111-551: The Donald E. Knuth Prize is a prize for outstanding contributions to the foundations of computer science , named after the American computer scientist Donald E. Knuth . The Knuth Prize has been awarded since 1996 and includes an award of US$ 5,000. The prize is awarded by ACM SIGACT and by IEEE Computer Society 's Technical Committee on the Mathematical Foundations of Computing. Prizes are awarded in alternating years at
222-428: A bi-quinary coded decimal -like system. The beads are usually rounded and made of hardwood . The beads are counted by moving them up or down towards the beam; beads moved toward the beam are counted, while those moved away from it are not. One of the top beads is 5, while one of the bottom beads is 1. Each rod has a number under it, showing the place value. The suanpan can be reset to the starting position instantly by
333-415: A decimal point can be imagined for fixed-point arithmetic . Any particular abacus design supports multiple methods to perform calculations, including addition , subtraction , multiplication , division , and square and cube roots . The beads are first arranged to represent a number, then are manipulated to perform a mathematical operation with another number, and their final position can be read as
444-542: A positional numeral system such as base ten (though some cultures used different numerical bases ). Roman and East Asian abacuses use a system resembling bi-quinary coded decimal , with a top deck (containing one or two beads) representing fives and a bottom deck (containing four or five beads) representing ones. Natural numbers are normally used, but some allow simple fractional components (e.g. 1 ⁄ 2 , 1 ⁄ 4 , and 1 ⁄ 12 in Roman abacus ), and
555-534: A 5-digit base-20 system. The word Nepōhualtzintzin Nahuatl pronunciation: [nepoːwaɬˈt͡sint͡sin] comes from Nahuatl , formed by the roots; Ne – personal -; pōhual or pōhualli Nahuatl pronunciation: [ˈpoːwalːi] – the account -; and tzintzin Nahuatl pronunciation: [ˈt͡sint͡sin] – small similar elements. Its complete meaning was taken as: counting with small similar elements. Its use
666-481: A bead frame similar to the Russian abacus but with straight wires and a vertical frame is common (see image). The wireframe may be used either with positional notation like other abacuses (thus the 10-wire version may represent numbers up to 9,999,999,999), or each bead may represent one unit (e.g. 74 can be represented by shifting all beads on 7 wires and 4 beads on the 8th wire, so numbers up to 100 may be represented). In
777-584: A calculation as quickly as with a physical instrument. The Chinese abacus migrated from China to Korea around 1400 AD. Koreans call it jupan (주판), supan (수판) or jusan (주산). The four-beads abacus (1:4) was introduced during the Goryeo Dynasty . The 5:1 abacus was introduced to Korea from China during the Ming Dynasty. Some sources mention the use of an abacus called a nepohualtzintzin in ancient Aztec culture. This Mesoamerican abacus used
888-570: A discipline, computer science spans a range of topics from theoretical studies of algorithms and the limits of computation to the practical issues of implementing computing systems in hardware and software. CSAB , formerly called Computing Sciences Accreditation Board—which is made up of representatives of the Association for Computing Machinery (ACM), and the IEEE Computer Society (IEEE CS) —identifies four areas that it considers crucial to
999-724: A distinct academic discipline in the 1950s and early 1960s. The world's first computer science degree program, the Cambridge Diploma in Computer Science , began at the University of Cambridge Computer Laboratory in 1953. The first computer science department in the United States was formed at Purdue University in 1962. Since practical computers became available, many applications of computing have become distinct areas of study in their own rights. Although first proposed in 1956,
1110-560: A diversity of forms and materials in other cultures. Sanchez wrote in Arithmetic in Maya that another base 5, base 4 abacus had been found in the Yucatán Peninsula that also computed calendar data. This was a finger abacus, on one hand, 0, 1, 2, 3, and 4 were used; and on the other hand 0, 1, 2, and 3 were used. Note the use of zero at the beginning and end of the two cycles. The quipu of
1221-464: A mathematical discipline argue that computer programs are physical realizations of mathematical entities and programs that can be deductively reasoned through mathematical formal methods . Computer scientists Edsger W. Dijkstra and Tony Hoare regard instructions for computer programs as mathematical sentences and interpret formal semantics for programming languages as mathematical axiomatic systems . A number of computer scientists have argued for
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#17328581104951332-443: A mathematics emphasis and with a numerical orientation consider alignment with computational science . Both types of departments tend to make efforts to bridge the field educationally if not across all research. Despite the word science in its name, there is debate over whether or not computer science is a discipline of science, mathematics, or engineering. Allen Newell and Herbert A. Simon argued in 1975, Computer science
1443-463: A network while using concurrency, this is known as a distributed system. Computers within that distributed system have their own private memory, and information can be exchanged to achieve common goals. This branch of computer science aims to manage networks between computers worldwide. Computer security is a branch of computer technology with the objective of protecting information from unauthorized access, disruption, or modification while maintaining
1554-540: A number of terms for the practitioners of the field of computing were suggested in the Communications of the ACM — turingineer , turologist , flow-charts-man , applied meta-mathematician , and applied epistemologist . Three months later in the same journal, comptologist was suggested, followed next year by hypologist . The term computics has also been suggested. In Europe, terms derived from contracted translations of
