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5,000 | Barlog confirmed that "God of War" would not have microtransactions post-launch, a feature that had become prominent with other games and criticized. Barlog also confirmed there would not be any post-release DLC, like an expansion pack. He said he had pitched an idea for DLC, "but it was too ambitious". His idea was si... | https://en.wikipedia.org/wiki?curid=50810460 |
5,001 | Since launch, Santa Monica has supported the game with patch updates to address software bugs. As well, the developers have added new features along with these free updates. A Photo Mode was released as part of update patch 1.20 on May 9, 2018. It allows players to take customized in-game screenshots. Players can adjus... | https://en.wikipedia.org/wiki?curid=50810460 |
5,002 | As part of Sony's larger efforts to port their first-party exclusive games to Windows (PC), Santa Monica Studio announced in October 2021 that "God of War" would be released for Windows on January 14, 2022. The port, handled by Jetpack Interactive with supervision by Santa Monica, includes additional graphic options su... | https://en.wikipedia.org/wiki?curid=50810460 |
5,003 | God of War: A Call from the Wilds is a text-based game playable through Facebook Messenger. To help further promote "God of War", Sony partnered with Facebook, Inc. to develop the play-by-web game, which released on February 1, 2018. Completing the game unlocks downloadable concept art. The short story follows Atreus o... | https://en.wikipedia.org/wiki?curid=50810460 |
5,004 | God of War: Mímir's Vision is a smartphone companion app that was released on April 17, 2018, for Apple and Android devices. Using alternate reality, it provides some background for the Norse setting of "God of War". | https://en.wikipedia.org/wiki?curid=50810460 |
5,005 | Raising Kratos is a YouTube documentary of Santa Monica Studio's five-year process in making the game, showing the "herculean effort" that went into reviving the franchise. The documentary was announced on April 20, 2019, the one year anniversary of the game's launch, and was released the following month on May 10. | https://en.wikipedia.org/wiki?curid=50810460 |
5,006 | "The Art of God of War" is a book collecting various pieces of artworks created for the game during its development. It was written by Evan Shamoon and published by Dark Horse on April 24, 2018. | https://en.wikipedia.org/wiki?curid=50810460 |
5,007 | An official novelization of the game, written by Cory Barlog's father, James M. Barlog, was released on August 28, 2018, by Titan Books. An audiobook version is also available, narrated by Alastair Duncan, who voiced Mímir in the game. | https://en.wikipedia.org/wiki?curid=50810460 |
5,008 | The novel retells the events of the game, but unlike the series' previous two novels, this one closely follows the source material with a few notable exceptions. The game never revealed how or why Kratos ended up in ancient Norway, or how much time had passed since the ending of "God of War III", but the novel gives so... | https://en.wikipedia.org/wiki?curid=50810460 |
5,009 | In the game, Kratos sees one last image on the mural in Jötunheim. It seemingly shows Atreus holding Kratos's dead body, but in the novel, this mural is partially broken and does not show the corpse that Atreus is holding. Brok and Sindri also reveal why they made the Leviathan Axe for Faye. She had come to them as the... | https://en.wikipedia.org/wiki?curid=50810460 |
5,010 | "God of War: B is For Boy" is an "ABC storybook for adults" in which the story of the game is retold in an abridged format with illustrations. The title comes from Kratos referring to Atreus as "boy" for most of the game. It was written by Andrea Robinson, with the illustrations being provided by Romina Tempest. It rel... | https://en.wikipedia.org/wiki?curid=50810460 |
5,011 | "God of War: Lore and Legends" is a tome that recreates Atreus' journal from the game. The book features new expanded lore that was written in collaboration with the writing team for the game. It was written by Rick Barba and published by Dark Horse on September 9, 2020. | https://en.wikipedia.org/wiki?curid=50810460 |
5,012 | "God of War" received "universal acclaim" according to review aggregator Metacritic, tying it with the original "God of War" for the highest score in the franchise. It has the fourth-highest score of all-time for a PlayStation 4 game, and the highest score for an original, non-remastered PlayStation 4 exclusive. It was... | https://en.wikipedia.org/wiki?curid=50810460 |
