288 relations: Abacus, Abstract machine, Ada Lovelace, Alan Turing, Alan Turing: The Enigma, Alexander of Villedieu, Alfred North Whitehead, Algorism, Algorithm, Algorithm characterizations, Algorithm engineering, Algorithmic composition, Algorithmic efficiency, Algorithmic entities, Algorithmic trading, Alonzo Church, Analog computer, Analysis of algorithms, Analytical Engine, Andrey Markov, Approximation algorithm, Arabic, Arithmetic, Array data structure, Artificial intelligence, Artificial neural network, Assembly language, Assignment (computer science), Association for Computing Machinery, Astronomer, Asymptotically optimal algorithm, Automata theory, Automated reasoning, Axiom, Babylonian astronomy, Backtracking, Baghdad, Baudot code, Benchmark (computing), Bertrand Russell, Big O notation, Binary search algorithm, Boolean algebra, Borůvka's algorithm, Brahmagupta, Branch and bound, Brute-force search, Bubble sort, Burali-Forti paradox, Busy beaver, ..., Calculation, Calculator, Calculus ratiocinator, Carl Benjamin Boyer, Charles Babbage, Chess, Church–Turing thesis, Claude Shannon, Clock, Cluster (spacecraft), Combinatorics, Communications of the ACM, Computability, Computability theory, Computation, Computational complexity theory, Computational geometry, Computer, Computer network, Computer program, Computer science, Control flow, Control table, Convex polytope, Coprime integers, Correctness (computer science), Cristopher Moore, Cryptography, Data compression, Data processing, Data structure, David Hilbert, Decidability (logic), Deductive reasoning, Determinism, Deterministic algorithm, Diamond v. Diehr, Difference engine, Differential equation, Distributed algorithm, Divide and conquer, Divide and conquer algorithm, Domain of a function, Donald Knuth, DRAKON, Dynamic programming, Effective method, Electrical network, Emil Leon Post, Empty string, Entscheidungsproblem, Euclid, Euclid's Elements, Euclidean algorithm, Execution (computing), Explainable Artificial Intelligence, Export of cryptography, Fast Fourier transform, Feedback, Finite-state machine, Flowchart, Floyd–Warshall algorithm, Formal system, Foundations of mathematics, Function (mathematics), Functional programming, Garbage in, garbage out, Genetic algorithm, Geoffrey Chaucer, Geographer, Georg Cantor, George Boole, George Dantzig, George Stibitz, Giuseppe Peano, Gottfried Wilhelm Leibniz, Gottlob Frege, Gottschalk v. Benson, Graph (discrete mathematics), Graph theory, Graph traversal, Greater Iran, Greatest common divisor, Greedy algorithm, Greek mathematics, Greenwood Publishing Group, Halting problem, Heuristic, Heuristic (computer science), High-level synthesis, Hindu–Arabic numeral system, House of Wisdom, Howard H. Aiken, Huffman coding, Human brain, Imperative programming, Inductive reasoning, Instance (computer science), Integer, Integer programming, Interpreter (computing), Introduction to Algorithms, Introduction to Arithmetic, Iteration, J. Barkley Rosser, Jacquard loom, Jacques Herbrand, John G. Kemeny, John Venn, John von Neumann, Jon Barwise, Joseph Marie Jacquard, Karnaugh map, Khwarezm, Kruskal's algorithm, Kurt Gödel, Lambda calculus, Las Vegas algorithm, Latin, Latinisation of names, Linear programming, List of algorithm general topics, List of algorithms, List of Indian mathematicians, List of Iranian mathematicians, Local optimum, Local search (optimization), Logic, Logic programming, London Mathematical Society, Lookup table, Machine code, Machine learning, Mathematical induction, Mathematical table, Mathematics, Max Planck Institute for Informatics, Maximum flow problem, Medical algorithm, Memoization, Memory, Merge algorithm, Merge sort, Methods of computing square roots, Modular arithmetic, Monte Carlo algorithm, Muhammad ibn Musa al-Khwarizmi, National Institute of Standards and Technology, Natural language, Neural circuit, Nicomachus, Nondeterministic algorithm, Numerical analysis, Oak Ridge National Laboratory, Operations research, Optimal substructure, Optimization problem, Overlapping subproblems, Oxford English Dictionary, P (complexity), P versus NP problem, Parallel algorithm, Parsing, Partial function, Persian people, Philosophy of mind, Pidgin code, Piotr Indyk, Post–Turing machine, Prim's algorithm, Principia Mathematica, Programming language, Pseudocode, Punched card, Quantity, Quantum algorithm, Quantum computing, Quantum entanglement, Quantum superposition, Randomized algorithm, Randomness, Recursion, Recursion (computer science), Reductio ad absurdum, Reduction (complexity), Register machine, Relay, Richard's paradox, Roman numerals, RP (complexity), Russell's paradox, Search algorithm, Selection algorithm, Semantics (computer science), Sieve of Eratosthenes, Simon & Schuster, Simplex algorithm, Simulated annealing, Software patent debate, Sorting algorithm, Spaghetti code, Stack (abstract data type), Stanford University, State diagram, State transition table, Stephen Cole Kleene, Stony Brook University, String (computer science), Structured program theorem, Syllogism, Synthetic rubber, Tabu search, Telegraphy, Teleprinter, The Compendious Book on Calculation by Completion and Balancing, Theory of computation, Thomas E. Kurtz, Ticker tape, Time complexity, Tower of Hanoi, Turing completeness, Turing machine, Turing reduction, Unary numeral system, Unisys, United States Patent and Trademark Office, University of Illinois at Urbana–Champaign, University of Indianapolis, University of Iowa, University of Tennessee, Uzbekistan, Verge escapement, Volume, William Stanley Jevons, Yuri Gurevich, ZPP (complexity), 0, 7400 series. Expand index (238 more) » « Shrink index
The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system.
