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# Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems. [1]

## Abacus

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.

## Abstract machine

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 Turing

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

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

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

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.

## Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

## Algorithm characterizations

Algorithm characterizations are attempts to formalize the word algorithm.

## Algorithm engineering

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

Algorithmic composition is the technique of using algorithms to create music.

## Algorithmic efficiency

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

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

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.

## Analog computer

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.

## Analysis of algorithms

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.

## Analytical Engine

The Analytical Engine was a proposed mechanical general-purpose computer designed by English mathematician and computer pioneer Charles Babbage.

## Andrey Markov

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.

## Approximation algorithm

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

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

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.

## Array data structure

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

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 network

Artificial neural networks (ANNs) or connectionist systems are computing systems vaguely inspired by the biological neural networks that constitute animal brains.

## Assembly language

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.

## Assignment (computer science)

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.

## Association for Computing Machinery

The Association for Computing Machinery (ACM) is an international learned society for computing.

## Astronomer

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.

## Asymptotically optimal algorithm

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

Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them.

## Automated reasoning

Automated reasoning is an area of computer science and mathematical logic dedicated to understanding different aspects of reasoning.

## Axiom

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.

## Babylonian astronomy

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

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.

## Baudot code

The Baudot code, invented by Émile Baudot, is a character set predating EBCDIC and ASCII.

## Benchmark (computing)

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 Russell

Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 &ndash; 2 February 1970) was a British philosopher, logician, mathematician, historian, writer, social critic, political activist, and Nobel laureate.

## Big O notation

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.

## Binary search algorithm

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.

## Boolean algebra

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

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

Brahmagupta (born, died) was an Indian mathematician and astronomer.

## Branch and bound

Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization.

## Brute-force search

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

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.

## Busy beaver

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.

## Calculation

A calculation is a deliberate process that transforms one or more inputs into one or more results, with variable change.

## Calculator

An electronic calculator is typically a portable electronic device used to perform calculations, ranging from basic arithmetic to complex mathematics.

## Calculus ratiocinator

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

Carl Benjamin Boyer (November 3, 1906 – April 26, 1976) was an American historian of sciences, and especially mathematics.

## Charles Babbage

Charles Babbage (26 December 1791 – 18 October 1871) was an English polymath.

## Chess

Chess is a two-player strategy board game played on a chessboard, a checkered gameboard with 64 squares arranged in an 8×8 grid.

## Church–Turing thesis

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 Shannon

Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as "the father of information theory".

## Clock

A clock is an instrument to measure, keep, and indicate time.

## Cluster (spacecraft)

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

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

Communications of the ACM is the monthly journal of the Association for Computing Machinery (ACM).

## Computability

Computability is the ability to solve a problem in an effective manner.

## Computability theory

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

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

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

Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry.

## Computer

A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.

## Computer network

A computer network, or data network, is a digital telecommunications network which allows nodes to share resources.

## Computer program

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

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

## Control flow

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 table

Control tables are tables that control the control flow or play a major part in program control.

## Convex polytope

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.

## Coprime integers

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.

## Correctness (computer science)

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 Moore

Cristopher David Moore, known as Cris Moore, (born March 12, 1968 in New Brunswick, New Jersey), retrieved 2012-03-10.

## Cryptography

Cryptography or cryptology (from κρυπτός|translit.

## Data compression

In signal processing, data compression, source coding, or bit-rate reduction involves encoding information using fewer bits than the original representation.

## Data processing

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.

## Data structure

In computer science, a data structure is a data organization and storage format that enables efficient access and modification.

## David Hilbert

David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician.

## Decidability (logic)

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

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

Determinism is the philosophical theory that all events, including moral choices, are completely determined by previously existing causes.

## Deterministic algorithm

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

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.

## Difference engine

A difference engine is an automatic mechanical calculator designed to tabulate polynomial functions.

## Differential equation

A differential equation is a mathematical equation that relates some function with its derivatives.

