In mathematics and computer science, an algorithm is a finite sequence of well-defined, computer-implementable instructions to solve a class of problems or to perform a computation. Algorithms are always unambiguous and are used as specifications for performing calculations, data processing, automated reasoning, other tasks; as an effective method, an algorithm can be expressed within a finite amount of space and time, in a well-defined formal language for calculating a function. Starting from an initial state and initial input, the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states producing "output" and terminating at a final ending state; the transition from one state to the next is not deterministic. The concept of algorithm has existed since antiquity. Arithmetic algorithms, such as a division algorithm, was used by ancient Babylonian mathematicians c. 2500 BC and Egyptian mathematicians c. 1550 BC. Greek mathematicians used algorithms in the sieve of Eratosthenes for finding prime numbers, the Euclidean algorithm for finding the greatest common divisor of two numbers.

Arabic mathematicians such as Al-Kindi in the 9th century used cryptographic algorithms for code-breaking, based on frequency analysis. The word algorithm itself is derived from the 9th-century Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī, Latinized Algoritmi. A partial formalization of what would become the modern concept of algorithm began with attempts to solve the Entscheidungsproblem posed by David Hilbert in 1928. Formalizations were framed as attempts to define "effective calculability" or "effective method"; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's Formulation 1 of 1936, Alan Turing's Turing machines of 1936–37 and 1939. The word'algorithm' has its roots in Latinizing the name of Persian mathematician Muhammad ibn Musa al-Khwarizmi in the first steps to algorismus. Al-Khwārizmī was a Persian mathematician, astronomer and scholar in the House of Wisdom in Baghdad, whose name means'the native of Khwarazm', a region, part of Greater Iran and is now in Uzbekistan.

About 825, al-Khwarizmi wrote an Arabic language treatise on the Hindu–Arabic numeral system, translated into Latin during the 12th century under the title Algoritmi de numero Indorum. This title means "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name. Al-Khwarizmi was the most read mathematician in Europe in the late Middle Ages through another of his books, the Algebra. In late medieval Latin, English'algorism', the corruption of his name meant the "decimal number system". In the 15th century, under the influence of the Greek word ἀριθμός'number', the Latin word was altered to algorithmus, the corresponding English term'algorithm' is first attested in the 17th century. In English, it was first used in about 1230 and by Chaucer in 1391. English adopted the French term, but it wasn't until the late 19th century that "algorithm" took on the meaning that it has in modern English. Another early use of the word is from 1240, in a manual titled Carmen de Algorismo composed by Alexandre de Villedieu.

It begins with: Haec algorismus ars praesens dicitur, in qua / Talibus Indorum fruimur bis quinque figuris. Which translates to: Algorism is the art by which at present we use those Indian figures, which number two times five; the poem is a few hundred lines long and summarizes the art of calculating with the new style of Indian dice, or Talibus Indorum, or Hindu numerals. An informal definition could be "a set of rules that defines a sequence of operations", which would include all computer programs, including programs that do not perform numeric calculations, any prescribed bureaucratic procedure. In general, a program is only an algorithm. A prototypical example of an algorithm is the Euclidean algorithm, used to determine the maximum common divisor of two integers. Boolos, Jeffrey & 1974, 1999 offer an informal meaning of the word "algorithm" in the following quotation: No human being can write fast enough, or long enough, or small enough† to list all members of an enumerably infinite set by writing out their names, one after another, in some notation.

But humans can do something useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human, capable of carrying out only elementary operations on symbols. An "enumerably infinite set" is one whose elements can be put into one-to-one correspondence with the integers, thus and Jeffrey are saying that an algorithm implies instructions for a process that "creates" output integers from an arbitrary "input" integer or integers that, in theory, can be arbitrarily large. For example, an algorithm can be an algebraic equation such as y = m + n, but various authors' attempts to define the notion indicate that the word imp

Samuel Alexander Muggleton is an English professional footballer who plays as a defender or midfielder. He was last contracted to Chesterfield. Muggleton was born in Melton Mowbray, Leicestershire and is the son of former footballer Carl Muggleton, he played for his local team Syston before joining Leicester City. He played for Leicester for several seasons at various youth levels before being released, being told he was too short. After this, he joined Holwell Sports, where he played for the first team in the East Midlands Counties League. Aged 16, he signed a two-year scholarship with Gillingham in November 2012, he made his first-team debut for Gillingham on the final day of the 2012–13 season, starting in a 3–2 away defeat to Burton Albion, as they were crowned champions of League Two. Muggleton joined Conference Premier club Barnet on 27 March 2014 on loan until the end of 2013–14. After making six appearances, he returned to Gillingham, he was released by Gillingham at the end of 2013–14, signing for Barnet permanently on 16 May 2014.

On 17 January 2017, Muggleton signed for National League club Eastleigh for an undisclosed fee with Luke Coulson moving to Barnet in the opposite direction. On 20 March 2017, Muggleton signed for Eastleigh's National League rivals York City on a contract until the end of 2016–17, he joined. He made his debut the same day, starting in Boston's 2–1 away defeat to Curzon Ashton. Muggleton returned to York. On 9 February 2018, he joined Northern Premier League Division One North club Scarborough Athletic on loan for the rest of the 2017–18 season, he made eight appearances. He was released at the end of the season. Muggleton signed for newly relegated National League club Chesterfield on 31 July 2018 on a one-year contract with the option of a further year, he joined National League North club Darlington on 8 February 2019 on a one-month loan. During his second appearance, he collided with an opponent and suffered a broken femur and three ruptured ligaments and a torn tendon in his left knee. Muggleton was released by Chesterfield at the end of the season.