An abstract machine, also called an abstract computer, is a theoretical model of a computer hardware or software system used in automata theory.
Augusta Ada King-Noel, Countess of Lovelace (née Byron; 10 December 1815 – 27 November 1852) was an English mathematician and writer, chiefly known for her work on Charles Babbage's proposed mechanical general-purpose computer, the Analytical Engine.
Alan Mathison Turing (23 June 1912 – 7 June 1954) was an English computer scientist, mathematician, logician, cryptanalyst, philosopher, and theoretical biologist.
Alan Turing: The Enigma (1983) is a biography of the British mathematician, codebreaker, and early computer scientist, Alan Turing (1912–1954) by Andrew Hodges.
Alexander of Villedieu was a French author, teacher and poet, who wrote text books on Latin grammar and arithmetic, everything in verse.
Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher.
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.
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
Algorithm characterizations are attempts to formalize the word algorithm.
Algorithm engineering focuses on the design, analysis, implementation, optimization, profiling and experimental evaluation of computer algorithms, bridging the gap between algorithm theory and practical applications of algorithms in software engineering.
Algorithmic composition is the technique of using algorithms to create music.
In computer science, algorithmic efficiency is a property of an algorithm which relates to the number of computational resources used by the algorithm.
Algorithmic entities are autonomous algorithms that operate without human control.
Algorithmic trading is a method of executing a large order (too large to fill all at once) using automated pre-programmed trading instructions accounting for variables such as time, price, and volume to send small slices of the order (child orders) out to the market over time.
Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician and logician who made major contributions to mathematical logic and the foundations of theoretical computer science.
An analog computer or analogue computer is a form of computer that uses the continuously changeable aspects of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved.
In computer science, the analysis of algorithms is the determination of the computational complexity of algorithms, that is the amount of time, storage and/or other resources necessary to execute them.
The Analytical Engine was a proposed mechanical general-purpose computer designed by English mathematician and computer pioneer Charles Babbage.
Andrey (Andrei) Andreyevich Markov (Андре́й Андре́евич Ма́рков, in older works also spelled Markoff) (14 June 1856 N.S. – 20 July 1922) was a Russian mathematician.
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to NP-hard optimization problems with provable guarantees on the distance of the returned solution to the optimal one.
Arabic (العَرَبِيَّة) or (عَرَبِيّ) or) is a Central Semitic language that first emerged in Iron Age northwestern Arabia and is now the lingua franca of the Arab world. It is named after the Arabs, a term initially used to describe peoples living from Mesopotamia in the east to the Anti-Lebanon mountains in the west, in northwestern Arabia, and in the Sinai peninsula. Arabic is classified as a macrolanguage comprising 30 modern varieties, including its standard form, Modern Standard Arabic, which is derived from Classical Arabic. As the modern written language, Modern Standard Arabic is widely taught in schools and universities, and is used to varying degrees in workplaces, government, and the media. The two formal varieties are grouped together as Literary Arabic (fuṣḥā), which is the official language of 26 states and the liturgical language of Islam. Modern Standard Arabic largely follows the grammatical standards of Classical Arabic and uses much of the same vocabulary. However, it has discarded some grammatical constructions and vocabulary that no longer have any counterpart in the spoken varieties, and has adopted certain new constructions and vocabulary from the spoken varieties. Much of the new vocabulary is used to denote concepts that have arisen in the post-classical era, especially in modern times. During the Middle Ages, Literary Arabic was a major vehicle of culture in Europe, especially in science, mathematics and philosophy. As a result, many European languages have also borrowed many words from it. Arabic influence, mainly in vocabulary, is seen in European languages, mainly Spanish and to a lesser extent Portuguese, Valencian and Catalan, owing to both the proximity of Christian European and Muslim Arab civilizations and 800 years of Arabic culture and language in the Iberian Peninsula, referred to in Arabic as al-Andalus. Sicilian has about 500 Arabic words as result of Sicily being progressively conquered by Arabs from North Africa, from the mid 9th to mid 10th centuries. Many of these words relate to agriculture and related activities (Hull and Ruffino). Balkan languages, including Greek and Bulgarian, have also acquired a significant number of Arabic words through contact with Ottoman Turkish. Arabic has influenced many languages around the globe throughout its history. Some of the most influenced languages are Persian, Turkish, Spanish, Urdu, Kashmiri, Kurdish, Bosnian, Kazakh, Bengali, Hindi, Malay, Maldivian, Indonesian, Pashto, Punjabi, Tagalog, Sindhi, and Hausa, and some languages in parts of Africa. Conversely, Arabic has borrowed words from other languages, including Greek and Persian in medieval times, and contemporary European languages such as English and French in modern times. Classical Arabic is the liturgical language of 1.8 billion Muslims and Modern Standard Arabic is one of six official languages of the United Nations. All varieties of Arabic combined are spoken by perhaps as many as 422 million speakers (native and non-native) in the Arab world, making it the fifth most spoken language in the world. Arabic is written with the Arabic alphabet, which is an abjad script and is written from right to left, although the spoken varieties are sometimes written in ASCII Latin from left to right with no standardized orthography.
Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.
In computer science, an array data structure, or simply an array, is a data structure consisting of a collection of elements (values or variables), each identified by at least one array index or key.
Artificial intelligence (AI, also machine intelligence, MI) is intelligence demonstrated by machines, in contrast to the natural intelligence (NI) displayed by humans and other animals.
Artificial neural networks (ANNs) or connectionist systems are computing systems vaguely inspired by the biological neural networks that constitute animal brains.
An assembly (or assembler) language, often abbreviated asm, is a low-level programming language, in which there is a very strong (but often not one-to-one) correspondence between the assembly program statements and the architecture's machine code instructions.
In computer programming, an assignment statement sets and/or re-sets the value stored in the storage location(s) denoted by a variable name; in other words, it copies a value into the variable.
The Association for Computing Machinery (ACM) is an international learned society for computing.
An astronomer is a scientist in the field of astronomy who concentrates their studies on a specific question or field outside the scope of Earth.
In computer science, an algorithm is said to be asymptotically optimal if, roughly speaking, for large inputs it performs at worst a constant factor (independent of the input size) worse than the best possible algorithm.
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them.
Automated reasoning is an area of computer science and mathematical logic dedicated to understanding different aspects of reasoning.
An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.
The history of astronomy in Mesopotamia, and the world, begins with the Sumerians who developed the earliest writing system—known as cuneiform—around 3500–3200 BC.
Backtracking is a general algorithm for finding all (or some) solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons a candidate ("backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution.
Baghdad (بغداد) is the capital of Iraq.
The Baudot code, invented by Émile Baudot, is a character set predating EBCDIC and ASCII.
In computing, a benchmark is the act of running a computer program, a set of programs, or other operations, in order to assess the relative performance of an object, normally by running a number of standard tests and trials against it.
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, historian, writer, social critic, political activist, and Nobel laureate.
Big O notation is a mathematical notation that describes the limiting behaviour of a function when the argument tends towards a particular value or infinity.
In computer science, binary search, also known as half-interval search,logarithmic search, or binary chop, is a search algorithm that finds the position of a target value within a sorted array.
In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.
Borůvka's algorithm is an algorithm for finding a minimum spanning tree in a graph for which all edge weights are distinct, or a minimum spanning forest in the case of a graph that is not connected.
Brahmagupta (born, died) was an Indian mathematician and astronomer.
Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization.
In computer science, brute-force search or exhaustive search, also known as generate and test, is a very general problem-solving technique that consists of systematically enumerating all possible candidates for the solution and checking whether each candidate satisfies the problem's statement.
Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the list to be sorted, compares each pair of adjacent items and swaps them if they are in the wrong order.
In set theory, a field of mathematics, the Burali-Forti paradox demonstrates that constructing "the set of all ordinal numbers" leads to a contradiction and therefore shows an antinomy in a system that allows its construction.
The busy beaver game consists of designing a halting, binary-alphabet Turing machine which writes the most 1s on the tape, using only a limited set of states.
A calculation is a deliberate process that transforms one or more inputs into one or more results, with variable change.
An electronic calculator is typically a portable electronic device used to perform calculations, ranging from basic arithmetic to complex mathematics.
The Calculus ratiocinator is a theoretical universal logical calculation framework, a concept described in the writings of Gottfried Leibniz, usually paired with his more frequently mentioned characteristica universalis, a universal conceptual language.
Carl Benjamin Boyer (November 3, 1906 – April 26, 1976) was an American historian of sciences, and especially mathematics.
Charles Babbage (26 December 1791 – 18 October 1871) was an English polymath.
Chess is a two-player strategy board game played on a chessboard, a checkered gameboard with 64 squares arranged in an 8×8 grid.
In computability theory, the Church–Turing thesis (also known as computability thesis, the Turing–Church thesis, the Church–Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis) is a hypothesis about the nature of computable functions.
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as "the father of information theory".
A clock is an instrument to measure, keep, and indicate time.
