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Software Logic
In mathematics and computer science, an algorithm () is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an effective method, an algorithm can be expressed within a finite amount of space and time"Any classical math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GCD Through Successive Subtractions
GCD may refer to: * Great-circle distance * GCD, Chinese Internet slang for the Chinese Communist Party () * General content descriptor, a wireless device file format * Geneva Consensus Declaration, a non-binding anti-abortion statement signed by a handful of nations * Global Cities Dialogue, an international development organisation * Grand Central Dispatch, a parallel computing framework * Grand Comics Database * Grant County Regional Airport, near John Day, Oregon, United States * Greatest common divisor ** Binary GCD algorithm ** Polynomial greatest common divisor ** Lehmer's GCD algorithm * Griffith College Dublin, in Dublin, Ireland * Yukulta language, spoken in Australia {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Empty String
In formal language theory, the empty string, or empty word, is the unique String (computer science), string of length zero. Formal theory Formally, a string is a finite, ordered sequence of character (symbol), characters such as letters, digits or spaces. The empty string is the special case where the sequence has length zero, so there are no symbols in the string. There is only one empty string, because two strings are only different if they have different lengths or a different sequence of symbols. In formal treatments, the empty string is denoted with ε or sometimes Λ or λ. The empty string should not be confused with the empty language ∅, which is a formal language (i.e. a set of strings) that contains no strings, not even the empty string. The empty string has several properties: * , ε, = 0. Its string (computer science)#Formal theory, string length is zero. * ε ⋅ s = s ⋅ ε = s. The empty string is the identity element of the concatenation operation. The set of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancrene Wisse
''Ancrene Wisse'' (; also known as the ''Ancrene Riwle'' or ''Guide for Anchoresses'') is an anonymous monastic rule (or manual) for anchoresses written in the early 13th century. The work consists of eight parts: divine service, keeping the heart, moral lessons and examples, temptation, confession, penance, love, and domestic matters. Parts 1 and 8 deal with what is called the "Outer Rule" (relating to the anchoresses' exterior life), while Parts 2–7 deal with the "Inner Rule" (relating to the anchoresses' interior life). It is written in Middle English, and was translated into Anglo-Norman and Latin. Community The adoption of an anchorite life was widespread all over medieval Europe, and was especially popular in England. By the early 13th century, the lives of anchorites or anchoresses were considered distinct from that of hermits. The hermit vocation permitted a change of location, whereas the anchorites were bound to one place of enclosure, generally a cell connected t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorism
Algorism is the technique of performing basic arithmetic by writing numbers in place value form and applying a set of memorized rules and facts to the digits. One who practices algorism is known as an algorist. This positional notation system has largely superseded earlier calculation systems that used a different set of symbols for each numerical magnitude, such as Roman numerals, and in some cases required a device such as an abacus. Etymology The word ''algorism'' comes from the name Al-Khwārizmī (c. 780–850), a Persian mathematician, astronomer, geographer and scholar in the House of Wisdom in Baghdad, whose name means "the native of Khwarezm", which is now in modern-day Uzbekistan. He wrote a treatise in Arabic language in the 9th century, which was translated into Latin in the 12th century under the title ''Algoritmi de numero Indorum''. This title means "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's Latinization of Al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latinisation Of Names
Latinisation (or Latinization) of names, also known as onomastic Latinisation (or onomastic Latinization), is the practice of rendering a ''non''-Latin name in a Neo-Latin, modern Latin style. It is commonly found with historical proper names, including personal names and toponyms, and in the standard binomial nomenclature of the life sciences. It goes further than romanisation, which is the transliteration of a word to the Latin alphabet from another script (e.g. Cyrillic). For authors writing in Latin, this change allows the name to function grammatically in a sentence through declension. In a scientific context, the main purpose of Latinisation may be to produce a name which is internationally consistent. Latinisation may be carried out by: * transforming the name into Latin sounds (e.g. for ), or * adding Latinate suffixes to the end of a name (e.g. for ''Heinrich Meibom (doctor), Meibom),'' or * translating a name with a specific meaning into Latin (e.g. for Italian ; b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adelard Of Bath
Adelard of Bath (; 1080? 1142–1152?) was a 12th-century English natural philosopher. He is known both for his original works and for translating many important Greek scientific works of astrology, astronomy, philosophy, alchemy and mathematics into Latin from Arabic versions, which were then introduced to Western Europe. The oldest surviving Latin translation of Euclid's ''Elements'' is a 12th-century translation by Adelard from an Arabic version. He is known as one of the first to introduce the Arabic numeral system to Europe. He stands at the convergence of three intellectual schools: the traditional learning of French schools, the Greek culture of Magna Graecia, Southern Italy, and the Arabic science of the East. Background Adelard's biography was incomplete in places, and leaves some aspects open to interpretation. Consequently, much of what is ascribed to Adelard is a product of his own testimony. Adelard claims to come from the Roman English city of Bath, Somerset, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Of Seville