Muggleton possesses a long throw-in. As of match played 16 February 2019 Barnet Conference Premier: 2014–15 Profile at the Chesterfield F. C. website Sam Muggleton at Soccerbase

Birjand is the capital of the Iranian province of South Khorasan. The city is known for its saffron, barberry and handmade carpet exports. Birjand had a population of 187,020 in 2013. Birjand is a major center of commerce in eastern Iran; the first citation of the city in the historical literature belongs to the famous book Mojem Alboldan, by Yaqut Homavi which introduces the Birjand as the most beautiful town in the Qohestan. Before this, Birjand had been not as big and important as a municipality but rather as a rural community. However, the Birjand geographical area had its historical and political importance long before the emergence of the city of Birjand. Many citations of the region are available in the original literature like Ehya -ol- Molook of the once important localities in the area. Apart from literature, the oldest evidence on the history of the region is the ancient Lakh-Mazar inscription in the Kooch village some 25 km south east of Birjand. Numerous fine drawings and inscriptions are carved on an igneous rock surface.

The inscriptions include pictograms as well as Arsacid Pahlavi, Sasanian Pahlavi and Persian scripts. The former tribe famous for the region of Birjand is called Sagarthian – in union with the Parthian. Birjand has emerged as the centre of Qohestan, following the decline of historical city of Qaen in the Safavid period. Since the Alam clan had ruled the region till the end of Qajar dynasty. During the semi-autonomous ruling of Alam clan, Great Britain and Russia established consular branches in Birjand, because of the important geographical location of the region in the vicinity of the Indian subcontinent. Amir Shokat Ul-Molk Alam, the father of the Asadollah Alam was still ruling the Qohestan's subprovince Qhaenat into the Pahlavi era, and the last tribal leader of Birjand Shah Seyyed Ali Kazemi was related with the Alam clan and the emperor Reza Shah Pahlavi. However Birjand lost its geopolitical importance following the emergence of Reza Shah Pahlavi and his policy of central government; the entire Qohestan region became a part of the modern Khorasan province.

The local people, started a movement to become an independent province at the middle of the second Pahlavi period. The move resulted after about forty years and Quhestan and Birjand regained their historical importance in 2004, after the official division of Khorasan to three smaller provinces by the Iranian government. Birjand has a cold desert climate with hot summers and cool winters and a significant difference between day and night temperatures. Precipitation falls in winter and spring, it is said that the Shokatiyeh School in Birjand together with Darolfonoon in Tehran were the first modern public schools of higher education in Iran in the mid-19th century. Since Birjand has amassed an abundance of institutions of higher education and become an important location for research and development; the city contains such universities and academic institutions as: University of Birjand Birjand University of Technology Birjand University of Medical Sciences Payame Noor University Islamic Azad University of Birjand University of Applied Science and Technology Academy of Tarbiat-e Moalem Academy of Amuzesh-e Aly Academy of Amuzesh-e Modiriat Dolaty Birjand Airport is located in a suburban region of Birjand.

Due to the geopolitical eminence of Birjand in the eastern parts of Iran, Birjand Airport began operating in 1933 as the 3rd airport in Iran. Birjand Airport offers non-stop daily flights to Mashhad, it became an international airport after the first international flight to Medina, Saudi Arabia in June 2008. In October 2009, runway 10/28 was closed for fundamental repair; the runway was strengthened, re-carpeted and extended to 4000 meters to accommodate wide-body aircraft. During the construction phase all flights were suspended while Aseman Airline utilized the older runway and began offering daily flights to Tehran. Abd al-Ali al-Birjandi, 16th century astronomer Hakim Nezari Quhestani Ibn Hessam Khusfi Amir Shokat Ul-Molk Alam, Amir of Qaen County and Governor of Quhestan at the end of Qajar Dynasty Amir Ali Khan Sheibany, PhD, founder and first CEO of Zob Ahan Esfahan Seyyed Mohammad Tadayyon Asadollah Alam, prime minister of Iran during Pahlavi dynasty Seyyed Gholam Reza Saeidi, writer Mohamad Haghgou, composer Sima Bina, Iranian folk music singer Ahmad Kamyabi Mask and renowned theater scholar Morteza Hassanpour, first Iranian male nurse Mohammad Hassan Ganji, geographer Mohammad Ismail Rezvani, historian Mohammad Reza Hafeznia Gholam Hossein Shokouei Kazem Motamadnejad Shah Seyyed Ali Kazemi, Last tribal leader in Moud and Birjand at the beginning of Pahlavi Dynasty Mohammad Hossain Ayati Mohammad Ibrahim Ayati Seyyed Hassan Tahami Ardalan Shoja Kaveh, actor Furg citadel Khorashad Mahmuei Mud All About Birjand