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Cox–Zucker Machine
In arithmetic geometry, the Cox–Zucker machine is an algorithm created by David A. Cox and Steven Zucker. This algorithm determines whether a given set of sections provides a basis (up to torsion) for the Mordell–Weil group of an elliptic surface ''E'' → ''S'', where ''S'' is isomorphic to the projective line. The algorithm was first published in the 1979 article "Intersection numbers of sections of elliptic surfaces" by Cox and Zucker and was later named the "Cox–Zucker machine" by Charles Schwartz in 1984. Name origin The name sounds similar to the obscenity "". This was a deliberate choice by Cox and Zucker, who, as first-year graduate students at Princeton University in 1970, conceived of the idea of coauthoring a paper for the express purpose of enabling this joke. They followed through on it five years later, as members of the faculty at Rutgers, the State University of New Jersey.. As Cox explained in a memorial tribute to Zucker in ''Notices of the American Mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Geometry
In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic variety, algebraic varieties. In more abstract terms, arithmetic geometry can be defined as the study of scheme (mathematics), schemes of Finite morphism#Morphisms of finite type, finite type over the spectrum of a ring, spectrum of the ring of integers. Overview The classical objects of interest in arithmetic geometry are rational points: solution set, sets of solutions of a system of polynomial equations over number fields, finite fields, p-adic fields, or Algebraic function field, function fields, i.e. field (mathematics), fields that are not algebraically closed excluding the real numbers. Rational points can be directly characterized by height functions which measure their arithmetic complexity. The structure of algebraic varieties defined over ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rutgers University
Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's College, and was affiliated with the Reformed Church in America, Dutch Reformed Church. It is the eighth-oldest college in the United States, the second-oldest in New Jersey (after Princeton University), and one of the nine U.S. colonial colleges that were chartered before the American Revolution.Stoeckel, Althea"Presidents, professors, and politics: the colonial colleges and the American revolution", ''Conspectus of History'' (1976) 1(3):45–56. In 1825, Queen's College was renamed Rutgers College in honor of Colonel Henry Rutgers, whose substantial gift to the school had stabilized its finances during a period of uncertainty. For most of its existence, Rutgers was a Private university, private liberal arts college but it has evolved int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1979 In Science
The year 1979 in science and technology involved some significant events, listed below. Astronomy and space exploration * February 7 – Pluto enters a 20-year period inside the orbit of Neptune for the first time in 230 years. * March 7 – The largest magnetar (soft gamma repeater) event is recorded. * July 11 – America's first space station, ''Skylab'', is deliberately allowed to burn up on atmospheric entry over the Indian Ocean due to its decaying orbit and the lack of time to build a new spaceship to boost it up. * September 1 – The American ''Pioneer 11'' becomes the first spacecraft to visit Saturn when it passes the planet at a distance of 21,000 km. * December 24 – The maiden launch of Ariane 1, the first rocket in the Ariane launcher family. * Amateur Achievement Award of the Astronomical Society of the Pacific given for the first time. Biology * Arthur William Baden Powell publishes ''New Zealand Mollusca''. Computer science * May 8 - Radio Shack rele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
English Profanity
Profanity, also known as cursing, cussing, swearing, bad language, foul language, obscenities, expletives or vulgarism, is a socially offensive use of language. Accordingly, profanity is language use that is sometimes deemed impolite, rude, indecent, or culturally offensive; in certain religions, it constitutes sin. It can show a debasement of someone or something, or be considered an expression of strong feeling towards something. Some words may also be used as intensifiers. In its older, more literal sense, "profanity" refers to a lack of respect for things that are held to be sacred, which implies anything inspiring or deserving of reverence, as well as behaviour showing similar disrespect or causing religious offense. Etymology The term ''profane'' originates from classical Latin , literally "before (outside) the temple", meaning 'outside' and meaning 'temple' or 'sanctuary'. The term ''profane'' carried the meaning of either "desecrating what is holy" or "with a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Humor
A mathematical joke is a form of humor which relies on aspects of mathematics or a stereotype of mathematicians. The humor may come from a pun, or from a double meaning of a mathematical term, or from a lay person's misunderstanding of a mathematical concept. Mathematician and author John Allen Paulos in his book ''Mathematics and Humor'' described several ways that mathematics, generally considered a dry, formal activity, overlaps with humor, a loose, irreverent activity: both are forms of "intellectual play"; both have "logic, pattern, rules, structure"; and both are "economical and explicit". Some performers combine mathematics and jokes to entertain and/or teach math. Humor of mathematicians may be classified into the esoteric and exoteric categories. Esoteric jokes rely on the intrinsic knowledge of mathematics and its terminology. Exoteric jokes are intelligible to the outsiders, and most of them compare mathematicians with representatives of other disciplines or with commo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Surfaces