Cluster was a constellation of four European Space Agency spacecraft which were launched on the maiden flight of the Ariane 5 rocket, Flight 501, and subsequently lost when that rocket failed to achieve orbit.
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.
Communications of the ACM is the monthly journal of the Association for Computing Machinery (ACM).
Computability is the ability to solve a problem in an effective manner.
Computability theory, also known as recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.
Computation is any type of calculation that includes both arithmetical and non-arithmetical steps and follows a well-defined model, for example an algorithm.
Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry.
A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.
A computer network, or data network, is a digital telecommunications network which allows nodes to share resources.
A computer program is a collection of instructions for performing a specific task that is designed to solve a specific class of problems.
Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.
In computer science, control flow (or flow of control) is the order in which individual statements, instructions or function calls of an imperative program are executed or evaluated.
Control tables are tables that control the control flow or play a major part in program control.
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.
In number theory, two integers and are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1.
In theoretical computer science, correctness of an algorithm is asserted when it is said that the algorithm is correct with respect to a specification.
Cristopher David Moore, known as Cris Moore, (born March 12, 1968 in New Brunswick, New Jersey), retrieved 2012-03-10.
Cryptography or cryptology (from κρυπτός|translit.
In signal processing, data compression, source coding, or bit-rate reduction involves encoding information using fewer bits than the original representation.
Data processing is, generally, "the collection and manipulation of items of data to produce meaningful information." In this sense it can be considered a subset of information processing, "the change (processing) of information in any manner detectable by an observer." Data processing is distinct from word processing, which is manipulation of text specifically rather than data generally.
In computer science, a data structure is a data organization and storage format that enables efficient access and modification.
David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician.
In logic, the term decidable refers to the decision problem, the question of the existence of an effective method for determining membership in a set of formulas, or, more precisely, an algorithm that can and will return a boolean true or false value that is correct (instead of looping indefinitely, crashing, returning "don't know" or returning a wrong answer).
Deductive reasoning, also deductive logic, logical deduction is the process of reasoning from one or more statements (premises) to reach a logically certain conclusion.
Determinism is the philosophical theory that all events, including moral choices, are completely determined by previously existing causes.
In computer science, a deterministic algorithm is an algorithm which, given a particular input, will always produce the same output, with the underlying machine always passing through the same sequence of states.
Diamond v. Diehr, 450 U.S. 175 (1981), was a United States Supreme Court decision which held that controlling the execution of a physical process, by running a computer program did not preclude patentability of the invention as a whole.
A difference engine is an automatic mechanical calculator designed to tabulate polynomial functions.
A differential equation is a mathematical equation that relates some function with its derivatives.
A distributed algorithm is an algorithm designed to run on computer hardware constructed from interconnected processors.
Divide and conquer or Divide and Conquer may refer to.
In computer science, divide and conquer is an algorithm design paradigm based on multi-branched recursion.
In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.
Donald Ervin Knuth (born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University.
DRAKON is an algorithmic visual programming language developed within the Buran space project following ergonomic design principles.
Dynamic programming is both a mathematical optimization method and a computer programming method.
In logic, mathematics and computer science, especially metalogic and computability theory, an effective methodHunter, Geoffrey, Metalogic: An Introduction to the Metatheory of Standard First-Order Logic, University of California Press, 1971 or effective procedure is a procedure for solving a problem from a specific class.
An electrical network is an interconnection of electrical components (e.g. batteries, resistors, inductors, capacitors, switches) or a model of such an interconnection, consisting of electrical elements (e.g. voltage sources, current sources, resistances, inductances, capacitances).
Emil Leon Post (February 11, 1897 – April 21, 1954) was an American mathematician and logician.
In formal language theory, the empty string, or empty word is the unique string of length zero.
In mathematics and computer science, the Entscheidungsproblem (German for "decision problem") is a challenge posed by David Hilbert in 1928.
Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".
The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.
. EXAMPLES CAN BE FOUND BELOW, E.G., IN THE "Matrix method" SECTION.
Execution in computer and software engineering is the process by which a computer or a virtual machine performs the instructions of a computer program.
An Explainable AI (XAI) or Transparent AI is an artificial intelligence (AI) whose actions can be easily understood by humans.
The export of cryptography is the transfer from one country to another of devices and technology related to cryptography.
A fast Fourier transform (FFT) is an algorithm that samples a signal over a period of time (or space) and divides it into its frequency components.
Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop.
A finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical model of computation.
A flowchart is a type of diagram that represents an algorithm, workflow or process.
In computer science, the Floyd–Warshall algorithm is an algorithm for finding shortest paths in a weighted graph with positive or negative edge weights (but with no negative cycles).
A formal system is the name of a logic system usually defined in the mathematical way.
Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics.
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
In computer science, functional programming is a programming paradigm—a style of building the structure and elements of computer programs—that treats computation as the evaluation of mathematical functions and avoids changing-state and mutable data.
