inventiones Mathematicae
''Inventiones Mathematicae'' is a mathematical journal published monthly by Springer Science+Business Media. It was established in 1966 and is regarded as one of the most prestigious mathematics journals in the world. The current managing editors are Camillo De Lellis (Institute for Advanced Study, Princeton) and Jean-Benoît Bost (University of Paris-Sud Paris-Sud University (French: ''Université Paris-Sud''), also known as University of Paris — XI (or as Université d'Orsay before 1971), was a French research university distributed among several campuses in the southern suburbs of Paris, in ...). Abstracting and indexing The journal is abstracted and indexed in: References External links *{{Official website, https://www.springer.com/journal/222 Mathematics journals Publications established in 1966 English-language journals Springer Science+Business Media academic journals Monthly journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolfgang M
Wolfgang is a German male given name traditionally popular in Germany, Austria and Switzerland. The name is a combination of the Old High German words ''wolf'', meaning "wolf", and ''gang'', meaning "path", "journey", "travel". Besides the regular "wolf", the first element also occurs in Old High German as the combining form "-olf". The earliest reference of the name being used was in the 8th century. The name was also attested as "Vulfgang" in the Reichenauer Verbrüderungsbuch in the 9th century. The earliest recorded famous bearer of the name was a tenth-century Saint Wolfgang of Regensburg. Due to the lack of conflict with the pagan reference in the name with Catholicism, it is likely a much more ancient name whose meaning had already been lost by the tenth century. Grimm (''Teutonic Mythology'' p. 1093) interpreted the name as that of a hero in front of whom walks the "wolf of victory". A Latin gloss by Arnold of St Emmeram interprets the name as ''Lupambulus''.E. Förs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