In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has complex dimension two (as a complex manifold, when it is non-singular) and so of dimension four as a smooth manifold. The theory of algebraic surfaces is much more complicated than that of algebraic curves (including the compact Riemann surfaces, which are genuine surfaces of (real) dimension two). Many results were obtained, however, in the Italian school of algebraic geometry, and are up to 100 years old. Classification by the Kodaira dimension In the case of dimension one varieties are classified by only the topological genus, but dimension two, the difference between the arithmetic genus p_a and the geometric genus p_g turns to be important because we cannot distinguish birationally only the topological genus. Then we introduce the irregularity for the classification of them. A summary of the results (in det ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Birational Geometry
In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational functions rather than polynomials; the map may fail to be defined where the rational functions have poles. Birational maps Rational maps A rational map from one variety (understood to be irreducible) X to another variety Y, written as a dashed arrow , is defined as a morphism from a nonempty open subset U \subset X to Y. By definition of the Zariski topology used in algebraic geometry, a nonempty open subset U is always dense in X, in fact the complement of a lower-dimensional subset. Concretely, a rational map can be written in coordinates using rational functions. Birational maps A birational map from ''X'' to ''Y'' is a rational map such that there is a rational map inverse to ''f''. A birational map induces an isomorphism from a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Manifolds
In differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disc in \mathbb^n, such that the transition maps are holomorphic. The term complex manifold is variously used to mean a complex manifold in the sense above (which can be specified as an integrable complex manifold), and an almost complex manifold. Implications of complex structure Since holomorphic functions are much more rigid than smooth functions, the theories of smooth and complex manifolds have very different flavors: compact complex manifolds are much closer to algebraic varieties than to differentiable manifolds. For example, the Whitney embedding theorem tells us that every smooth ''n''-dimensional manifold can be embedded as a smooth submanifold of R2''n'', whereas it is "rare" for a complex manifold to have a holomorphic embedding into C''n''. Consider for example any compact connected complex manifold ''M'': any holomorphic function on it is cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cox Ring
In algebraic geometry, a Cox ring is a sort of universal homogeneous coordinate ring for a projective variety, and is (roughly speaking) a direct sum of the spaces of sections of all isomorphism classes of line bundles. Cox rings were introduced by , based on an earlier construction by David A. Cox in 1995 for toric varieties In algebraic geometry, a toric variety or torus embedding is an algebraic variety containing an algebraic torus as an open dense subset, such that the action of the torus on itself extends to the whole variety. Some authors also require it to be no .... References * * * Algebraic geometry {{algebraic-geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Notices Of The American Mathematical Society
''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume appeared in 1953. Each issue of the magazine since January 1995 is available in its entirety on the journal web site. Articles are peer-reviewed by an editorial board of mathematical experts. Since 2019, the editor-in-chief is Erica Flapan. The cover regularly features mathematical visualization Mathematical phenomena can be understood and explored via visualization. Classically this consisted of two-dimensional drawings or building three-dimensional models (particularly plaster models in the 19th and early 20th century), while today it ...s. The ''Notices'' is self-described to be the world's most widely read mathematical journal. As the membership journal of the American Mathematical Society, the ''Notices'' is sent to the approximately 30,000 AMS members worldwide, one-third of whom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University
Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution. It is one of the highest-ranked universities in the world. The institution moved to Newark, New Jersey, Newark in 1747, and then to the current site nine years later. It officially became a university in 1896 and was subsequently renamed Princeton University. It is a member of the Ivy League. The university is governed by the Trustees of Princeton University and has an endowment of $37.7 billion, the largest List of colleges and universities in the United States by endowment, endowment per student in the United States. Princeton provides undergraduate education, undergraduate and graduate education, graduate in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