## Distributed algorithm

A distributed algorithm is an algorithm designed to run on computer hardware constructed from interconnected processors.

## Divide and conquer

Divide and conquer or Divide and Conquer may refer to.

## Divide and conquer algorithm

In computer science, divide and conquer is an algorithm design paradigm based on multi-branched recursion.

## Domain of a function

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 Knuth

Donald Ervin Knuth (born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University.

## DRAKON

DRAKON is an algorithmic visual programming language developed within the Buran space project following ergonomic design principles.

## Dynamic programming

Dynamic programming is both a mathematical optimization method and a computer programming method.

## Effective 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.

## Electrical network

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

Emil Leon Post (February 11, 1897 – April 21, 1954) was an American mathematician and logician.

## Empty string

In formal language theory, the empty string, or empty word is the unique string of length zero.

## Entscheidungsproblem

In mathematics and computer science, the Entscheidungsproblem (German for "decision problem") is a challenge posed by David Hilbert in 1928.

## Euclid

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".

## Euclid's Elements

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.

## Euclidean algorithm

. EXAMPLES CAN BE FOUND BELOW, E.G., IN THE "Matrix method" SECTION.

## Execution (computing)

Execution in computer and software engineering is the process by which a computer or a virtual machine performs the instructions of a computer program.

## Explainable Artificial Intelligence

An Explainable AI (XAI) or Transparent AI is an artificial intelligence (AI) whose actions can be easily understood by humans.

## Export of cryptography

The export of cryptography is the transfer from one country to another of devices and technology related to cryptography.

## Fast Fourier transform

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

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.

## Finite-state machine

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.

## Flowchart

A flowchart is a type of diagram that represents an algorithm, workflow or process.

## Floyd–Warshall algorithm

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).

## Formal system

A formal system is the name of a logic system usually defined in the mathematical way.

## Foundations of mathematics

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.

## Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

## Functional programming

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.

## Garbage in, garbage out

In computer science, garbage in, garbage out (GIGO) is where flawed, or nonsense input data produces nonsense output or "garbage".

## Genetic algorithm

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

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.

## Geographer

A geographer is a scholar whose area of study is geography, the study of Earth's natural environment and human society.

## Georg Cantor

Georg Ferdinand Ludwig Philipp Cantor (– January 6, 1918) was a German mathematician.

## George Boole

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 Dantzig

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 Stibitz

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

Giuseppe Peano (27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist.

## Gottfried Wilhelm Leibniz

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.

## Gottlob Frege

Friedrich Ludwig Gottlob Frege (8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician.

## Gottschalk v. Benson

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.

## Graph (discrete mathematics)

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".

## Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

## Graph traversal

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

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).

## Greatest common divisor

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.

## Greedy algorithm

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

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.

## Greenwood Publishing Group

ABC-CLIO/Greenwood is an educational and academic publisher (middle school through university level) which is today part of ABC-CLIO.

## Halting problem

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.

## Heuristic

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.

## Heuristic (computer science)

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

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.

## Hindu–Arabic numeral system

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.

## House of Wisdom

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 H. Aiken

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.

## Huffman coding

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.

## Human brain

The human brain is the central organ of the human nervous system, and with the spinal cord makes up the central nervous system.

## Imperative programming

In computer science, imperative programming is a programming paradigm that uses statements that change a program's state.

## Inductive reasoning

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.

## Instance (computer science)

In object-oriented programming (OOP), an instance is a concrete occurrence of any object, existing usually during the runtime of a computer program.

## Integer

An integer (from the Latin ''integer'' meaning "whole")Integer&#x2009;'s first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

## Integer programming

An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers.

## Interpreter (computing)

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

Introduction to Algorithms is a book by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein.

## Introduction to Arithmetic

The book Introduction to Arithmetic (Ἀριθμητικὴ εἰσαγωγή, Arithmetike eisagoge) is the only extant work on mathematics by Nicomachus (60&ndash;120 AD).

## Iteration

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.