5,013 | The story was well praised. Nick Plessas of "Electronic Gaming Monthly" ("EGM") said the story's most memorable moments were the interactions between Kratos and Atreus. He also noted, "there is often some comic relief to be found when Kratos's curtness and Atreus' charming naivety collide." He felt the presence of Atre... | https://en.wikipedia.org/wiki?curid=50810460 |
5,014 | In terms of the game's combat system, Plessas said that unlike previous games, which often relied on the player to use many combos in a sequential fashion, this game is "more about individual moves strung together in response to the assortment of enemies being fought." Although that difference may be small, he said tha... | https://en.wikipedia.org/wiki?curid=50810460 |
5,015 | Writing for "Polygon", Chris Plante praised the camerawork as a technical marvel, noting the seamless nature of the game shifting from cinematic back to the gameplay. Juba said the decision to shift the camera closer to Kratos "[proved] immensely rewarding during big moments by giving [the player] an intimate view." Fa... | https://en.wikipedia.org/wiki?curid=50810460 |
5,016 | Despite the game's grandeur, Plessas felt that the boss fights "do not hit quite the same frequency as they did in the past few games." However, the few boss fights in the game "do the series proud". As to the vast world of "God of War", Faulkner said that, "The great thing about the exploration in "God of War" is that... | https://en.wikipedia.org/wiki?curid=50810460 |
5,017 | Plessas felt that the RPG elements present in the game make this installment "unique" compared to previous entries. He said the game allows players to "specialize Kratos to meet the specific task at hand, or develop a build that best suits a preferred playstyle." Although this did not make the game easier, he felt it d... | https://en.wikipedia.org/wiki?curid=50810460 |
5,018 | In terms of flaws, Plessas said that ""God of War" is so good that its most egregious failing is not letting fans play more of it", as New Game Plus was not an option at the time of the review. Juba said that ""God of War"s momentum rarely falters, and when it does, the inconvenience is brief." One example he gave was ... | https://en.wikipedia.org/wiki?curid=50810460 |
5,019 | During its release week in the United Kingdom, "God of War" became the fastest-selling entry in the franchise, selling 35% more physical copies than "God of War III". The game remained at the top of the all format sales chart for six consecutive weeks through April and May, setting a record for a PlayStation 4 exclusiv... | https://en.wikipedia.org/wiki?curid=50810460 |
5,020 | "God of War" won Game of the Year awards from several gaming publications, including British Academy Games Awards, "The Blade", CNET, "Destructoid", D.I.C.E. Awards, "Empire", "Entertainment Weekly", G1, The Game Awards, Game Developers Choice Awards, "Game Informer", "Game Revolution", "GamesRadar+", "IGN", Nerdist, N... | https://en.wikipedia.org/wiki?curid=50810460 |
5,021 | The game was nominated for Game of the Show, Best PlayStation 4 Game, and Best Action Game at "IGN"s Best of E3 2016 Awards. It won the award for Game of the Year, Best PlayStation 4 Game, Best Action-Adventure Game, Best Art Direction, and Best Story at "IGN"s Best of 2018 Awards. It was a runner-up for Best Graphics,... | https://en.wikipedia.org/wiki?curid=50810460 |
5,022 | Following "God of War"s announcement in mid-2016, Barlog confirmed that it would not be Kratos' last game. He also said that future games could see the series tackling Egyptian or Mayan mythology, and although the 2018 installment focuses on Norse mythology, it alludes to the fact there are other mythologies co-existin... | https://en.wikipedia.org/wiki?curid=50810460 |
5,023 | A sequel, "God of War Ragnarök", was officially announced at the PlayStation 5 Showcase event in September 2020 and was originally scheduled to be released in 2021. However, the game was delayed, in part due to the COVID-19 pandemic, and released worldwide on November 9, 2022, for both the PlayStation 4 and PlayStation... | https://en.wikipedia.org/wiki?curid=50810460 |
