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Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically 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 use Conditional (computer programming), 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 (computer science), 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 e ... [...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] |
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] |
Automated Decision-making
Automated decision-making (ADM) is the use of data, machines and algorithms to make decisions in a range of contexts, including public administration, business, health, education, law, employment, transport, media and entertainment, with varying degrees of human oversight or intervention. ADM may involve large-scale data from a range of sources, such as databases, text, social media, sensors, images or speech, that is processed using various technologies including computer software, algorithms, machine learning, natural language processing, artificial intelligence, augmented intelligence and robotics. The increasing use of automated decision-making systems (ADMS) across a range of contexts presents many benefits and challenges to human society requiring consideration of the technical, legal, ethical, societal, educational, economic and health consequences. Overview There are different definitions of ADM based on the level of automation involved. Some definitions suggests ADM inv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recommender System
A recommender system (RecSys), or a recommendation system (sometimes replacing ''system'' with terms such as ''platform'', ''engine'', or ''algorithm'') and sometimes only called "the algorithm" or "algorithm", is a subclass of information filtering system that provides suggestions for items that are most pertinent to a particular user. Recommender systems are particularly useful when an individual needs to choose an item from a potentially overwhelming number of items that a service may offer. Modern recommendation systems such as those used on large social media sites make extensive use of AI, machine learning and related techniques to learn the behavior and preferences of each user and categorize content to tailor their feed individually. Typically, the suggestions refer to various decision-making processes, such as what product to purchase, what music to listen to, or what online news to read. Recommender systems are used in a variety of areas, with commonly recognised ex ... [...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] |
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] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heuristic (computer Science)
A heuristic or heuristic technique (''problem solving'', ''Heuristic (psychology), mental shortcut'', ''rule of thumb'') is any approach to problem solving that employs a Pragmatism, pragmatic method that is not fully Mathematical optimisation, optimized, perfected, or Rationality, rationalized, but is nevertheless "good enough" as an approximation or attribute substitution. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution. Heuristics can be mental shortcuts that ease the cognitive load of Decision-making, making a decision. Context Gigerenzer & Gaissmaier (2011) state that Set (mathematics), sub-sets of ''strategy'' include heuristics, regression analysis, and Bayesian inference. Heuristics are strategies based on rules to generate optimal decisions, like the anchoring effect and utility maximization problem. These strategies depend on using readily accessible, thoug ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effective Method
In metalogic, mathematical logic, and computability theory, an effective method or effective procedure is a finite-time, deterministic procedure for solving a problem from a specific class. An effective method is sometimes also called a mechanical method or procedure. Definition Formally, a method is called effective to a specific class of problems when it satisfies the following criteria: * It consists of a finite number of exact, finite instructions. * When it is applied to a problem from its class: ** It always finishes (''terminates'') after a finite number of steps. ** It always produces a correct answer. * In principle, it can be done by a human without any aids except writing materials. * Its instructions need only to be followed rigorously to succeed. In other words, it requires no ingenuity to succeed.The Cambridge Dictionary of Philosophy, ''effective procedure'' Optionally, it may also be required that the method never returns a result as if it were an answer wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zero
0 (zero) is a number representing an empty quantity. Adding (or subtracting) 0 to any number leaves that number unchanged; in mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 results in 0, and consequently division by zero has no meaning in arithmetic. As a numerical digit, 0 plays a crucial role in decimal notation: it indicates that the power of ten corresponding to the place containing a 0 does not contribute to the total. For example, "205" in decimal means two hundreds, no tens, and five ones. The same principle applies in place-value notations that uses a base other than ten, such as binary and hexadecimal. The modern use of 0 in this manner derives from Indian mathematics that was transmitted to Europe via medieval Islamic mathematicians and popularized by Fibonacci. It was independently used by the Maya. Common name ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inference
Inferences are steps in logical reasoning, moving from premises to logical consequences; etymologically, the word '' infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle (300s BC). Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular evidence to a universal conclusion. A third type of inference is sometimes distinguished, notably by Charles Sanders Peirce, contradistinguishing abduction from induction. Various fields study how inference is done in practice. Human inference (i.e. how humans draw conclusions) is traditionally studied within the fields of logic, argumentation studies, and cognitive psychology; artificial intelligence researchers develop automated inference systems to emulate human inference. Statist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
