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Qaiser Mushtaq
Qaiser Mushtaq (born 28 February 1954), ( D.Phil.(Oxon), ASA, KIA), is a Pakistani mathematician and academic who has made numerous contributions in the field of Group theory and Semigroup. He has been vice-chancellor of The Islamia University Bahawalpur from December 2014 to December 2018. Mushtaq is one of the leading mathematicians and educationists in Pakistan. Through his research and writings, he has exercised a profound influence on mathematics in Pakistan. Mushtaq is an honorary full professor at the Mathematics Division of the Institute for Basic Research, Florida, US. His research contributions in the fields of group theory and LA-semigroup theory have won him recognition at both national and international levels. In Graham Higman's words, "''he has laid the foundation of coset diagrams for the modular group''", to study the actions of groups on various spaces and projective lines over Galois fields. This work has been cited in the Encyclopedia of Design Theory. Bio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sheikhupura
Sheikhupura ( pa, ; ur, ) also known as Qila Sheikhupura, is a city in the Pakistani province of Punjab, Pakistan, Punjab. Founded by the Mughal Empire, Mughal Emperor Jahangir, Jehangir in 1607, Sheikhupura is the List of most populous cities in Pakistan, 16th largest city of Pakistan by population and is the headquarters of Sheikhupura District. The city is an industrial center, and satellite town, located about 38 km northwest of Lahore. It is also connected to District Kasur. The old name of Sheikhupura was “Virkgarh” due to large number of Virk jatts, Jats settled in the area. The Virks are still strong in this area both politically and economically. There are around 132 villages in this area which belong to the Virks. Etymology The region around Sheikhupura was previous known as ''Virk Garh, or'' "''Virk'' Fort", in reference to the Jat people, Jat tribe that inhabited the area. The city, founded in 1607, was named by Mughal Empire, Mughal Emperor Jahangir, J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Khwarizmi
Muḥammad ibn Mūsā al-Khwārizmī ( ar, محمد بن موسى الخوارزمي, Muḥammad ibn Musā al-Khwārazmi; ), or al-Khwarizmi, was a Persian polymath from Khwarazm, who produced vastly influential works in mathematics, astronomy, and geography. Around 820 CE, he was appointed as the astronomer and head of the library of the House of Wisdom in Baghdad.Maher, P. (1998), "From Al-Jabr to Algebra", ''Mathematics in School'', 27(4), 14–15. Al-Khwarizmi's popularizing treatise on algebra (''The Compendious Book on Calculation by Completion and Balancing'', c. 813–833 CEOaks, J. (2009), "Polynomials and Equations in Arabic Algebra", ''Archive for History of Exact Sciences'', 63(2), 169–203.) presented the first systematic solution of linear and quadratic equations. One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square, for which he provided geometric justifications. Because he was the firs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convent Of Jesus And Mary, Sialkot
The Convent of Jesus and Mary, Sialkot was the first Catholic school in the Punjab and second in British India after Agra. It was established in 1856 by five nuns headed by Mother St. Gonzaga Bergonhoux and was opened at the request of the Archbishop of Agra. It is one of the oldest mission school in Punjab Punjab (; Punjabi: پنجاب ; ਪੰਜਾਬ ; ; also romanised as ''Panjāb'' or ''Panj-Āb'') is a geopolitical, cultural, and historical region in South Asia, specifically in the northern part of the Indian subcontinent, comprising .... Its educational system, characterized by a blend of intellectual depth and polished structure, contributed significantly to the broader cultural shifts in the region. The school is located at 128 Haider Road, Sialkot Cantt 51300. History The first Catholic school in Punjab was the Convent of Jesus and Mary, Sialkot, which was opened at the request of the Archbishop of Agra, His Lordship, Msgr. Michael Angelo Jacobi. Msgr. Jacob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolfson College, Oxford
Wolfson College () is a constituent college of the University of Oxford in England. Located in north Oxford along the River Cherwell, Wolfson is an all-graduate college with around sixty governing body fellows, in addition to both research and junior research fellows. It caters to a wide range of subjects, from the humanities to the social and natural sciences. Like the majority of Oxford's newer colleges, it has been coeducational since its foundation in 1965. The liberal philosopher Sir Isaiah Berlin was the college's first president, and was instrumental not only in its founding, but establishing its tradition of academic excellence and egalitarianism. The college houses ''The Isaiah Berlin Literary Trust'' and hosts an annual ''Isaiah Berlin Lecture''. From 2017, the president of the college has been Sir Tim Hitchens. As of 2021, the college had a financial endowment of £60.3 million. The college is registered as a charity. History Wolfson's first president Sir Is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National University Of Singapore