1665-495: A particular kind of mathematically based technique for the specification , development and verification of software and hardware systems. The use of formal methods for software and hardware design is motivated by the expectation that, as in other engineering disciplines, performing appropriate mathematical analysis can contribute to the reliability and robustness of a design. They form an important theoretical underpinning for software engineering, especially where safety or security
1776-506: A quick movement along the horizontal axis to spin all the beads away from the horizontal beam at the center. The prototype of the Chinese abacus appeared during the Han dynasty , and the beads are oval. The Song dynasty and earlier used the 1:4 type or four-beads abacus similar to the modern abacus including the shape of the beads commonly known as Japanese-style abacus. In the early Ming dynasty ,
1887-402: A scoring system in non- electronic table games. Others may use an abacus due to visual impairment that prevents the use of a calculator. The abacus is still used to teach the fundamentals of mathematics to children in most countries. The word abacus dates to at least 1387 AD when a Middle English work borrowed the word from Latin that described a sandboard abacus. The Latin word
1998-535: A season of the year lasts, two Nepōhualtzitzin (182) is the number of days of the corn's cycle, from its sowing to its harvest, three Nepōhualtzintzin (273) is the number of days of a baby's gestation, and four Nepōhualtzintzin (364) completed a cycle and approximated one year. When translated into modern computer arithmetic, the Nepōhualtzintzin amounted to the rank from 10 to 18 in floating point , which precisely calculated large and small amounts, although round off
2109-512: A significant amount of computer science does not involve the study of computers themselves. Because of this, several alternative names have been proposed. Certain departments of major universities prefer the term computing science , to emphasize precisely that difference. Danish scientist Peter Naur suggested the term datalogy , to reflect the fact that the scientific discipline revolves around data and data treatment, while not necessarily involving computers. The first scientific institution to use
2220-408: A single slanted deck, with ten beads on each wire (except one wire with four beads for quarter- ruble fractions). 4-bead wire was introduced for quarter- kopeks , which were minted until 1916. The Russian abacus is used vertically, with each wire running horizontally. The wires are usually bowed upward in the center, to keep the beads pinned to either side. It is cleared when all the beads are moved to
2331-410: A specific application. Codes are used for data compression , cryptography , error detection and correction , and more recently also for network coding . Codes are studied for the purpose of designing efficient and reliable data transmission methods. Data structures and algorithms are the studies of commonly used computational methods and their computational efficiency. Programming language theory
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#17328581104952442-506: A switch on the computer in either an "on" or "off" position. An adapted abacus, invented by Tim Cranmer, and called a Cranmer abacus is commonly used by visually impaired users. A piece of soft fabric or rubber is placed behind the beads, keeping them in place while the users manipulate them. The device is then used to perform the mathematical functions of multiplication, division, addition, subtraction, square root, and cube root. Although blind students have benefited from talking calculators,
2553-415: Is a branch of computer science that deals with the design, implementation, analysis, characterization, and classification of programming languages and their individual features . It falls within the discipline of computer science, both depending on and affecting mathematics, software engineering, and linguistics . It is an active research area, with numerous dedicated academic journals. Formal methods are
2664-407: Is a one while placing the wick on the number hundred means it is called a hundred, and on the number one thousand means it is a thousand". It is unclear exactly what this arrangement may have been. Around the 5th century, Indian clerks were already finding new ways of recording the contents of the abacus. Hindu texts used the term śūnya (zero) to indicate the empty column on the abacus. In Japan,
2775-422: Is an empirical discipline. We would have called it an experimental science, but like astronomy, economics, and geology, some of its unique forms of observation and experience do not fit a narrow stereotype of the experimental method. Nonetheless, they are experiments. Each new machine that is built is an experiment. Actually constructing the machine poses a question to nature; and we listen for the answer by observing
2886-484: Is an open problem in the theory of computation. Information theory, closely related to probability and statistics , is related to the quantification of information. This was developed by Claude Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and communicating data. Coding theory is the study of the properties of codes (systems for converting information from one form to another) and their fitness for
2997-475: Is associated in the popular mind with robotic development , but the main field of practical application has been as an embedded component in areas of software development , which require computational understanding. The starting point in the late 1940s was Alan Turing's question " Can computers think? ", and the question remains effectively unanswered, although the Turing test is still used to assess computer output on
3108-518: Is called an abacist . The Sumerian abacus appeared between 2700 and 2300 BC. It held a table of successive columns which delimited the successive orders of magnitude of their sexagesimal (base 60) number system. Some scholars point to a character in Babylonian cuneiform that may have been derived from a representation of the abacus. It is the belief of Old Babylonian scholars, such as Ettore Carruccio, that Old Babylonians "seem to have used