5,024 | On March 7, 2022, "Deadline" reported that a live action television (TV) series was said to be in negotiations at Amazon Prime Video by Mark Fergus and Hawk Ostby, creators of "The Expanse", and Rafe Judkins, the showrunner for "The Wheel of Time". During an investor briefing on May 26, 2022, Sony Interactive Entertain... | https://en.wikipedia.org/wiki?curid=50810460 |
5,025 | Google Scholar is a freely accessible web search engine that indexes the full text or metadata of scholarly literature across an array of publishing formats and disciplines. Released in beta in November 2004, the Google Scholar index includes peer-reviewed online academic journals and books, conference papers, theses a... | https://en.wikipedia.org/wiki?curid=1520204 |
5,026 | Google Scholar uses a web crawler, or web robot, to identify files for inclusion in the search results. For content to be indexed in Google Scholar, it must meet certain specified criteria. An earlier statistical estimate published in PLOS One using a mark and recapture method estimated approximately 80–90% coverage of... | https://en.wikipedia.org/wiki?curid=1520204 |
5,027 | The University of Michigan Library and other libraries whose collections Google scanned for Google Books and Google Scholar retained copies of the scans and have used them to create the HathiTrust Digital Library. | https://en.wikipedia.org/wiki?curid=1520204 |
5,028 | Google Scholar arose out of a discussion between Alex Verstak and Anurag Acharya, both of whom were then working on building Google's main web index. Their goal was to "make the world's problem solvers 10% more efficient" by allowing easier and more accurate access to scientific knowledge. This goal is reflected in the... | https://en.wikipedia.org/wiki?curid=1520204 |
5,029 | Scholar has gained a range of features over time. In 2006, a citation importing feature was implemented supporting bibliography managers, such as RefWorks, RefMan, EndNote, and BibTeX. In 2007, Acharya announced that Google Scholar had started a program to digitize and host journal articles in agreement with their publ... | https://en.wikipedia.org/wiki?curid=1520204 |
5,030 | A major enhancement was rolled out in 2012, with the possibility for individual scholars to create personal "Scholar Citations profiles". A feature introduced in November 2013 allows logged-in users to save search results into the "Google Scholar library", a personal collection which the user can search separately and ... | https://en.wikipedia.org/wiki?curid=1520204 |
5,031 | Google Scholar allows users to search for digital or physical copies of articles, whether online or in libraries. It indexes "full-text journal articles, technical reports, preprints, theses, books, and other documents, including selected Web pages that are deemed to be 'scholarly.'" Because many of Google Scholar's se... | https://en.wikipedia.org/wiki?curid=1520204 |
5,032 | Using its "group of" feature, it shows the available links to journal articles. In the 2005 version, this feature provided a link to both subscription-access versions of an article and to free full-text versions of articles; for most of 2006, it provided links to only the publishers' versions. Since December 2006, it h... | https://en.wikipedia.org/wiki?curid=1520204 |
5,033 | Through its "cited by" feature, Google Scholar provides access to abstracts of articles that have cited the article being viewed. It is this feature in particular that provides the citation indexing previously only found in CiteSeer, Scopus, and Web of Science. Google Scholar also provides links so that citations can b... | https://en.wikipedia.org/wiki?curid=1520204 |
5,034 | "Scholar Citations profiles" are public author profiles that are editable by authors themselves. Individuals, logging on through a Google account with a bona fide address usually linked to an academic institution, can now create their own page giving their fields of interest and citations. Google Scholar automatically ... | https://en.wikipedia.org/wiki?curid=1520204 |
5,035 | Through its "Related articles" feature, Google Scholar presents a list of closely related articles, ranked primarily by how similar these articles are to the original result, but also taking into account the relevance of each paper. | https://en.wikipedia.org/wiki?curid=1520204 |
5,036 | Google Scholar's legal database of US cases is extensive. Users can search and read published opinions of US state appellate and supreme court cases since 1950, US federal district, appellate, tax, and bankruptcy courts since 1923 and US Supreme Court cases since 1791. Google Scholar embeds clickable citation links wit... | https://en.wikipedia.org/wiki?curid=1520204 |