In computer science, garbage in, garbage out (GIGO) is where flawed, or nonsense input data produces nonsense output or "garbage".
In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA).
Geoffrey Chaucer (c. 1343 – 25 October 1400), known as the Father of English literature, is widely considered the greatest English poet of the Middle Ages.
A geographer is a scholar whose area of study is geography, the study of Earth's natural environment and human society.
Georg Ferdinand Ludwig Philipp Cantor (– January 6, 1918) was a German mathematician.
George Boole (2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ireland.
George Bernard Dantzig (November 8, 1914 – May 13, 2005) was an American mathematical scientist who made important contributions to operations research, computer science, economics, and statistics.
George Robert Stibitz (April 30, 1904 – January 31, 1995) was a Bell Labs researcher internationally recognized as one of the fathers of the modern first digital computer.
Giuseppe Peano (27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist.
Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.
Friedrich Ludwig Gottlob Frege (8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician.
Gottschalk v. Benson, 409 U.S. 63 (1972), was a United States Supreme Court case in which the Court ruled that a process claim directed to a numerical algorithm, as such, was not patentable because "the patent would wholly pre-empt the mathematical formula and in practical effect would be a patent on the algorithm itself." That would be tantamount to allowing a patent on an abstract idea, contrary to precedent dating back to the middle of the 19th century.
In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
In computer science, graph traversal (also known as graph search) refers to the process of visiting (checking and/or updating) each vertex in a graph.
Greater Iran (ایران بزرگ) is a term used to refer to the regions of the Caucasus, West Asia, Central Asia, and parts of South Asia that have significant Iranian cultural influence due to having been either long historically ruled by the various imperial dynasties of Persian Empire (such as those of the Medes, Achaemenids, Parthians, Sassanians, Samanids, Safavids, and Afsharids and the Qajars), having considerable aspects of Persian culture due to extensive contact with the various imperial dynasties of Iran (e.g., those regions and peoples in the North Caucasus that were not under direct Iranian rule), or are simply nowadays still inhabited by a significant amount of Iranic peoples who patronize their respective cultures (as it goes for the western parts of South Asia, Bahrain and Tajikistan).
In mathematics, the greatest common divisor (gcd) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.
A greedy algorithm is an algorithmic paradigm that follows the problem solving heuristic of making the locally optimal choice at each stage with the intent of finding a global optimum.
Greek mathematics refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean.
ABC-CLIO/Greenwood is an educational and academic publisher (middle school through university level) which is today part of ABC-CLIO.
In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running (i.e., halt) or continue to run forever.
A heuristic technique (εὑρίσκω, "find" or "discover"), often called simply a heuristic, is any approach to problem solving, learning, or discovery that employs a practical method, not guaranteed to be optimal, perfect, logical, or rational, but instead sufficient for reaching an immediate goal.
In computer science, artificial intelligence, and mathematical optimization, a heuristic (from Greek εὑρίσκω "I find, discover") is a technique designed for solving a problem more quickly when classic methods are too slow, or for finding an approximate solution when classic methods fail to find any exact solution.
High-level synthesis (HLS), sometimes referred to as C synthesis, electronic system-level (ESL) synthesis, algorithmic synthesis, or behavioral synthesis, is an automated design process that interprets an algorithmic description of a desired behavior and creates digital hardware that implements that behavior.
The Hindu–Arabic numeral systemDavid Eugene Smith and Louis Charles Karpinski,, 1911 (also called the Arabic numeral system or Hindu numeral system) is a positional decimal numeral system that is the most common system for the symbolic representation of numbers in the world.
The House of Wisdom (بيت الحكمة; Bayt al-Hikma) refers either to a major Abbasid public academy and intellectual center in Baghdad or to a large private library belonging to the Abbasid Caliphs during the Islamic Golden Age.
Howard Hathaway Aiken (March 8, 1900 – March 14, 1973) was an American physicist and a pioneer in computing, being the original conceptual designer behind IBM's Harvard Mark I computer.
In computer science and information theory, a Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression.
The human brain is the central organ of the human nervous system, and with the spinal cord makes up the central nervous system.
In computer science, imperative programming is a programming paradigm that uses statements that change a program's state.
Inductive reasoning (as opposed to ''deductive'' reasoning or ''abductive'' reasoning) is a method of reasoning in which the premises are viewed as supplying some evidence for the truth of the conclusion.
In object-oriented programming (OOP), an instance is a concrete occurrence of any object, existing usually during the runtime of a computer program.
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers.
In computer science, an interpreter is a computer program that directly executes, i.e. performs, instructions written in a programming or scripting language, without requiring them previously to have been compiled into a machine language program.
Introduction to Algorithms is a book by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein.
The book Introduction to Arithmetic (Ἀριθμητικὴ εἰσαγωγή, Arithmetike eisagoge) is the only extant work on mathematics by Nicomachus (60–120 AD).
Iteration is the act of repeating a process, to generate a (possibly unbounded) sequence of outcomes, with the aim of approaching a desired goal, target or result.