3219-543: Is connected to many other fields in computer science, including computer vision , image processing , and computational geometry , and is heavily applied in the fields of special effects and video games . Information can take the form of images, sound, video or other multimedia. Bits of information can be streamed via signals . Its processing is the central notion of informatics, the European view on computing, which studies information processing algorithms independently of
3330-409: Is considered by some to have a much closer relationship with mathematics than many scientific disciplines, with some observers saying that computing is a mathematical science. Early computer science was strongly influenced by the work of mathematicians such as Kurt Gödel , Alan Turing , John von Neumann , Rózsa Péter and Alonzo Church and there continues to be a useful interchange of ideas between
3441-468: Is derived from ancient Greek ἄβαξ ( abax ) which means something without a base, and colloquially, any piece of rectangular material. Alternatively, without reference to ancient texts on etymology, it has been suggested that it means "a square tablet strewn with dust", or "drawing-board covered with dust (for the use of mathematics)" (the exact shape of the Latin perhaps reflects the genitive form of
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3552-508: Is determining what can and cannot be automated. The Turing Award is generally recognized as the highest distinction in computer science. The earliest foundations of what would become computer science predate the invention of the modern digital computer . Machines for calculating fixed numerical tasks such as the abacus have existed since antiquity, aiding in computations such as multiplication and division. Algorithms for performing computations have existed since antiquity, even before
3663-630: Is generally considered the province of disciplines other than computer science. For example, the study of computer hardware is usually considered part of computer engineering , while the study of commercial computer systems and their deployment is often called information technology or information systems . However, there has been exchange of ideas between the various computer-related disciplines. Computer science research also often intersects other disciplines, such as cognitive science , linguistics , mathematics , physics , biology , Earth science , statistics , philosophy , and logic . Computer science
3774-584: Is intended to organize, store, and retrieve large amounts of data easily. Digital databases are managed using database management systems to store, create, maintain, and search data, through database models and query languages . Data mining is a process of discovering patterns in large data sets. The philosopher of computing Bill Rapaport noted three Great Insights of Computer Science : Programming languages can be used to accomplish different tasks in different ways. Common programming paradigms include: Many languages offer support for multiple paradigms, making
3885-426: Is involved. Formal methods are a useful adjunct to software testing since they help avoid errors and can also give a framework for testing. For industrial use, tool support is required. However, the high cost of using formal methods means that they are usually only used in the development of high-integrity and life-critical systems , where safety or security is of utmost importance. Formal methods are best described as
3996-545: Is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. It aims to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. According to Peter Denning, the fundamental question underlying computer science is, "What can be automated?" Theory of computation is focused on answering fundamental questions about what can be computed and what amount of resources are required to perform those computations. In an effort to answer
4107-569: Is next to the four beads, and pressing the "clearing" button puts the upper bead in the upper position, and the lower bead in the lower position. The abacus is still manufactured in Japan, despite the proliferation, practicality, and affordability of pocket electronic calculators . The use of the soroban is still taught in Japanese primary schools as part of mathematics , primarily as an aid to faster mental calculation. Using visual imagery, one can complete
4218-519: Is of high quality, affordable, maintainable, and fast to build. It is a systematic approach to software design, involving the application of engineering practices to software. Software engineering deals with the organizing and analyzing of software—it does not just deal with the creation or manufacture of new software, but its internal arrangement and maintenance. For example software testing , systems engineering , technical debt and software development processes . Artificial intelligence (AI) aims to or
4329-473: Is often used, either on a string of beads or on a rigid framework. Physicist Richard Feynman was noted for facility in mathematical calculations. He wrote about an encounter in Brazil with a Japanese abacus expert, who challenged him to speed contests between Feynman's pen and paper, and the abacus. The abacus was much faster for addition, somewhat faster for multiplication, but Feynman was faster at division. When
4440-575: Is required to synthesize goal-orientated processes such as problem-solving, decision-making, environmental adaptation, learning, and communication found in humans and animals. From its origins in cybernetics and in the Dartmouth Conference (1956), artificial intelligence research has been necessarily cross-disciplinary, drawing on areas of expertise such as applied mathematics , symbolic logic, semiotics , electrical engineering , philosophy of mind , neurophysiology , and social intelligence . AI
4551-432: Is the field of study and research concerned with the design and use of computer systems , mainly based on the analysis of the interaction between humans and computer interfaces . HCI has several subfields that focus on the relationship between emotions , social behavior and brain activity with computers . Software engineering is the study of designing, implementing, and modifying the software in order to ensure it