## J. Barkley Rosser

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.

## Jacquard loom

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

Jacques Herbrand (12 February 1908 – 27 July 1931) was a French mathematician.

## John G. Kemeny

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

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

John von Neumann (Neumann János Lajos,; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, and polymath.

## Jon Barwise

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 Jacquard

Joseph Marie Charles dit (called or nicknamed) Jacquard (7 July 1752 – 7 August 1834), was a French weaver and merchant.

## Karnaugh map

The Karnaugh map (KM or K-map) is a method of simplifying Boolean algebra expressions.

## Khwarezm

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

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 Gödel

Kurt Friedrich Gödel (April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher.

## Lambda calculus

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.

## Las Vegas algorithm

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 (Latin: lingua latīna) is a classical language belonging to the Italic branch of the Indo-European languages.

## Latinisation of names

Latinisation or Latinization is the practice of rendering a non-Latin name (or word) in a Latin style.

## Linear programming

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.

## List of algorithm general topics

This is a list of algorithm general topics.

## List of algorithms

The following is a list of algorithms along with one-line descriptions for each.

## List of Indian mathematicians

The chronology of Indian mathematicians spans from the Indus Valley Civilization and the Vedas to Modern India.

## List of Iranian mathematicians

The following is a list of Iranian mathematicians including ethnic Iranian mathematicians.

## Local optimum

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.

## Local search (optimization)

In computer science, local search is a heuristic method for solving computationally hard optimization problems.

## Logic

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

Logic programming is a type of programming paradigm which is largely based on formal logic.

## London Mathematical Society

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)).

## Lookup table

In computer science, a lookup table is an array that replaces runtime computation with a simpler array indexing operation.

## Machine code

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

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

Mathematical induction is a mathematical proof technique.

## Mathematical table

Mathematical tables are lists of numbers showing the results of calculation with varying arguments.

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

## Max Planck Institute for Informatics

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.

## Maximum flow problem

In optimization theory, maximum flow problems involve finding a feasible flow through a single-source, single-sink flow network that is maximum.

## Medical algorithm

A medical algorithm is any computation, formula, statistical survey, nomogram, or look-up table, useful in healthcare.

## Memoization

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

Memory is the faculty of the mind by which information is encoded, stored, and retrieved.

## Merge algorithm

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.

## Merge sort

In computer science, merge sort (also commonly spelled mergesort) is an efficient, general-purpose, comparison-based sorting algorithm.

## Methods of computing square roots

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.

## Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

## Monte Carlo algorithm

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.

## National Institute of Standards and Technology

The National Institute of Standards and Technology (NIST) is one of the oldest physical science laboratories in the United States.

## Natural language

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.

## Neural circuit

A neural circuit, is a population of neurons interconnected by synapses to carry out a specific function when activated.

## Nicomachus

Nicomachus of Gerasa (Νικόμαχος; c. 60 &ndash; c. 120 AD) was an important ancient mathematician best known for his works Introduction to Arithmetic and Manual of Harmonics in Greek.

## Nondeterministic algorithm

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

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

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

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.

## Optimal substructure

In computer science, a problem is said to have optimal substructure if an optimal solution can be constructed from optimal solutions of its subproblems.

## Optimization problem

In mathematics and computer science, an optimization problem is the problem of finding the best solution from all feasible solutions.

## Overlapping subproblems

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.

## Oxford English Dictionary

The Oxford English Dictionary (OED) is the main historical dictionary of the English language, published by the Oxford University Press.

## P (complexity)

In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class.

## P versus NP problem

The P versus NP problem is a major unsolved problem in computer science.

## Parallel algorithm

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

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.

## Partial function

In mathematics, a partial function from X to Y (written as or) is a function, for some subset X ′ of X.

## Persian people

The Persians--> are an Iranian ethnic group that make up over half the population of Iran.

## Philosophy of mind

Philosophy of mind is a branch of philosophy that studies the nature of the mind.

