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Algorithm
In mathematics and computer science, an algorithm (/ˈælɡərɪðəm/ ( listen) AL-gə-ridh-əm) is an unambiguous specification of how to solve a class of problems. Algorithms can perform calculation, data processing and automated reasoning tasks. An algorithm is an effective method that can be expressed within a finite amount of space and time[1] and in a well-defined formal language[2] for calculating a function.[3] Starting from an initial state and initial input (perhaps empty),[4] the instructions describe a computation that, when executed, proceeds through a finite[5] number of well-defined successive states, eventually producing "output"[6] and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.[7] The concept of algorithm has existed for centuries and the use of the concept can be ascribed to Greek mathematicians, e.g
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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). Logical systems such as propositional logic are decidable if membership in their set of logically valid formulas (or theorems) can be effectively determined. A theory (set of sentences closed under logical consequence) in a fixed logical system is decidable if there is an effective method for determining whether arbitrary formulas are included in the theory
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Baghdad
Baghdad
Baghdad
(/ˈbæɡdæd, bəɡˈdæd/; Arabic: بغداد‎ [baɣˈdaːd] ( listen)) is the capital of Iraq. The population of Baghdad, as of 2016[update], is approximately 8,765,000,[citation needed][note 1] making it the largest city in Iraq, the second largest city in the Arab world
Arab world
(after Cairo, Egypt), and the second largest city in Western Asia
Western Asia
(after Tehran, Iran). Located along the Tigris
Tigris
River, the city was founded in the 8th century and became the capital of the Abbasid Caliphate
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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. It is a universal model of computation that can be used to simulate any Turing machine. It was first introduced by mathematician Alonzo Church in the 1930s as part of his research of the foundations of mathematics. Lambda calculus consists of constructing lambda terms and performing reduction operations on them. In the simplest form of lambda calculus, terms are built using only the following rules:Syntax Name Descriptionx Variable A character or string representing a parameter or mathematical/logical value(λx.M) Abstraction Function definition (M is a lambda term). The variable x becomes bound in the expression.(M N) Application Applying a function to an argument
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Emil Post
Emil Leon Post
Emil Leon Post
(February 11, 1897 – April 21, 1954) was an American mathematician and logician. He is best known for his work in the field that eventually became known as computability theory.Contents1 Life 2 Early work 3 Recursion theory 4 Polyadic groups 5 Selected papers 6 See also 7 Notes 8 References 9 Further reading 10 External linksLife[edit] Post was born in Augustów, Suwałki Governorate, Russian Empire
Russian Empire
(now Poland) into a Polish-Jewish family that immigrated to New York City in May 1904. His parents were Arnold and Pearl Post.[2] Post had been interested in astronomy, but at the age of twelve lost his left arm in a car accident. This loss was a significant obstacle to being a professional astronomer
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Persian Language
Persian (/ˈpɜːrʒən/ or /ˈpɜːrʃən/), also known by its endonym Farsi[8][9] (فارسی fārsi [fɒːɾˈsiː] ( listen)), is one of the Western Iranian languages within the Indo-Iranian branch of the Indo-European language family. It is primarily spoken in Iran, Afghanistan
Afghanistan
(officially known as Dari since 1958),[10] and Tajikistan
Tajikistan
(officially known as Tajiki since the Soviet era),[11] and some other regions which historically were Persianate societies and considered part of Greater Iran
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Persian People
The Persians are an Iranian ethnic group that make up over half the population of Iran.[3][2] They share a common cultural system and are native speakers of the Persian language,[4][5][6] as well as closely related languages.[7][8] The ancient Persians were a nomadic branch of the ancient Iranian population that entered modern-day Iran
Iran
by the early 10th century BC.[9][10] Together with their compatriot allies, they established and ruled some of the world's most powerful empires,[11][12] well-recognized for their massive cultural, political, and social influence covering much of the territory and population of the anc
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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. They look at stars, planets, moons, comets and galaxies, as well as many other celestial objects — either in observational astronomy, in analyzing the data, or in theoretical astronomy. Examples of topics or fields astronomers work on include: planetary science, solar astronomy, the origin or evolution of stars, or the formation of galaxies. There are also related but distinct subjects like physical cosmology which studies the Universe
Universe
as a whole. Astronomers usually fit into two types: observational and theoretical. Observational astronomers make direct observations of planets, stars and galaxies, and analyze the data. In contrast, theoretical astronomers create and investigate models of things that cannot be observed