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4662-783: Is the field of study concerned with constructing mathematical models and quantitative analysis techniques and using computers to analyze and solve scientific problems. A major usage of scientific computing is simulation of various processes, including computational fluid dynamics , physical, electrical, and electronic systems and circuits, as well as societies and social situations (notably war games) along with their habitats, among many others. Modern computers enable optimization of such designs as complete aircraft. Notable in electrical and electronic circuit design are SPICE, as well as software for physical realization of new (or modified) designs. The latter includes essential design software for integrated circuits . Human–computer interaction (HCI)
4773-405: Is the quick development of this relatively new field requires rapid review and distribution of results, a task better handled by conferences than by journals. Abacus An abacus ( pl. : abaci or abacuses ), also called a counting frame , is a hand -operated calculating tool which was used from ancient times in the ancient Near East , Europe, China, and Russia, until the adoption of
4884-454: The Hindu–Arabic numeral system . An abacus consists of a two-dimensional array of slidable beads (or similar objects). In their earliest designs, the beads could be loose on a flat surface or sliding in grooves. Later the beads were made to slide on rods and built into a frame, allowing faster manipulation. Each rod typically represents one digit of a multi-digit number laid out using
4995-469: The Incas was a system of colored knotted cords used to record numerical data, like advanced tally sticks – but not used to perform calculations. Calculations were carried out using a yupana ( Quechua for "counting tool"; see figure) which was still in use after the conquest of Peru. The working principle of a yupana is unknown, but in 2001 Italian mathematician De Pasquale proposed an explanation. By comparing
5106-470: The Middle East would have provided direct contact with India, allowing them to acquire the concept of zero and the decimal point from Indian merchants and mathematicians. The Abhidharmakośabhāṣya of Vasubandhu (316–396), a Sanskrit work on Buddhist philosophy , says that the second-century CE philosopher Vasumitra said that "placing a wick (Sanskrit vartikā ) on the number one ( ekāṅka ) means it
5217-463: The Muromachi era . It adopts the form of the upper deck one bead and the bottom four beads. The top bead on the upper deck was equal to five and the bottom one is similar to the Chinese or Korean abacus, and the decimal number can be expressed, so the abacus is designed as a 1:4 device. The beads are always in the shape of a diamond. The quotient division is generally used instead of the division method; at
5328-638: The Soviet Union . The Russian abacus began to lose popularity only after the mass production of domestic microcalculators in 1974. The Russian abacus was brought to France around 1820 by mathematician Jean-Victor Poncelet , who had served in Napoleon 's army and had been a prisoner of war in Russia. The abacus had fallen out of use in western Europe in the 16th century with the rise of decimal notation and algorismic methods. To Poncelet's French contemporaries, it
5439-475: The "technocratic paradigm" (which might be found in engineering approaches, most prominently in software engineering), and the "scientific paradigm" (which approaches computer-related artifacts from the empirical perspective of natural sciences , identifiable in some branches of artificial intelligence ). Computer science focuses on methods involved in design, specification, programming, verification, implementation and testing of human-made computing systems. As
5550-554: The 100th anniversary of the invention of the arithmometer, Torres presented in Paris the Electromechanical Arithmometer , a prototype that demonstrated the feasibility of an electromechanical analytical engine, on which commands could be typed and the results printed automatically. In 1937, one hundred years after Babbage's impossible dream, Howard Aiken convinced IBM, which was making all kinds of punched card equipment and
5661-508: The 1st century AD. It has eight long grooves containing up to five beads in each and eight shorter grooves having either one or no beads in each. The groove marked I indicates units, X tens, and so on up to millions. The beads in the shorter grooves denote fives (five units, five tens, etc.) resembling a bi-quinary coded decimal system related to the Roman numerals . The short grooves on the right may have been used for marking Roman "ounces" (i.e. fractions). The Roman system of 'counter casting'
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#17328581104955772-451: The 2nd of the only two designs for mechanical analytical engines in history. In 1914, the Spanish engineer Leonardo Torres Quevedo published his Essays on Automatics , and designed, inspired by Babbage, a theoretical electromechanical calculating machine which was to be controlled by a read-only program. The paper also introduced the idea of floating-point arithmetic . In 1920, to celebrate
5883-669: The ACM Symposium on Theory of Computing and at the IEEE Symposium on Foundations of Computer Science , which are among the most prestigious conferences in theoretical computer science . The recipient of the Knuth Prize delivers a lecture at the conference. For instance, David S. Johnson "used his Knuth Prize lecture to push for practical applications for algorithms." In contrast with the Gödel Prize , which recognizes outstanding papers,
5994-618: The Analytical Engine, Ada Lovelace wrote, in one of the many notes she included, an algorithm to compute the Bernoulli numbers , which is considered to be the first published algorithm ever specifically tailored for implementation on a computer. Around 1885, Herman Hollerith invented the tabulator , which used punched cards to process statistical information; eventually his company became part of IBM . Following Babbage, although unaware of his earlier work, Percy Ludgate in 1909 published
6105-554: The Chinese, Korean, and Japanese models, the Roman model used grooves, presumably making arithmetic calculations much slower.) Another possible source of the suanpan is Chinese counting rods , which operated with a decimal system but lacked the concept of zero as a placeholder. The zero was probably introduced to the Chinese in the Tang dynasty (618–907) when travel in the Indian Ocean and