5,037 | While most academic databases and search engines allow users to select one factor (e.g. relevance, citation counts, or publication date) to rank results, Google Scholar ranks results with a combined ranking algorithm in a "way researchers do, weighing the full text of each article, the author, the publication in which ... | https://en.wikipedia.org/wiki?curid=1520204 |
5,038 | Some searchers found Google Scholar to be of comparable quality and utility to subscription-based databases when looking at citations of articles in some specific journals. The reviews recognize that its "cited by" feature in particular poses serious competition to Scopus and Web of Science. A study looking at the biom... | https://en.wikipedia.org/wiki?curid=1520204 |
5,039 | Google Scholar does not publish a list of journals crawled or publishers included, and the frequency of its updates is uncertain. Bibliometric evidence suggests Google Scholar's coverage of the sciences and social sciences is competitive with other academic databases; as of 2017, Scholar's coverage of the arts and huma... | https://en.wikipedia.org/wiki?curid=1520204 |
5,040 | Google Scholar puts high weight on citation counts in its ranking algorithm and therefore is being criticized for strengthening the Matthew effect; as highly cited papers appear in top positions they gain more citations while new papers hardly appear in top positions and therefore get less attention by the users of Goo... | https://en.wikipedia.org/wiki?curid=1520204 |
5,041 | Google Scholar is vulnerable to spam. Researchers from the University of California, Berkeley and Otto-von-Guericke University Magdeburg demonstrated that citation counts on Google Scholar can be manipulated and complete non-sense articles created with SCIgen were indexed within Google Scholar. These researchers conclu... | https://en.wikipedia.org/wiki?curid=1520204 |
5,042 | Search engine optimization (SEO) for traditional web search engines such as Google has been popular for many years. For several years, SEO has also been applied to academic search engines such as Google Scholar. SEO for academic articles is also called "academic search engine optimization" (ASEO) and defined as "the cr... | https://en.wikipedia.org/wiki?curid=1520204 |
5,043 | 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 analysi... | https://en.wikipedia.org/wiki?curid=18831 |
5,044 | 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 with certain properties, called axioms. A "proof" consists of a succession of applica... | https://en.wikipedia.org/wiki?curid=18831 |
5,045 | Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science and the social sciences. The fundamental truths of mathematics are independent from any scientific experimentation, although mathematics is extensively used for modeling phenomena. Some areas of mathematics, such as stati... | https://en.wikipedia.org/wiki?curid=18831 |
5,046 | Historically, the concept of a proof and its associated mathematical rigour first appeared in Greek mathematics, most notably in Euclid's "Elements". Since its beginning, mathematics was essentially divided into geometry and arithmetic (the manipulation of natural numbers and fractions), until the 16th and 17th centuri... | https://en.wikipedia.org/wiki?curid=18831 |
5,047 | The word "mathematics" comes from Ancient Greek "máthēma" (""), meaning "that which is learnt," "what one gets to know," hence also "study" and "science". The word for "mathematics" came to have the narrower and more technical meaning "mathematical study" even in Classical times. Its adjective is "mathēmatikós" (), mea... | https://en.wikipedia.org/wiki?curid=18831 |
5,048 | Similarly, one of the two main schools of thought in Pythagoreanism was known as the "mathēmatikoi" (μαθηματικοί)which at the time meant "learners" rather than "mathematicians" in the modern sense. The Pythagoreans were likely the first to constrain the use of the word to just the study of arithmetic and geometry. By t... | https://en.wikipedia.org/wiki?curid=18831 |
5,049 | In Latin, and in English until around 1700, the term "mathematics" more commonly meant "astrology" (or sometimes "astronomy") rather than "mathematics"; the meaning gradually changed to its present one from about 1500 to 1800. This has resulted in several mistranslations. For example, Saint Augustine's warning that Chr... | https://en.wikipedia.org/wiki?curid=18831 |