John Barkley Rosser Sr. (December 6, 1907 – September 5, 1989) was an American logician, a student of Alonzo Church, and known for his part in the Church–Rosser theorem, in lambda calculus.
The Jacquard machine is a device fitted to a power loom that simplifies the process of manufacturing textiles with such complex patterns as brocade, damask and matelassé.
Jacques Herbrand (12 February 1908 – 27 July 1931) was a French mathematician.
John George Kemeny; May 31, 1926 – December 26, 1992) was a Jewish-American mathematician, computer scientist, and educator best known for co-developing the BASIC programming language in 1964 with Thomas E. Kurtz. Kemeny served as the 13th President of Dartmouth College from 1970 to 1981 and pioneered the use of computers in college education. Kemeny chaired the presidential commission that investigated the Three Mile Island accident in 1979. According to György Marx he was one of The Martians.
John Venn, FRS, FSA, (4 August 1834 – 4 April 1923) was an English logician and philosopher noted for introducing the Venn diagram, used in the fields of set theory, probability, logic, statistics, and computer science.
John von Neumann (Neumann János Lajos,; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, and polymath.
Kenneth Jon Barwise (June 29, 1942 – March 5, 2000) was an American mathematician, philosopher and logician who proposed some fundamental revisions to the way that logic is understood and used.
Joseph Marie Charles dit (called or nicknamed) Jacquard (7 July 1752 – 7 August 1834), was a French weaver and merchant.
The Karnaugh map (KM or K-map) is a method of simplifying Boolean algebra expressions.
Khwarezm, or Chorasmia (خوارزم, Xvârazm) is a large oasis region on the Amu Darya river delta in western Central Asia, bordered on the north by the (former) Aral Sea, on the east by the Kyzylkum desert, on the south by the Karakum desert, and on the west by the Ustyurt Plateau.
Kruskal's algorithm is a minimum-spanning-tree algorithm which finds an edge of the least possible weight that connects any two trees in the forest.
Kurt Friedrich Gödel (April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher.
Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution.
In computing, a Las Vegas algorithm is a randomized algorithm that always gives correct results; that is, it always produces the correct result or it informs about the failure.
Latin (Latin: lingua latīna) is a classical language belonging to the Italic branch of the Indo-European languages.
Latinisation or Latinization is the practice of rendering a non-Latin name (or word) in a Latin style.
Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.
This is a list of algorithm general topics.
The following is a list of algorithms along with one-line descriptions for each.
The chronology of Indian mathematicians spans from the Indus Valley Civilization and the Vedas to Modern India.
The following is a list of Iranian mathematicians including ethnic Iranian mathematicians.
In applied mathematics and computer science, a local optimum of an optimization problem is a solution that is optimal (either maximal or minimal) within a neighboring set of candidate solutions.
In computer science, local search is a heuristic method for solving computationally hard optimization problems.
Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.
Logic programming is a type of programming paradigm which is largely based on formal logic.
The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS) and the Institute of Mathematics and its Applications (IMA)).
In computer science, a lookup table is an array that replaces runtime computation with a simpler array indexing operation.
Machine code is a computer program written in machine language instructions that can be executed directly by a computer's central processing unit (CPU).
Machine learning is a subset of artificial intelligence in the field of computer science that often uses statistical techniques to give computers the ability to "learn" (i.e., progressively improve performance on a specific task) with data, without being explicitly programmed.
Mathematical induction is a mathematical proof technique.
Mathematical tables are lists of numbers showing the results of calculation with varying arguments.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
The Max Planck Institute for Informatics (German: Max-Planck-Institut für Informatik, abbreviated MPI-INF or MPII) is a research institute in computer science with a focus on algorithms and their applications in a broad sense.
In optimization theory, maximum flow problems involve finding a feasible flow through a single-source, single-sink flow network that is maximum.
A medical algorithm is any computation, formula, statistical survey, nomogram, or look-up table, useful in healthcare.
In computing, memoization or memoisation is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again.
Memory is the faculty of the mind by which information is encoded, stored, and retrieved.
Merge algorithms are a family of algorithms that take multiple sorted lists as input and produce a single list as output, containing all the elements of the inputs lists in sorted order.
In computer science, merge sort (also commonly spelled mergesort) is an efficient, general-purpose, comparison-based sorting algorithm.
In numerical analysis, a branch of mathematics, there are several square root algorithms or methods of computing the principal square root of a non-negative real number.
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).
In computing, a Monte Carlo algorithm is a randomized algorithm whose output may be incorrect with a certain (typically small) probability.
There is some confusion in the literature on whether al-Khwārizmī's full name is ابو عبد الله محمد بن موسى الخوارزمي or ابو جعفر محمد بن موسی الخوارزمی.
The National Institute of Standards and Technology (NIST) is one of the oldest physical science laboratories in the United States.
In neuropsychology, linguistics, and the philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation.
A neural circuit, is a population of neurons interconnected by synapses to carry out a specific function when activated.
