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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 and in a well-defined formal language for calculating a function . Starting from an initial state and initial input (perhaps empty ), the instructions describe a computation that, when executed , proceeds through a finite number of well-defined successive states, eventually producing "output" 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
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Alexander Of Villedieu
ALEXANDER OF VILLEDIEU was a French author , teacher and poet , who wrote text books on Latin grammar
Latin grammar
and arithmetic , everything in verse. He was born around 1175 in Villedieu-les-Poêles in Normandy
Normandy
, studied in Paris
Paris
, and later taught at Dol in Brittany
Brittany
. His greatest fame stems from his versified Latin grammar
Latin grammar
book, the Doctrinale Puerorum. He died in 1240, or perhaps in 1250. He was a Franciscan
Franciscan
and a Master of the University of Paris
Paris
. His Doctrinale puerorum, a versified grammar , soon became a classic. It was composed around 1200, and was all written in leonine hexameters . Even after several centuries, with the advent of printing, it appeared in countless editions in Italy, Germany and France
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Geoffrey Chaucer
GEOFFREY CHAUCER (/ˈtʃɔːsər/ ; c. 1343 – 25 October 1400), known as the Father of English literature
English literature
, is widely considered the greatest English poet of the Middle Ages
Middle Ages
. He was the first poet to be buried in Poets\' Corner of Westminster Abbey . While he achieved fame during his lifetime as an author, philosopher, and astronomer , composing a scientific treatise on the astrolabe for his ten-year-old son Lewis, Chaucer also maintained an active career in the civil service as a bureaucrat, courtier and diplomat. Among his many works are The Book of the Duchess , The House of Fame , The Legend of Good Women and Troilus and Criseyde . He is best known today for The Canterbury Tales
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Latin
LATIN (Latin: lingua latīna, IPA: ) is a classical language belonging to the Italic branch of the Indo-European languages . The Latin alphabet is derived from the Etruscan and Greek alphabets , and ultimately from the Phoenician alphabet
Phoenician alphabet
. Latin
Latin
was originally spoken in Latium
Latium
, in the Italian Peninsula
Italian Peninsula
. Through the power of the Roman Republic , it became the dominant language, initially in Italy and subsequently throughout the Roman Empire . Vulgar Latin developed into the Romance languages
Romance languages
, such as Italian , Portuguese , Spanish , French , and Romanian . Latin
Latin
, Italian and French have contributed many words to the English language
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Emil 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 . CONTENTS * 1 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 links LIFEPost was born in Augustów
Augustów
, Suwałki Governorate
Suwałki Governorate
, Russian Empire (now Poland
Poland
) into a Polish-Jewish family that immigrated to New York City in May 1904. His parents were Arnold and Pearl Post. 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. He decided to pursue mathematics, rather than astronomy
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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 single-taped Turing machine and 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 DESCRIPTION a 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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Al-Jabr
THE COMPENDIOUS BOOK ON CALCULATION BY COMPLETION AND BALANCING (Arabic : الكتاب المختصر في حساب الجبر والمقابلة‎, Al-kitāb al-mukhtaṣar fī ḥisāb al-ğabr wa’l-muqābala; Latin : 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
Baghdad
. Translated into Latin by Robert of Chester in 1145, it introduced the term "algebra " (الجبر, al-jabr) to European languages. The Compendious Book provided an exhaustive account of solving for the positive roots of polynomial equations up to the second degree
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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. Many important problems are undecidable , that is, it has been proven that no effective method for determining membership (returning a correct answer after finite, though possibly very long, time in all cases) can exist for them
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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 . He is best known for the lambda calculus , Church–Turing thesis , proving the undecidability of the Entscheidungsproblem , Frege–Church ontology , and the Church–Rosser theorem . CONTENTS * 1 Life * 2 Mathematical work * 3 Students * 4 Books * 5 See also * 6 Notes * 7 References * 8 External links LIFE Alonzo Church
Alonzo Church
was born on June 14, 1903, in Washington, D.C.
Washington, D.C.
, where his father, Samuel Robbins Church, was the judge of the Municipal Court for the District of Columbia. The family later moved to Virginia after his father lost this position because of failing eyesight
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Greek Language
GREEK ( Modern Greek : ελληνικά , elliniká, "Greek", ελληνική γλώσσα ( listen ), ellinikí glóssa, "Greek language") is an independent branch of the Indo-European family of languages, native to Greece
Greece
and other parts of the Eastern Mediterranean . It has the longest documented history of any living Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the major part of its history; other systems, such as Linear B
Linear B
and the Cypriot syllabary , were used previously. The alphabet arose from the Phoenician script and was in turn the basis of the Latin
Latin
, Cyrillic
Cyrillic
, Armenian , Coptic , Gothic and many other writing systems
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Persian Language
PERSIAN (/ˈpɜːrʒən/ or /ˈpɜːrʃən/ ), also known by its endonym FARSI (فارسی fārsi ( 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
Iran
, Afghanistan (officially known as DARI since 1958), and Tajikistan (officially known as TAJIKI since the Soviet era), and some other regions which historically were Persianate societies and considered part of Greater Iran
Iran
. It is written in the Persian alphabet , a modified variant of the Arabic script . The Persian language
Persian language
is classified as a continuation of Middle Persian , the official religious and literary language of the Sasanian Empire , itself a continuation of Old Persian , the language of the Achaemenid Empire
Achaemenid Empire

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Baghdad
BAGHDAD ( Arabic
Arabic
: بغداد‎‎, ( listen )) is the capital of Iraq
Iraq
. The population of Baghdad, as of 2016 , is approximately 8,765,000, making it the largest city in Iraq, the second largest city in the Arab world (after Cairo
Cairo
, Egypt
Egypt
), and the second largest city in Western Asia (after Tehran
Tehran
, Iran
Iran
). Located along the Tigris
Tigris
River , the city was founded in the 8th century and became the capital of the Abbasid Caliphate
Abbasid Caliphate

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Greater Iran
GREATER IRAN (Persian : ایران بزرگ‎‎, Irān-e Bozorg), also referred to as GREATER PERSIA (سرزمین پارس, Sarzamin-e Pārs), is a term used to refer to the regions of the Caucasus
Caucasus
, West Asia , Central Asia
Central Asia

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Uzbekistan
Coordinates : 41°N 69°E / 41°N 69°E / 41; 69 Republic
Republic
of Uzbekistan Oʻzbekiston Respublikasi (Uzbek ) Республика Узбекистан (Russian ) Flag State emblem ANTHEM: Oʻzbekiston Respublikasining Davlat Madhiyasi State Anthem of the Republic
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House Of Wisdom
The HOUSE OF WISDOM ( Arabic
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 Caliph
Caliph
Harun al-Rashid
Harun al-Rashid
(reigned 786 – 809) 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. Based in Baghdad
Baghdad
from the 9th to 13th centuries, beside Muslim
Muslim
scholars, people of Jewish or Christian background were allowed to study here
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Geographer
A GEOGRAPHER is a scholar whose area of study is geography , the study of Earth
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. Modern geographers are the primary practitioners of the GIS (geographic information system ), who are often employed by local, state, and federal government agencies as well as in the private sector by environmental and engineering firms
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