6216-561: The Greek word, ἄβακoς ( abakos )). While the table strewn with dust definition is popular, some argue evidence is insufficient for that conclusion. Greek ἄβαξ probably borrowed from a Northwest Semitic language like Phoenician , evidenced by a cognate with the Hebrew word ʾābāq ( אבק ), or "dust" (in the post-Biblical sense "sand used as a writing surface"). Both abacuses and abaci are used as plurals. The user of an abacus
6327-508: The Knuth Prize is awarded to individuals for their overall impact in the field. Since the prize was instituted in 1996, it has been awarded to the following individuals, with the citation for each award quoted (not always in full): Computer science Computer science is the study of computation , information , and automation . Computer science spans theoretical disciplines (such as algorithms , theory of computation , and information theory ) to applied disciplines (including
6438-547: The Machine Organization department in IBM's main research center in 1959. Concurrency is a property of systems in which several computations are executing simultaneously, and potentially interacting with each other. A number of mathematical models have been developed for general concurrent computation including Petri nets , process calculi and the parallel random access machine model. When multiple computers are connected in
6549-615: The Qingming Festival painted by Zhang Zeduan during the Song dynasty (960–1297), a suanpan is clearly visible beside an account book and doctor's prescriptions on the counter of an apothecary 's (Feibao). The similarity of the Roman abacus to the Chinese one suggests that one could have inspired the other, given evidence of a trade relationship between the Roman Empire and China. However, no direct connection has been demonstrated, and
6660-546: The UK (as in the School of Informatics, University of Edinburgh ). "In the U.S., however, informatics is linked with applied computing, or computing in the context of another domain." A folkloric quotation, often attributed to—but almost certainly not first formulated by— Edsger Dijkstra , states that "computer science is no more about computers than astronomy is about telescopes." The design and deployment of computers and computer systems
6771-465: The abacus began to appear in a 1:5 ratio. The upper deck had one bead and the bottom had five beads. In the late Ming dynasty, the abacus styles appeared in a 2:5 ratio. The upper deck had two beads, and the bottom had five. Various calculation techniques were devised for Suanpan enabling efficient calculations. Some schools teach students how to use it. In the long scroll Along the River During
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#17328581104956882-682: The abacus for the operations of addition and subtraction; however, this primitive device proved difficult to use for more complex calculations". Greek historian Herodotus mentioned the abacus in Ancient Egypt . He wrote that the Egyptians manipulated the pebbles from right to left, opposite in direction to the Greek left-to-right method. Archaeologists have found ancient disks of various sizes that are thought to have been used as counters. However, wall depictions of this instrument are yet to be discovered. At around 600 BC, Persians first began to use
6993-447: The abacus is called soroban ( 算盤, そろばん , lit. "counting tray"). It was imported from China in the 14th century. It was probably in use by the working class a century or more before the ruling class adopted it, as the class structure obstructed such changes. The 1:4 abacus, which removes the seldom-used second and fifth bead, became popular in the 1940s. Today's Japanese abacus is a 1:4 type, four-bead abacus, introduced from China in
7104-489: The abacus is often taught to these students in early grades. Blind students can also complete mathematical assignments using a braille-writer and Nemeth code (a type of braille code for mathematics) but large multiplication and long division problems are tedious. The abacus gives these students a tool to compute mathematical problems that equals the speed and mathematical knowledge required by their sighted peers using pencil and paper. Many blind people find this number machine
7215-399: The abacus was used for more complex operations, i.e. cube roots, Feynman won easily. However, the number chosen at random was close to a number Feynman happened to know was an exact cube, allowing him to use approximate methods. Learning how to calculate with the abacus may improve capacity for mental calculation. Abacus-based mental calculation (AMC), which was derived from the abacus, is
7326-555: The abacus, during the Achaemenid Empire . Under the Parthian , Sassanian , and Iranian empires, scholars concentrated on exchanging knowledge and inventions with the countries around them – India, China, and the Roman Empire – which is how the abacus may have been exported to other countries. The earliest archaeological evidence for the use of the Greek abacus dates to the 5th century BC. Demosthenes (384–322 BC) complained that
7437-516: The accessibility and usability of the system for its intended users. Historical cryptography is the art of writing and deciphering secret messages. Modern cryptography is the scientific study of problems relating to distributed computations that can be attacked. Technologies studied in modern cryptography include symmetric and asymmetric encryption , digital signatures , cryptographic hash functions , key-agreement protocols , blockchain , zero-knowledge proofs , and garbled circuits . A database
7548-507: The act of performing calculations, including addition, subtraction, multiplication, and division, in the mind by manipulating an imagined abacus. It is a high-level cognitive skill that runs calculations with an effective algorithm. People doing long-term AMC training show higher numerical memory capacity and experience more effectively connected neural pathways. They are able to retrieve memory to deal with complex processes. AMC involves both visuospatial and visuomotor processing that generate