5,050 | The apparent plural form in English goes back to the Latin neuter plural (Cicero), based on the Greek plural "ta mathēmatiká" () and means roughly "all things mathematical", although it is plausible that English borrowed only the adjective "mathematic(al)" and formed the noun "mathematics" anew, after the pattern of "p... | https://en.wikipedia.org/wiki?curid=18831 |
5,051 | Before the Renaissance, mathematics was divided into two main areas: arithmeticregarding the manipulation of numbers, and geometryregarding the study of shapes. Some types of pseudoscience, such as numerology and astrology, were not then clearly distinguished from mathematics. | https://en.wikipedia.org/wiki?curid=18831 |
5,052 | During the Renaissance, two more areas appeared. Mathematical notation led to algebra, which, roughly speaking, consists of the study and the manipulation of formulas. Calculus, consisting of the two subfields "differential calculus" and "integral calculus", is the study of continuous functions, which model the typical... | https://en.wikipedia.org/wiki?curid=18831 |
5,053 | At the end of the 19th century, the foundational crisis in mathematics and the resulting systematization of the axiomatic method led to an explosion of new areas of mathematics. The 2020 Mathematics Subject Classification contains no less than first-level areas. Some of these areas correspond to the older division, as ... | https://en.wikipedia.org/wiki?curid=18831 |
5,054 | Number theory began with the manipulation of numbers, that is, natural numbers formula_1 and later expanded to integers formula_2 and rational numbers formula_3 Formerly, number theory was called arithmetic, but nowadays this term is mostly used for numerical calculations. The origin of number theory dates back to anci... | https://en.wikipedia.org/wiki?curid=18831 |
5,055 | Many easily-stated number problems have solutions that require sophisticated methods from across mathematics. One prominent example is Fermat's last theorem. This conjecture was stated in 1637 by Pierre de Fermat, but it was proved only in 1994 by Andrew Wiles, who used tools including scheme theory from algebraic geom... | https://en.wikipedia.org/wiki?curid=18831 |
5,056 | Number theory includes several subareas, including analytic number theory, algebraic number theory, geometry of numbers (method oriented), diophantine equations, and transcendence theory (problem oriented). | https://en.wikipedia.org/wiki?curid=18831 |
5,057 | Geometry is one of the oldest branches of mathematics. It started with empirical recipes concerning shapes, such as lines, angles and circles, which were developed mainly for the needs of surveying and architecture, but has since blossomed out into many other subfields. | https://en.wikipedia.org/wiki?curid=18831 |
5,058 | A fundamental innovation was the introduction of the concept of proofs by ancient Greeks, with the requirement that every assertion must be "proved". For example, it is not sufficient to verify by measurement that, say, two lengths are equal; their equality must be proven via reasoning from previously accepted results ... | https://en.wikipedia.org/wiki?curid=18831 |
5,059 | The resulting Euclidean geometry is the study of shapes and their arrangements constructed from lines, planes and circles in the Euclidean plane (plane geometry) and the (three-dimensional) Euclidean space. | https://en.wikipedia.org/wiki?curid=18831 |
5,060 | Euclidean geometry was developed without change of methods or scope until the 17th century, when René Descartes introduced what is now called Cartesian coordinates. This was a major change of paradigm, since instead of defining real numbers as lengths of line segments (see number line), it allowed the representation of... | https://en.wikipedia.org/wiki?curid=18831 |
5,061 | Analytic geometry allows the study of curves that are not related to circles and lines. Such curves can be defined as graph of functions (whose study led to differential geometry). They can also be defined as implicit equations, often polynomial equations (which spawned algebraic geometry). Analytic geometry also makes... | https://en.wikipedia.org/wiki?curid=18831 |
5,062 | In the 19th century, mathematicians discovered non-Euclidean geometries, which do not follow the parallel postulate. By questioning the truth of that postulate, this discovery has been viewed as joining Russel's paradox in revealing the foundational crisis of mathematics.This aspect of the crisis was solved by systemat... | https://en.wikipedia.org/wiki?curid=18831 |