John of Seville (Latin: ''Johannes Hispalensis'' or ''Johannes Hispaniensis'') (fl. 1133-53) was one of the main translators from Arabic into Castilian in partnership with Dominicus Gundissalinus during the early days of the Toledo School of Translators. John of Seville translated a litany of Arabic astrological works in addition to being credited with the production of several original works in Latin. Life and Context John of Seville was a baptized Jew, whose Jewish name (now unknown) has been corrupted into "Avendeut", "Avendehut", "Avendar" or "Aven Daud". This evolved into the middle name "David", so that, as a native of Toledo, he is frequently referred to as Johannes (David) Toletanus. However, Avendehut's translations typically translated Arabic text into Spanish vernacular. John of Seville was capable of translating Arabic directly into Latin, creating a distinction between himself and Avendehut. Some historians argue that in fact there were two different persons with a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic
Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type of numbers they operate on. Integer arithmetic is about calculations with positive and negative integers. Rational number arithmetic involves operations on fractions of integers. Real number arithmetic is about calculations with real numbers, which include both rational and irrational numbers. Another distinction is based on the numeral system employed to perform calculations. Decimal arithmetic is the most common. It uses the basic numerals from 0 to 9 and their combinations to express numbers. Binary arithmetic, by contrast, is used by most computers and represents numbers as combinations of the basic numerals 0 and 1. Computer arithmetic deals with the specificities of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hindu–Arabic Numeral System
The Hindu–Arabic numeral system (also known as the Indo-Arabic numeral system, Hindu numeral system, and Arabic numeral system) is a positional notation, positional Decimal, base-ten numeral system for representing integers; its extension to non-integers is the decimal, decimal numeral system, which is presently the most common numeral system. The system was invented between the 1st and 4th centuries by Indian mathematics, Indian mathematicians. By the 9th century, the system was adopted by Arabic mathematics, Arabic mathematicians who extended it to include fraction (mathematics), fractions. It became more widely known through the writings in Arabic of the Persian mathematician Al-Khwārizmī (''On the Calculation with Hindu Numerals'', ) and Arab mathematician Al-Kindi (''On the Use of the Hindu Numerals'', ). The system had spread to medieval Europe by the High Middle Ages, notably following Fibonacci's 13th century ''Liber Abaci''; until the evolution of the printing pre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Al-Khwarizmi
Muhammad ibn Musa al-Khwarizmi , or simply al-Khwarizmi, was a mathematician active during the Islamic Golden Age, who produced Arabic-language works in mathematics, astronomy, and geography. Around 820, he worked at the House of Wisdom in Baghdad, the contemporary capital city of the Abbasid Caliphate. One of the most prominent scholars of the period, his works were widely influential on later authors, both in the Islamic world and Europe. His popularizing treatise on algebra, compiled between 813 and 833 as '' Al-Jabr'' (''The Compendious Book on Calculation by Completion and Balancing''),Oaks, J. (2009), "Polynomials and Equations in Arabic Algebra", ''Archive for History of Exact Sciences'', 63(2), 169–203. presented the first systematic solution of linear and quadratic equations. One of his achievements in algebra was his demonstration of how to solve quadratic equations by completing the square, for which he provided geometric justifications. Because al-Khwarizmi was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Randomized Algorithm
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are random variables. There is a distinction between algorithms that use the random input so that they always terminate with the correct answer, but where the expected running time is finite (Las Vegas algorithms, for example Quicksort), and algorithms which have a chance of producing an incorrect result ( Monte Carlo algorithms, for example the Monte Carlo algorithm for the MFAS problem) or fail to produce a result either by signaling a failure or failing to terminate. In some cases, probabilistic algorithms are the only practical means of solving a problem. In common practice, randomized alg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deterministic
Determinism is the metaphysical view that all events within the universe (or multiverse) can occur only in one possible way. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and considerations. Like eternalism, determinism focuses on particular events rather than the future as a concept. Determinism is often contrasted with free will, although some philosophers claim that the two are compatible. A more extreme antonym of determinism is indeterminism, or the view that events are not deterministically caused but rather occur due to random chance. Historically, debates about determinism have involved many philosophical positions and given rise to multiple varieties or interpretations of determinism. One topic of debate concerns the scope of determined systems. Some philosophers have maintained that the entire universe is a single determinate system, while others identify more limited determinate systems. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