## Pidgin code

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

Piotr Indyk is a Professor in the Theory of Computation Group at the Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology.

## Post–Turing machine

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.

## Prim's algorithm

In computer science, Prim's algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph.

## Principia Mathematica

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.

## Programming language

A programming language is a formal language that specifies a set of instructions that can be used to produce various kinds of output.

## Pseudocode

Pseudocode is an informal high-level description of the operating principle of a computer program or other algorithm.

## Punched card

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

Quantity is a property that can exist as a multitude or magnitude.

## Quantum algorithm

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

Quantum computing is computing using quantum-mechanical phenomena, such as superposition and entanglement.

## Quantum 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

Quantum superposition is a fundamental principle of quantum mechanics.

## Randomized algorithm

A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic.

## Randomness

Randomness is the lack of pattern or predictability in events.

## Recursion

Recursion occurs when a thing is defined in terms of itself or of its type.

## Recursion (computer science)

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.

## Reduction (complexity)

In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem.

## Register machine

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.

## Relay

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.

## Roman numerals

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.

## RP (complexity)

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.

## Search algorithm

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.

## Selection algorithm

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.

## Semantics (computer science)

In programming language theory, semantics is the field concerned with the rigorous mathematical study of the meaning of programming languages.

## Sieve of Eratosthenes

In mathematics, the sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit.

## Simon & Schuster

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.

## Simplex algorithm

In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming.

## Simulated annealing

Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function.

## Software patent debate

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.

## Sorting algorithm

In computer science, a sorting algorithm is an algorithm that puts elements of a list in a certain order.

## Spaghetti code

Spaghetti code is a pejorative phrase for unstructured and difficult to maintain source code, broadly construed.

## Stack (abstract data type)

In computer science, a stack is an abstract data type that serves as a collection of elements, with two principal operations.

## Stanford University

Stanford University (officially Leland Stanford Junior University, colloquially the Farm) is a private research university in Stanford, California.

## State diagram

A state diagram is a type of diagram used in computer science and related fields to describe the behavior of systems.

## State transition table

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

Stephen Cole Kleene (January 5, 1909 – January 25, 1994) was an American mathematician.

## Stony Brook University

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.

## String (computer science)

In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable.

## Structured program theorem

The structured program theorem, also called Böhm-Jacopini theorem, is a result in programming language theory.

## Syllogism

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.

## Synthetic rubber

A synthetic rubber is any artificial elastomer.

## Tabu search

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

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.

## Teleprinter

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

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.

## Theory of computation

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 E. Kurtz

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

Ticker tape was the earliest digital electronic communications medium, transmitting stock price information over telegraph lines, in use between around 1870 through 1970.

## Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.

## Tower of Hanoi

The Tower of Hanoi (also called the Tower of Brahma or Lucas' Tower and sometimes pluralized) is a mathematical game or puzzle.

## Turing completeness

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.

## 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.

## Turing reduction

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).

## Unary numeral system

The unary numeral system is the bijective base-1 numeral system.

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## United States Patent and Trademark Office

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.

## University of Illinois at Urbana–Champaign

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.

## University of Indianapolis

The University of Indianapolis, or UIndy, is a university located in Indianapolis, Indiana, United States, which is affiliated with the United Methodist Church.

## University of Iowa

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.

## University of Tennessee

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

Uzbekistan, officially also the Republic of Uzbekistan (Oʻzbekiston Respublikasi), is a doubly landlocked Central Asian Sovereign state.

## Verge escapement

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

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

William Stanley Jevons FRS (1 September 1835 – 13 August 1882) was an English economist and logician.

## Yuri Gurevich

Yuri Gurevich is an American computer scientist and mathematician and the inventor of abstract state machines.

## ZPP (complexity)

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

0 (zero) is both a number and the numerical digit used to represent that number in numerals.

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## 7400 series

The 7400 series of transistor–transistor logic (TTL) integrated circuits are the most popular family of TTL integrated circuit logic.

## References

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