Nicomachus of Gerasa (Νικόμαχος; c. 60 – c. 120 AD) was an important ancient mathematician best known for his works Introduction to Arithmetic and Manual of Harmonics in Greek.
In computer science, a nondeterministic algorithm is an algorithm that, even for the same input, can exhibit different behaviors on different runs, as opposed to a deterministic algorithm.
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
Oak Ridge National Laboratory (ORNL) is an American multiprogram science and technology national laboratory sponsored by the U.S. Department of Energy (DOE) and administered, managed, and operated by UT-Battelle as a federally funded research and development center (FFRDC) under a contract with the DOE.
Operations research, or operational research in British usage, is a discipline that deals with the application of advanced analytical methods to help make better decisions.
In computer science, a problem is said to have optimal substructure if an optimal solution can be constructed from optimal solutions of its subproblems.
In mathematics and computer science, an optimization problem is the problem of finding the best solution from all feasible solutions.
In computer science, a problem is said to have overlapping subproblems if the problem can be broken down into subproblems which are reused several times or a recursive algorithm for the problem solves the same subproblem over and over rather than always generating new subproblems.
The Oxford English Dictionary (OED) is the main historical dictionary of the English language, published by the Oxford University Press.
In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class.
The P versus NP problem is a major unsolved problem in computer science.
In computer science, a parallel algorithm, as opposed to a traditional serial algorithm, is an algorithm which can be executed a piece at a time on many different processing devices, and then combined together again at the end to get the correct result.
Parsing, syntax analysis or syntactic analysis is the process of analysing a string of symbols, either in natural language, computer languages or data structures, conforming to the rules of a formal grammar.
In mathematics, a partial function from X to Y (written as or) is a function, for some subset X ′ of X.
The Persians--> are an Iranian ethnic group that make up over half the population of Iran.
Philosophy of mind is a branch of philosophy that studies the nature of the mind.
In computer programming, pidgin code is a mixture of several programming languages in the same program, or pseudocode that is a mixture of a programming language with natural language descriptions.
Piotr Indyk is a Professor in the Theory of Computation Group at the Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology.
A Post–Turing machine is a "program formulation" of an especially simple type of Turing machine, comprising a variant of Emil Post's Turing-equivalent model of computation described below.
In computer science, Prim's algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph.
The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913.
A programming language is a formal language that specifies a set of instructions that can be used to produce various kinds of output.
Pseudocode is an informal high-level description of the operating principle of a computer program or other algorithm.
A punched card or punch card is a piece of stiff paper that can be used to contain digital data represented by the presence or absence of holes in predefined positions.
Quantity is a property that can exist as a multitude or magnitude.
In quantum computing, a quantum algorithm is an algorithm which runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation.
Quantum computing is computing using quantum-mechanical phenomena, such as superposition and entanglement.
Quantum entanglement is a physical phenomenon which occurs when pairs or groups of particles are generated, interact, or share spatial proximity in ways such that the quantum state of each particle cannot be described independently of the state of the other(s), even when the particles are separated by a large distance—instead, a quantum state must be described for the system as a whole.
Quantum superposition is a fundamental principle of quantum mechanics.
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic.
Randomness is the lack of pattern or predictability in events.
Recursion occurs when a thing is defined in terms of itself or of its type.
Recursion in computer science is a method of solving a problem where the solution depends on solutions to smaller instances of the same problem (as opposed to iteration).
In logic, reductio ad absurdum ("reduction to absurdity"; also argumentum ad absurdum, "argument to absurdity") is a form of argument which attempts either to disprove a statement by showing it inevitably leads to a ridiculous, absurd, or impractical conclusion, or to prove one by showing that if it were not true, the result would be absurd or impossible.
In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem.
In mathematical logic and theoretical computer science a register machine is a generic class of abstract machines used in a manner similar to a Turing machine.
A relay is an electrically operated switch.
In logic, Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in 1905.
The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages.
In computational complexity theory, randomized polynomial time (RP) is the complexity class of problems for which a probabilistic Turing machine exists with these properties.
In the foundations of mathematics, Russell's paradox (also known as Russell's antinomy), discovered by Bertrand Russell in 1901, showed that some attempted formalizations of the naïve set theory created by Georg Cantor led to a contradiction.
In computer science, a search algorithm is any algorithm which solves the search problem, namely, to retrieve information stored within some data structure, or calculated in the search space of a problem domain.
In computer science, a selection algorithm is an algorithm for finding the kth smallest number in a list or array; such a number is called the kth order statistic.
In programming language theory, semantics is the field concerned with the rigorous mathematical study of the meaning of programming languages.
In mathematics, the sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit.
Simon & Schuster, Inc., a subsidiary of CBS Corporation, is an American publishing company founded in New York City in 1924 by Richard Simon and Max Schuster.
In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming.
Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function.
The software patent debate is the argument about the extent to which, as a matter of public policy, it should be possible to patent software and computer-implemented inventions.