7659-433: The application of a fairly broad variety of theoretical computer science fundamentals, in particular logic calculi, formal languages , automata theory , and program semantics , but also type systems and algebraic data types to problems in software and hardware specification and verification. Computer graphics is the study of digital visual contents and involves the synthesis and manipulation of image data. The study
7770-459: The bead frame shown, the gap between the 5th and 6th wire, corresponding to the color change between the 5th and the 6th bead on each wire, suggests the latter use. Teaching multiplication, e.g. 6 times 7, may be represented by shifting 7 beads on 6 wires. The red-and-white abacus is used in contemporary primary schools for a wide range of number-related lessons. The twenty bead version, referred to by its Dutch name rekenrek ("calculating frame"),
7881-410: The binary number system. In 1820, Thomas de Colmar launched the mechanical calculator industry when he invented his simplified arithmometer , the first calculating machine strong enough and reliable enough to be used daily in an office environment. Charles Babbage started the design of the first automatic mechanical calculator , his Difference Engine , in 1822, which eventually gave him the idea of
7992-471: The design and implementation of hardware and software ). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities . Computer graphics and computational geometry address
8103-467: The development of sophisticated computing equipment. Wilhelm Schickard designed and constructed the first working mechanical calculator in 1623. In 1673, Gottfried Leibniz demonstrated a digital mechanical calculator, called the Stepped Reckoner . Leibniz may be considered the first computer scientist and information theorist, because of various reasons, including the fact that he documented
8214-583: The discipline of computer science: theory of computation , algorithms and data structures , programming methodology and languages , and computer elements and architecture . In addition to these four areas, CSAB also identifies fields such as software engineering, artificial intelligence, computer networking and communication, database systems, parallel computation, distributed computation, human–computer interaction, computer graphics, operating systems, and numerical and symbolic computation as being important areas of computer science. Theoretical computer science
8325-424: The distinction more a matter of style than of technical capabilities. Conferences are important events for computer science research. During these conferences, researchers from the public and private sectors present their recent work and meet. Unlike in most other academic fields, in computer science, the prestige of conference papers is greater than that of journal publications. One proposed explanation for this
8436-459: The distinction of three separate paradigms in computer science. Peter Wegner argued that those paradigms are science, technology, and mathematics. Peter Denning 's working group argued that they are theory, abstraction (modeling), and design. Amnon H. Eden described them as the "rationalist paradigm" (which treats computer science as a branch of mathematics, which is prevalent in theoretical computer science, and mainly employs deductive reasoning),
8547-511: The expression "automatic information" (e.g. "informazione automatica" in Italian) or "information and mathematics" are often used, e.g. informatique (French), Informatik (German), informatica (Italian, Dutch), informática (Spanish, Portuguese), informatika ( Slavic languages and Hungarian ) or pliroforiki ( πληροφορική , which means informatics) in Greek . Similar words have also been adopted in
8658-457: The first programmable mechanical calculator , his Analytical Engine . He started developing this machine in 1834, and "in less than two years, he had sketched out many of the salient features of the modern computer". "A crucial step was the adoption of a punched card system derived from the Jacquard loom " making it infinitely programmable. In 1843, during the translation of a French article on
8769-477: The first question, computability theory examines which computational problems are solvable on various theoretical models of computation . The second question is addressed by computational complexity theory , which studies the time and space costs associated with different approaches to solving a multitude of computational problems. The famous P = NP? problem, one of the Millennium Prize Problems ,
8880-519: The form of several yupanas, researchers found that calculations were based using the Fibonacci sequence 1, 1, 2, 3, 5 and powers of 10, 20, and 40 as place values for the different fields in the instrument. Using the Fibonacci sequence would keep the number of grains within any one field at a minimum. The Russian abacus, the schoty ( Russian : счёты , plural from Russian : счёт , counting), usually has
8991-461: The generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of repositories of data. Human–computer interaction investigates the interfaces through which humans and computers interact, and software engineering focuses on the design and principles behind developing software. Areas such as operating systems , networks and embedded systems investigate
9102-502: The machine in operation and analyzing it by all analytical and measurement means available. It has since been argued that computer science can be classified as an empirical science since it makes use of empirical testing to evaluate the correctness of programs , but a problem remains in defining the laws and theorems of computer science (if any exist) and defining the nature of experiments in computer science. Proponents of classifying computer science as an engineering discipline argue that
9213-482: The need to use pebbles for calculations was too difficult. A play by Alexis from the 4th century BC mentions an abacus and pebbles for accounting, and both Diogenes and Polybius use the abacus as a metaphor for human behavior, stating "that men that sometimes stood for more and sometimes for less" like the pebbles on an abacus. The Greek abacus was a table of wood or marble, pre-set with small counters in wood or metal for mathematical calculations. This Greek abacus