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Geographer
A geographer is a scholar whose area of study is geography, the study of Earth's natural environment and human society. Although geographers are historically known as people who make maps, map making is actually the field of study of cartography, a subset of geography. Geographers do not study only the details of the natural environment or human society, but they also study the reciprocal relationship between these two. For example, they study how the natural environment contributes to the human society and how the human society affects the natural environment. In particular, physical geographers study the natural environment while human geographers study human society
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House Of Wisdom
The House of Wisdom
House of Wisdom
(Arabic: بيت الحكمة‎; Bayt al-Hikma) was a major intellectual center during the Islamic Golden Age. The House of Wisdom
House of Wisdom
was founded as a library for private use by the Abbasid
Abbasid
Caliph
Caliph
Harun al-Rashid
Harun al-Rashid
(reigned 786–809)[1][2] and culminated in prominence under his son al-Ma'mun (reigned 813–833) who is credited with its formal institution. Al-Ma'mun
Al-Ma'mun
is also credited with bringing many well-known scholars to share information, ideas, and culture in the House of Wisdom. The library was based in Baghdad, and from the 9th to 13th centuries Muslim
Muslim
scholars, as well as people of Jewish or Christian
Christian
background[3] were allowed to study there
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Greater Iran
Greater Iran
Iran
(Persian: ایران بزرگ‎, Irān-e Bozorg), also referred to as Greater Persia[2][3][4] (سرزمین پارس, Sarzamin-e Pārs), is a term used to refer to the regions of the Caucasus, West Asia, Central Asia, and parts of South Asia
South Asia
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Jacques Herbrand
Jacques Herbrand (12 February 1908 – 27 July 1931) was a French mathematician. Although he died at age 23, he was already considered one of "the greatest mathematicians of the younger generation" by his professors Helmut Hasse, and Richard Courant.[1] He worked in mathematical logic and class field theory. He introduced recursive functions. Herbrand's theorem refers to either of two completely different theorems. One is a result from his doctoral thesis in proof theory, and the other one half of the Herbrand–Ribet theorem. The Herbrand quotient is a type of Euler characteristic, used in homological algebra. He contributed to Hilbert's program in the foundations of mathematics by providing a constructive consistency proof for a weak system of arithmetic
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Uzbekistan
Coordinates: 42°N 63°E / 42°N 63°E / 42; 63 Republic
Republic
of Uzbekistan O'zbekiston Respublikasi  (Uzbek)FlagState emblem[1]Anthem:  Oʻzbekiston Respublikasining Davlat Madhiyasi State Anthem of the Republic
Republic
of Uzbeki
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Arabic Language
Arabic
Arabic
(Arabic: العَرَبِيَّة‎) al-ʻarabiyyah [ʔalʕaraˈbijːah] ( listen) or (Arabic: عَرَبِيّ‎) ʻarabī [ˈʕarabiː] ( listen) or [ʕaraˈbij]) is a Central Semitic language that first emerged in Iron Age northwestern Arabia and is now the lingua franca of the Arab world.[4] It is named after the Arabs, a term initially used to describe peoples living from Mesopotamia
Mesopotamia
in the east to the Anti- Lebanon
Lebanon
mountains in the west, in northwestern Arabia, and in the Sinai peninsula. Arabic
Arabic
is classified as a macrolanguage comprising 30 modern varieties, including its standard form (Modern Standard Arabic) [5]. The modern written language (Modern Standard Arabic) is derived from Classical Arabic
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Hindu–Arabic Numeral System
The Hindu– Arabic
Arabic
numeral system[1] (also called the Arabic
Arabic
numeral system or Hindu
Hindu
numeral system)[2][note 1] is a positional decimal numeral system that is the most common system for the symbolic representation of numbers in the world. It was an ancient Indian numeral system which was re-introduced in the book On the Calculation with Hindu
Hindu
Numerals written by the medieval-era Iranian mathematician and engineer al-Khwarizmi, whose name was latinized as Algoritmi.[note 2][3] The system later spread to medieval Europe
Europe
by the High Middle Ages. The system is based upon ten (originally nine) different glyphs. The symbols (glyphs) used to represent the system are in principle independent of the system itself
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Latin
Latin
Latin
(Latin: lingua latīna, IPA: [ˈlɪŋɡʷa laˈtiːna]) is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet
Latin alphabet
is derived from the Etruscan and Greek alphabets, and ultimately from the Phoenician alphabet. Latin
Latin
was originally spoken in Latium, in the Italian Peninsula.[3] Through the power of the Roman Republic, it became the dominant language, initially in Italy and subsequently throughout the Roman Empire. Vulgar Latin
Vulgar Latin
developed into the Romance languages, such as Italian, Portuguese, Spanish, French, and Romanian. Latin, Greek and French have contributed many words to the English language
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