5,063 | Algebra is the art of manipulating equations and formulas. Diophantus (3rd century) and al-Khwarizmi (9th century) were the two main precursors of algebra. The first one solved some equations involving unknown natural numbers by deducing new relations until he obtained the solution. The second one introduced systematic... | https://en.wikipedia.org/wiki?curid=18831 |
5,064 | Algebra became an area in its own right only with François Viète (1540–1603), who introduced the use of variables for representing unknown or unspecified numbers. This allows mathematicians to describe the operations that have to be done on the numbers represented using mathematical formulas. | https://en.wikipedia.org/wiki?curid=18831 |
5,065 | Until the 19th century, algebra consisted mainly of the study of linear equations (presently "linear algebra"), and polynomial equations in a single unknown, which were called "algebraic equations" (a term that is still in use, although it may be ambiguous). During the 19th century, mathematicians began to use variable... | https://en.wikipedia.org/wiki?curid=18831 |
5,066 | Some types of algebraic structures have useful and often fundamental properties, in many areas of mathematics. Their study became autonomous parts of algebra, and include: | https://en.wikipedia.org/wiki?curid=18831 |
5,067 | The study of types of algebraic structures as mathematical objects is the purpose of universal algebra and category theory. The latter applies to every mathematical structure (not only algebraic ones). At its origin, it was introduced, together with homological algebra for allowing the algebraic study of non-algebraic ... | https://en.wikipedia.org/wiki?curid=18831 |
5,068 | Calculus, formerly called infinitesimal calculus, was introduced independently and simultaneously by 17th-century mathematicians Newton and Leibniz. It is fundamentally the study of the relationship of variables that depend on each other. Calculus was expanded in the 18th century by Euler with the introduction of the c... | https://en.wikipedia.org/wiki?curid=18831 |
5,069 | Analysis is further subdivided into real analysis, where variables represent real numbers, and complex analysis, where variables represent complex numbers. Analysis includes many subareas shared by other areas of mathematics which include: | https://en.wikipedia.org/wiki?curid=18831 |
5,070 | Discrete mathematics, broadly speaking, is the study of individual, countable mathematical objects. An example is the set of all integers. Because the objects of study here are discrete, the methods of calculus and mathematical analysis do not directly apply. Algorithmsespecially their implementation and computational ... | https://en.wikipedia.org/wiki?curid=18831 |
5,071 | The four color theorem and optimal sphere packing were two major problems of discrete mathematics solved in the second half of the 20th century. The P versus NP problem, which remains open to this day, is also important for discrete mathematics, since its solution would potentially impact a large number of computationa... | https://en.wikipedia.org/wiki?curid=18831 |
5,072 | The two subjects of mathematical logic and set theory have belonged to mathematics since the end of the 19th century. Before this period, sets were not considered to be mathematical objects, and logic, although used for mathematical proofs, belonged to philosophy and was not specifically studied by mathematicians. | https://en.wikipedia.org/wiki?curid=18831 |
5,073 | Before Cantor's study of infinite sets, mathematicians were reluctant to consider actually infinite collections, and considered infinity to be the result of endless enumeration. Cantor's work offended many mathematicians not only by considering actually infinite sets but by showing that this implies different sizes of ... | https://en.wikipedia.org/wiki?curid=18831 |
5,074 | In the same period, various areas of mathematics concluded the former intuitive definitions of the basic mathematical objects were insufficient for ensuring mathematical rigour. Examples of such intuitive definitions are "a set is a collection of objects", "natural number is what is used for counting", "a point is a sh... | https://en.wikipedia.org/wiki?curid=18831 |