9324-478: The principal focus of computer science is studying the properties of computation in general, while the principal focus of software engineering is the design of specific computations to achieve practical goals, making the two separate but complementary disciplines. The academic, political, and funding aspects of computer science tend to depend on whether a department is formed with a mathematical emphasis or with an engineering emphasis. Computer science departments with
9435-615: The principles and design behind complex systems . Computer architecture describes the construction of computer components and computer-operated equipment. Artificial intelligence and machine learning aim to synthesize goal-orientated processes such as problem-solving, decision-making, environmental adaptation, planning and learning found in humans and animals. Within artificial intelligence, computer vision aims to understand and process image and video data, while natural language processing aims to understand and process textual and linguistic data. The fundamental concern of computer science
9546-484: The reliability of computational systems is investigated in the same way as bridges in civil engineering and airplanes in aerospace engineering . They also argue that while empirical sciences observe what presently exists, computer science observes what is possible to exist and while scientists discover laws from observation, no proper laws have been found in computer science and it is instead concerned with creating phenomena. Proponents of classifying computer science as
9657-556: The result (or can be used as the starting number for subsequent operations). In the ancient world, abacuses were a practical calculating tool. Although calculators and computers are commonly used today instead of abacuses, abacuses remain in everyday use in some countries. The abacus has an advantage of not requiring a writing implement and paper (needed for algorism ) or an electric power source . Merchants, traders, and clerks in some parts of Eastern Europe , Russia, China, and Africa use abacuses. The abacus remains in common use as
9768-402: The right. During manipulation, beads are moved to the left. For easy viewing, the middle 2 beads on each wire (the 5th and 6th bead) usually are of a different color from the other eight. Likewise, the left bead of the thousands wire (and the million wire, if present) may have a different color. The Russian abacus was in use in shops and markets throughout the former Soviet Union , and its usage
9879-597: The same time, in order to make the multiplication and division digits consistently use the division multiplication. Later, Japan had a 3:5 abacus called 天三算盤, which is now in the Ize Rongji collection of Shansi Village in Yamagata City. Japan also used a 2:5 type abacus. The four-bead abacus spread, and became common around the world. Improvements to the Japanese abacus arose in various places. In China, an abacus with an aluminium frame and plastic beads has been used. The file
9990-409: The scale of human intelligence. But the automation of evaluative and predictive tasks has been increasingly successful as a substitute for human monitoring and intervention in domains of computer application involving complex real-world data. Computer architecture, or digital computer organization, is the conceptual design and fundamental operational structure of a computer system. It focuses largely on
10101-537: The semicircle at the top of the intersection; the third, sixth and ninth of these lines are marked with a cross where they intersect with the vertical line. Also from this time frame, the Darius Vase was unearthed in 1851. It was covered with pictures, including a "treasurer" holding a wax tablet in one hand while manipulating counters on a table with the other. The normal method of calculation in ancient Rome, as in Greece,
10212-449: The similarity of the abacuses may be coincidental, both ultimately arising from counting with five fingers per hand. Where the Roman model (like most modern Korean and Japanese ) has 4 plus 1 bead per decimal place, the standard suanpan has 5 plus 2. Incidentally, this allows use with a hexadecimal numeral system (or any base up to 18) which may have been used for traditional Chinese measures of weight. (Instead of running on wires as in
10323-399: The tablet's center is a set of 5 parallel lines equally divided by a vertical line, capped with a semicircle at the intersection of the bottom-most horizontal line and the single vertical line. Below these lines is a wide space with a horizontal crack dividing it. Below this crack is another group of eleven parallel lines, again divided into two sections by a line perpendicular to them, but with
10434-559: The term computer came to refer to the machines rather than their human predecessors. As it became clear that computers could be used for more than just mathematical calculations, the field of computer science broadened to study computation in general. In 1945, IBM founded the Watson Scientific Computing Laboratory at Columbia University in New York City . The renovated fraternity house on Manhattan's West Side
10545-743: The term "computer science" appears in a 1959 article in Communications of the ACM , in which Louis Fein argues for the creation of a Graduate School in Computer Sciences analogous to the creation of Harvard Business School in 1921. Louis justifies the name by arguing that, like management science , the subject is applied and interdisciplinary in nature, while having the characteristics typical of an academic discipline. His efforts, and those of others such as numerical analyst George Forsythe , were rewarded: universities went on to create such departments, starting with Purdue in 1962. Despite its name,
10656-561: The term was the Department of Datalogy at the University of Copenhagen, founded in 1969, with Peter Naur being the first professor in datalogy. The term is used mainly in the Scandinavian countries. An alternative term, also proposed by Naur, is data science ; this is now used for a multi-disciplinary field of data analysis, including statistics and databases. In the early days of computing,
10767-443: The two fields in areas such as mathematical logic , category theory , domain theory , and algebra . The relationship between computer science and software engineering is a contentious issue, which is further muddied by disputes over what the term "software engineering" means, and how computer science is defined. David Parnas , taking a cue from the relationship between other engineering and science disciplines, has claimed that