The National University of Singapore (NUS) is a national public research university in Singapore. Founded in 1905 as the Straits Settlements and Federated Malay States Government Medical School, NUS is the oldest autonomous university in the country. It offers degree programmes in a wide range of disciplines at both the undergraduate and postgraduate levels, including in the sciences, medicine and dentistry, design and environment, law, arts and social sciences, engineering, business, computing, and music. NUS is one of the most highly-ranked academic institutions in the world. It has consistently featured in the top 30 of the Quacquarelli Symonds (QS) World University Rankings and the Times Higher Education (THE) World University Rankings, and in the top 100 of the Academic Ranking of World Universities (ARWU). As of 2022-2023, NUS is 11th worldwide according to QS and 19th worldwide according to THE. NUS's main campus is located in the southwestern part of Singapore, adja ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gujranwala
Gujranwala ( ur, , label=none; ) is a city and capital of Gujranwala Division located in Pakistan. It is also known as "City of Wrestlers" and is quite famous for its food. It is the 5th most populous city proper after Karachi, Lahore, Faisalabad and Rawalpindi respectively. Founded in the 18th century, Gujranwala is a relatively modern town compared to the many nearby millennia-old cities of northern Punjab. The city served as the capital of the Sukerchakia Misl state between 1763 and 1799, and is the birthplace of the founder of the Sikh Empire, Maharaja Ranjit Singh. Gujranwala is now Pakistan's third largest industrial centre after Karachi and Faisalabad, and contributes 5% to 9% of Pakistan's national GDP. The city is part of a network of large urban centres in north-east Punjab province that forms one of Pakistan's mostly highly industrialized regions. Along with the nearby cities of Sialkot and Gujrat, Gujranwala forms part of the so-called "Golden Triangle" of industri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galois Fields
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are given by the integers mod when is a prime number. The ''order'' of a finite field is its number of elements, which is either a prime number or a prime power. For every prime number and every positive integer there are fields of order p^k, all of which are isomorphic. Finite fields are fundamental in a number of areas of mathematics and computer science, including number theory, algebraic geometry, Galois theory, finite geometry, cryptography and coding theory. Properties A finite field is a finite set which is a field; this means that multiplication, addition, subtraction and division (excluding division by zero) are def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Group
In mathematics, the modular group is the projective special linear group of matrices with integer coefficients and determinant 1. The matrices and are identified. The modular group acts on the upper-half of the complex plane by fractional linear transformations, and the name "modular group" comes from the relation to moduli spaces and not from modular arithmetic. Definition The modular group is the group of linear fractional transformations of the upper half of the complex plane, which have the form :z\mapsto\frac, where , , , are integers, and . The group operation is function composition. This group of transformations is isomorphic to the projective special linear group , which is the quotient of the 2-dimensional special linear group over the integers by its center . In other words, consists of all matrices :\begin a & b \\ c & d \end where , , , are integers, , and pairs of matrices and are considered to be identical. The group operation is the usual mult ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field (mathematics), fields, and vector spaces, can all be seen as groups endowed with additional operation (mathematics), operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, and Standard Model, three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pakistan
Pakistan ( ur, ), officially the Islamic Republic of Pakistan ( ur, , label=none), is a country in South Asia. It is the world's List of countries and dependencies by population, fifth-most populous country, with a population of almost 243 million people, and has the world's Islam by country#Countries, second-largest Muslim population just behind Indonesia. Pakistan is the List of countries and dependencies by area, 33rd-largest country in the world by area and 2nd largest in South Asia, spanning . It has a coastline along the Arabian Sea and Gulf of Oman in the south, and is bordered by India to India–Pakistan border, the east, Afghanistan to Durand Line, the west, Iran to Iran–Pakistan border, the southwest, and China to China–Pakistan border, the northeast. It is separated narrowly from Tajikistan by Afghanistan's Wakhan Corridor in the north, and also shares a maritime border with Oman. Islamabad is the nation's capital, while Karachi is its largest city and fina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematicians
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. The binary operation of a semigroup is most often denoted multiplicatively: ''x''·''y'', or simply ''xy'', denotes the result of applying the semigroup operation to the ordered pair . Associativity is formally expressed as that for all ''x'', ''y'' and ''z'' in the semigroup. Semigroups may be considered a special case of magmas, where the operation is associative, or as a generalization of groups, without requiring the existence of an identity element or inverses. The closure axiom is implied by the definition of a binary operation on a set. Some authors thus omit it and specify three axioms for a group and only one axiom (associativity) for a semigroup. As in the case of groups or magmas, the semigroup operation need not be commutative, so ''x''·''y'' is not necessarily equal to ''y''·''x''; a well-known example of an operation that is as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