5,075 | This became the foundational crisis of mathematics. It was eventually solved in mainstream mathematics by systematizing the axiomatic method inside a formalized set theory. Roughly speaking, each mathematical object is defined by the set of all similar objects and the properties that these objects must have. For exampl... | https://en.wikipedia.org/wiki?curid=18831 |
5,076 | The "nature" of the objects defined this way is a philosophical problem that mathematicians leave to philosophers, even if many mathematicians have opinions on this nature, and use their opinionsometimes called "intuition"to guide their study and proofs. The approach allows considering "logics" (that is, sets of allowe... | https://en.wikipedia.org/wiki?curid=18831 |
5,077 | These problems and debates led to a wide expansion of mathematical logic, with subareas such as model theory (modeling some logical theories inside other theories), proof theory, type theory, computability theory and computational complexity theory. Although these aspects of mathematical logic were introduced before th... | https://en.wikipedia.org/wiki?curid=18831 |
5,078 | The field of statistics is a mathematical application that is employed for the collection and processing of data samples, using procedures based on mathematical methods especially probability theory. Statisticians generate data with random sampling or randomized experiments. The design of a statistical sample or experi... | https://en.wikipedia.org/wiki?curid=18831 |
5,079 | Statistical theory studies decision problems such as minimizing the risk (expected loss) of a statistical action, such as using a procedure in, for example, parameter estimation, hypothesis testing, and selecting the best. In these traditional areas of mathematical statistics, a statistical-decision problem is formulat... | https://en.wikipedia.org/wiki?curid=18831 |
5,080 | Computational mathematics is the study of mathematical problems that are typically too large for human, numerical capacity. Numerical analysis studies methods for problems in analysis using functional analysis and approximation theory; numerical analysis broadly includes the study of approximation and discretization wi... | https://en.wikipedia.org/wiki?curid=18831 |
5,081 | The history of mathematics is an ever-growing series of abstractions. Evolutionarily speaking, the first abstraction to ever be discovered, one shared by many animals, was probably that of numbers: the realization that, for example, a collection of two apples and a collection of two oranges (say) have something in comm... | https://en.wikipedia.org/wiki?curid=18831 |
5,082 | Evidence for more complex mathematics does not appear until around 3000 , when the Babylonians and Egyptians began using arithmetic, algebra, and geometry for taxation and other financial calculations, for building and construction, and for astronomy. The oldest mathematical texts from Mesopotamia and Egypt are from 20... | https://en.wikipedia.org/wiki?curid=18831 |
5,083 | In the 6th century BC, Greek mathematics began to emerge as a distinct discipline and some Ancient Greeks such as the Pythagoreans appeared to have considered it a subject in its own right. Around 300 BC, Euclid organized mathematical knowledge by way of postulates and first principles, which evolved into the axiomatic... | https://en.wikipedia.org/wiki?curid=18831 |
5,084 | The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition an... | https://en.wikipedia.org/wiki?curid=18831 |
5,085 | During the Golden Age of Islam, especially during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics. The most notable achievement of Islamic mathematics was the development of algebra. Other achievements of the Islamic period include advances in spherical trigonometry ... | https://en.wikipedia.org/wiki?curid=18831 |
5,086 | During the early modern period, mathematics began to develop at an accelerating pace in Western Europe, with innovations that revolutionized mathematics, such as the introduction of variables and symbolic notation by François Viète (1540–1603), the introduction of coordinates by René Descartes (1596–1650) for reducing ... | https://en.wikipedia.org/wiki?curid=18831 |
5,087 | Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made to this very day. According to Mikhail B. Sevryuk, in the January 2006 issue of the "Bulletin of the American Mathematical Society"... | https://en.wikipedia.org/wiki?curid=18831 |