10878-481: The type of information carrier – whether it is electrical, mechanical or biological. This field plays important role in information theory , telecommunications , information engineering and has applications in medical image computing and speech synthesis , among others. What is the lower bound on the complexity of fast Fourier transform algorithms? is one of the unsolved problems in theoretical computer science . Scientific computing (or computational science)
10989-407: The value of the respective beads of the upper rows, it is enough to multiply by 20 (by each row), the value of the corresponding count in the first row. The device featured 13 rows with 7 beads, 91 in total. This was a basic number for this culture. It had a close relation to natural phenomena, the underworld, and the cycles of the heavens. One Nepōhualtzintzin (91) represented the number of days that
11100-468: The visual abacus and move the imaginary beads. Since it only requires that the final position of beads be remembered, it takes less memory and less computation time. The binary abacus is used to explain how computers manipulate numbers. The abacus shows how numbers, letters, and signs can be stored in a binary system on a computer, or via ASCII . The device consists of a series of beads on parallel wires arranged in three separate rows. The beads represent
11211-438: The way by which the central processing unit performs internally and accesses addresses in memory. Computer engineers study computational logic and design of computer hardware, from individual processor components, microcontrollers , personal computers to supercomputers and embedded systems . The term "architecture" in computer literature can be traced to the work of Lyle R. Johnson and Frederick P. Brooks Jr. , members of
11322-440: Was IBM's first laboratory devoted to pure science. The lab is the forerunner of IBM's Research Division, which today operates research facilities around the world. Ultimately, the close relationship between IBM and Columbia University was instrumental in the emergence of a new scientific discipline, with Columbia offering one of the first academic-credit courses in computer science in 1946. Computer science began to be established as
11433-536: Was also in the calculator business to develop his giant programmable calculator, the ASCC/Harvard Mark I , based on Babbage's Analytical Engine, which itself used cards and a central computing unit. When the machine was finished, some hailed it as "Babbage's dream come true". During the 1940s, with the development of new and more powerful computing machines such as the Atanasoff–Berry computer and ENIAC ,
11544-457: Was by moving counters on a smooth table. Originally pebbles ( Latin : calculi ) were used. Marked lines indicated units, fives, tens, etc. as in the Roman numeral system. Writing in the 1st century BC, Horace refers to the wax abacus, a board covered with a thin layer of black wax on which columns and figures were inscribed using a stylus. One example of archaeological evidence of the Roman abacus , shown nearby in reconstruction, dates to
11655-418: Was more easily moved. The earliest known written documentation of the Chinese abacus dates to the 2nd century BC. The Chinese abacus, also known as the suanpan (算盤/算盘, lit. "calculating tray"), comes in various lengths and widths, depending on the operator. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads each in the bottom one, to represent numbers in
11766-499: Was not allowed. The rediscovery of the Nepōhualtzintzin was due to the Mexican engineer David Esparza Hidalgo, who in his travels throughout Mexico found diverse engravings and paintings of this instrument and reconstructed several of them in gold, jade, encrustations of shell, etc. Very old Nepōhualtzintzin are attributed to the Olmec culture, and some bracelets of Mayan origin, as well as
11877-578: Was something new. Poncelet used it, not for any applied purpose, but as a teaching and demonstration aid. The Turks and the Armenian people used abacuses similar to the Russian schoty. It was named a coulba by the Turks and a choreb by the Armenians. Around the world, abacuses have been used in pre-schools and elementary schools as an aid in teaching the numeral system and arithmetic . In Western countries,
11988-499: Was taught in most schools until the 1990s. Even the 1874 invention of mechanical calculator , Odhner arithmometer , had not replaced them in Russia. According to Yakov Perelman , some businessmen attempting to import calculators into the Russian Empire were known to leave in despair after watching a skilled abacus operator. Likewise, the mass production of Felix arithmometers since 1924 did not significantly reduce abacus use in
12099-520: Was taught in the Calmecac to the temalpouhqueh Nahuatl pronunciation: [temaɬˈpoʍkeʔ] , who were students dedicated to taking the accounts of skies, from childhood. The Nepōhualtzintzin was divided into two main parts separated by a bar or intermediate cord. In the left part were four beads. Beads in the first row have unitary values (1, 2, 3, and 4), and on the right side, three beads had values of 5, 10, and 15, respectively. In order to know
12210-687: Was used in Achaemenid Persia, the Etruscan civilization , Ancient Rome, and the Western Christian world until the French Revolution . The Salamis Tablet , found on the Greek island Salamis in 1846 AD, dates to 300 BC, making it the oldest counting board discovered so far. It is a slab of white marble 149 cm (59 in) in length, 75 cm (30 in) wide, and 4.5 cm (2 in) thick, on which are 5 groups of markings. In
12321-477: Was used widely in medieval Europe, and persisted in limited use into the nineteenth century. Wealthy abacists used decorative minted counters, called jetons . Due to Pope Sylvester II 's reintroduction of the abacus with modifications, it became widely used in Europe again during the 11th century It used beads on wires, unlike the traditional Roman counting boards, which meant the abacus could be used much faster and
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