In computer science, a sorting algorithm is an algorithm that puts elements of a list in a certain order.
Spaghetti code is a pejorative phrase for unstructured and difficult to maintain source code, broadly construed.
In computer science, a stack is an abstract data type that serves as a collection of elements, with two principal operations.
Stanford University (officially Leland Stanford Junior University, colloquially the Farm) is a private research university in Stanford, California.
A state diagram is a type of diagram used in computer science and related fields to describe the behavior of systems.
In automata theory and sequential logic, a state transition table is a table showing what state (or states in the case of a nondeterministic finite automaton) a finite semiautomaton or finite state machine will move to, based on the current state and other inputs.
Stephen Cole Kleene (January 5, 1909 – January 25, 1994) was an American mathematician.
The State University of New York at Stony Brook (also known as Stony Brook University or SUNY Stony Brook) is a public sea-grant and space-grant research university in the eastern United States.
In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable.
The structured program theorem, also called Böhm-Jacopini theorem, is a result in programming language theory.
A syllogism (συλλογισμός syllogismos, "conclusion, inference") is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.
A synthetic rubber is any artificial elastomer.
Tabu search, created by Fred W. Glover in 1986 and formalized in 1989, is a metaheuristic search method employing local search methods used for mathematical optimization.
Telegraphy (from Greek: τῆλε têle, "at a distance" and γράφειν gráphein, "to write") is the long-distance transmission of textual or symbolic (as opposed to verbal or audio) messages without the physical exchange of an object bearing the message.
A teleprinter (teletypewriter, Teletype or TTY) is an electromechanical typewriter that can be used to send and receive typed messages through various communications channels, in both point-to-point and point-to-multipoint configurations.
The Compendious Book on Calculation by Completion and Balancing (الكتاب المختصر في حساب الجبر والمقابلة, Al-kitāb al-mukhtaṣar fī ḥisāb al-ğabr wa’l-muqābala; Liber Algebræ et Almucabola) is an Arabic treatise on mathematics written by Persian polymath Muḥammad ibn Mūsā al-Khwārizmī around 820 CE while he was in the Abbasid capital of Baghdad.
In theoretical computer science and mathematics, the theory of computation is the branch that deals with how efficiently problems can be solved on a model of computation, using an algorithm.
Thomas Eugene Kurtz (born February 22, 1928) is a retired Dartmouth professor of mathematics and computer scientist, who along with his colleague John G. Kemeny set in motion the then revolutionary concept of making computers as freely available to college students as library books were, by implementing the concept of time-sharing at Dartmouth College.
Ticker tape was the earliest digital electronic communications medium, transmitting stock price information over telegraph lines, in use between around 1870 through 1970.
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
The Tower of Hanoi (also called the Tower of Brahma or Lucas' Tower and sometimes pluralized) is a mathematical game or puzzle.
In computability theory, a system of data-manipulation rules (such as a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing complete or computationally universal if it can be used to simulate any Turing machine.
A Turing machine is a mathematical model of computation that defines an abstract machine, which manipulates symbols on a strip of tape according to a table of rules.
In computability theory, a Turing reduction from a problem A to a problem B, is a reduction which solves A, assuming the solution to B is already known (Rogers 1967, Soare 1987).
The unary numeral system is the bijective base-1 numeral system.
The United States Patent and Trademark Office (USPTO) is an agency in the U.S. Department of Commerce that issues patents to inventors and businesses for their inventions, and trademark registration for product and intellectual property identification.
The University of Illinois Urbana–Champaign (also known as U of I, Illinois, or colloquially as the University of Illinois or UIUC) is a public research university in the U.S. state of Illinois and the flagship institution of the University of Illinois System.
The University of Indianapolis, or UIndy, is a university located in Indianapolis, Indiana, United States, which is affiliated with the United Methodist Church.
The University of Iowa (also known as the UI, U of I, UIowa, or simply Iowa) is a flagship public research university in Iowa City, Iowa.
The University of Tennessee (also referred to as The University of Tennessee, Knoxville, UT Knoxville, UTK, or UT) is a public sun- and land-grant university in Knoxville, Tennessee, United States.
Uzbekistan, officially also the Republic of Uzbekistan (Oʻzbekiston Respublikasi), is a doubly landlocked Central Asian Sovereign state.
The verge (or crown wheel) escapement is the earliest known type of mechanical escapement, the mechanism in a mechanical clock that controls its rate by allowing the gear train to advance at regular intervals or 'ticks'.
Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.
William Stanley Jevons FRS (1 September 1835 – 13 August 1882) was an English economist and logician.
Yuri Gurevich is an American computer scientist and mathematician and the inventor of abstract state machines.
In complexity theory, ZPP (zero-error probabilistic polynomial time) is the complexity class of problems for which a probabilistic Turing machine exists with these properties.
0 (zero) is both a number and the numerical digit used to represent that number in numerals.
The 7400 series of transistor–transistor logic (TTL) integrated circuits are the most popular family of TTL integrated circuit logic.
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