5,088 | Mathematical notation is widely used in science and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. This notation consists of symbols used for representing operations, unspecified numbers, relations and any other mathematical objects, and then assembling them in... | https://en.wikipedia.org/wiki?curid=18831 |
5,089 | Mathematics has developed a rich terminology covering a broad range of fields that study the properties of various abstract, idealized objects and how they interact. It is based on rigorous definitions that provide a standard foundation for communication. An axiom or postulate is a mathematical statement that is taken ... | https://en.wikipedia.org/wiki?curid=18831 |
5,090 | Numerous technical terms used in mathematics are neologisms, such as "polynomial" and "homeomorphism". Other technical terms are words of the common language that are used in an accurate meaning that may differs slightly from their common meaning. For example, in mathematics, "or" means "one, the other or both", while,... | https://en.wikipedia.org/wiki?curid=18831 |
5,091 | Mathematics is used in most sciences for modeling phenomena, which then allows predictions to be made from experimental laws. The independence of mathematical truth from any experimentation implies that the accuracy of such predictions depends only on the adequacy of the model. Inaccurate predictions, rather than being... | https://en.wikipedia.org/wiki?curid=18831 |
5,092 | There is still a philosophical debate whether mathematics is a science. However, in practice, mathematicians are typically grouped with scientists, and mathematics shares much in common with the physical sciences. Like them, it is falsifiable, which means in mathematics that, if a result or a theory is wrong, this can ... | https://en.wikipedia.org/wiki?curid=18831 |
5,093 | Until the 19th century, the development of mathematics in the West was mainly motivated by the needs of technology and science, and there was no clear distinction between pure and applied mathematics. For example, the natural numbers and arithmetic were introduced for the need of counting, and geometry was motivated by... | https://en.wikipedia.org/wiki?curid=18831 |
5,094 | In the 19th century, mathematicians such as Karl Weierstrass and Richard Dedekind increasingly focused their research on internal problems, that is, "pure mathematics". This led to split mathematics into "pure mathematics" and "applied mathematics", the latter being often considered as having a lower value among mathem... | https://en.wikipedia.org/wiki?curid=18831 |
5,095 | The aftermath of World War II led to a surge in the development of applied mathematics in the US and elsewhere. Many of the theories developed for applications were found interesting from the point of view of pure mathematics, and many results of pure mathematics were shown to have applications outside mathematics; in ... | https://en.wikipedia.org/wiki?curid=18831 |
5,096 | An example of the first case is the theory of distributions, introduced by Laurent Schwartz for validating computations done in quantum mechanics, which became immediately an important tool of (pure) mathematical analysis. An example of the second case is the decidability of the first-order theory of the real numbers, ... | https://en.wikipedia.org/wiki?curid=18831 |
5,097 | In the present day, the distinction between pure and applied mathematics is more a question of personal research aim of mathematicians than a division of mathematics into broad areas. The Mathematics Subject Classification has a section for "general applied mathematics" but does not mention "pure mathematics". However,... | https://en.wikipedia.org/wiki?curid=18831 |
5,098 | The unreasonable effectiveness of mathematics is a phenomenon that was named and first made explicit by physicist Eugene Wigner. It is the fact that many mathematical theories, even the "purest" have applications outside their initial object. These applications may be completely outside their initial area of mathematic... | https://en.wikipedia.org/wiki?curid=18831 |
5,099 | A notable example is the prime factorization of natural numbers that was discovered more than 2,000 years before its common use for secure internet communications through the RSA cryptosystem. A second historical example is the theory of ellipses. They were studied by the ancient Greek mathematicians as conic sections ... | https://en.wikipedia.org/wiki?curid=18831 |
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