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University of London
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The University of London is a collegiate research university located in London, England, consisting of 18 constituent colleges, nine research institutes and a number of central bodies. The university moved to a structure in 1900. The specialist colleges of the university include the London Business School, Imperial College London was formerly a member before leaving the university in 2007. City is the most recent constituent college, having joined on 1 September 2016, in post-nominals, the University of London is commonly abbreviated as Lond. or, more rarely, Londin. From the Latin Universitas Londiniensis, after its degree abbreviations, University College London was founded under the name London University in 1826 as a secular alternative to the religious universities of Oxford and Cambridge. In response to the controversy surrounding such educational establishment, Kings College London was founded and was the first to be granted a royal charter. Yet to receive a charter, UCL in 1834 renewed its application for a royal charter as a university. In response to this, opposition to exclusive rights grew among the London medical schools, the idea of a general degree awarding body for the schools was discussed in the medical press. And in evidence taken by the Select Committee on Medical Education, in 1835, the government announced the response to UCLs petition for a charter. Following the issuing of its charter on 28 November 1836, the university started drawing up regulations for degrees in March 1837. The death of William IV in June, however, resulted in a problem – the charter had been granted during our Royal will and pleasure, queen Victoria issued a second charter on 5 December 1837, reincorporating the university. The university awarded its first degrees in 1839, all to students from UCL, the university established by the charters of 1836 and 1837 was essentially an examining board with the right to award degrees in arts, laws and medicine. However, the university did not have the authority to grant degrees in theology, in medicine, the university was given the right to determine which medical schools provided sufficient medical training. Beyond the right to students for examination, there was no other connection between the affiliated colleges and the university. In 1849 the university held its first graduation ceremony at Somerset House following a petition to the senate from the graduates, about 250 students graduated at this ceremony. The London academic robes of this period were distinguished by their rich velvet facings, the list of affiliated colleges grew by 1858 to include over 50 institutions, including all other British universities. In that year, a new charter effectively abolished the affiliated colleges system by opening up the examinations to everyone whether they attended a college or not. The expanded role meant the university needed more space, particularly with the number of students at the provincial university colleges

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Analytic number theory
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In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlets 1837 introduction of Dirichlet L-functions to give the first proof of Dirichlets theorem on arithmetic progressions and it is well known for its results on prime numbers and additive number theory. Analytic number theory can be split up two major parts, divided more by the type of problems they attempt to solve than fundamental differences in technique. Additive number theory is concerned with the structure of the integers. One of the results in additive number theory is the solution to Warings problem. Much of analytic number theory was inspired by the prime number theorem, let π be the prime-counting function that gives the number of primes less than or equal to x, for any real number x. For example, π =4 because there are four prime numbers less than or equal to 10, adrien-Marie Legendre conjectured in 1797 or 1798 that π is approximated by the function a/, where A and B are unspecified constants. In the second edition of his book on number theory he made a more precise conjecture. But Gauss never published this conjecture, in 1838 Peter Gustav Lejeune Dirichlet came up with his own approximating function, the logarithmic integral li. In 1837 he published Dirichlets theorem on arithmetic progressions, using mathematical concepts to tackle an algebraic problem. In proving the theorem, he introduced the Dirichlet characters and L-functions, in 1841 he generalized his arithmetic progressions theorem from integers to the ring of Gaussian integers Z. In two papers from 1848 and 1850, the Russian mathematician Pafnuty Lvovich Chebyshev attempted to prove the law of distribution of prime numbers. In a single paper, he investigated the Riemann zeta function. He made a series of conjectures about properties of the zeta function, extending the ideas of Riemann, two proofs of the prime number theorem were obtained independently by Jacques Hadamard and Charles Jean de la Vallée-Poussin and appeared in the same year. The biggest technical change after 1950 has been the development of sieve methods and these are combinatorial in nature, and quite varied. The extremal branch of combinatorial theory has in return been greatly influenced by the value placed in number theory on quantitative upper and lower bounds. Developments within analytic number theory are often refinements of earlier techniques, for example, the circle method of Hardy and Littlewood was conceived as applying to power series near the unit circle in the complex plane, it is now thought of in terms of finite exponential sums. The fields of approximation and transcendence theory have expanded, to the point that the techniques have been applied to the Mordell conjecture

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Fellow of the Royal Society
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As of 2016, there are around 1600 living Fellows, Foreign and Honorary Members. Fellowship of the Royal Society has been described by The Guardian newspaper as “the equivalent of a lifetime achievement Oscar” with several institutions celebrating their announcement each year. Up to 60 new Fellows, honorary and foreign members are elected annually usually in May, each candidate is considered on their merits and can be proposed from any sector of the scientific community. Fellows are elected for life on the basis of excellence in science and are entitled to use the post-nominal letters FRS, see Category, Fellows of the Royal Society and Category, Female Fellows of the Royal Society. Every year, Fellows elect up to ten new Foreign Members, like Fellows, Foreign Members are elected for life through peer review on the basis of excellence in science. As of 2016 there are around 165 Foreign Members, who are entitled to use the post-nominal ForMemRS, see Category, Foreign Members of the Royal Society. Honorary Fellows include Bill Bryson, Melvyn Bragg, Robin Saxby, David Sainsbury, Baron Sainsbury of Turville, Honorary Fellows are entitled to use the post nominal letters HonFRS. Others including John Maddox, Patrick Moore and Lisa Jardine were elected as honorary fellows, statute 12 is a legacy mechanism for electing members before official honorary membership existed in 1997. Fellows elected under statute 12 include David Attenborough and John Palmer, prime Ministers of the United Kingdom such as Margaret Thatcher, Neville Chamberlain, H. H. Asquith were elected under statute 12, see Category, Fellows of the Royal Society. The Council of the Royal Society can recommend members of the British Royal Family for election as Royal Fellows of the Royal Society. As of 2016 there are five royal fellows, Charles, Prince of Wales, Anne, Princess Royal, Prince Edward, Duke of Kent, Prince William, Duke of Cambridge and Prince Andrew, Duke of York. Her Majesty the Queen, Elizabeth II is not a Royal Fellow, Prince Philip, Duke of Edinburgh was elected under statute 12, not as a Royal Fellow. The election of new fellows is announced annually in May, after their nomination, each candidate for Fellowship or Foreign Membership is nominated by two Fellows of the Royal Society, who sign a certificate of proposal. Previously, nominations required at least five fellows to support each nomination by the proposer, the certificate of election includes a statement of the principal grounds on which the proposal is being made. There is no limit on the number of nominations each year. In 2015, there were 654 candidates for election as Fellows and 106 candidates for Foreign Membership. The final list of up to 52 Fellowship candidates and up to 10 Foreign Membership candidates is confirmed by the Council in April, a candidate is elected if he or she secures two-thirds of votes of those Fellows present and voting. A further maximum of six can be ‘Honorary’, ‘General’ or ‘Royal’ Fellows, nominations for Fellowship are peer reviewed by sectional committees, each with fifteen members and a chair

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Mathematician
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A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, quantity, structure, space, models, one of the earliest known mathematicians was Thales of Miletus, 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, the number of known mathematicians grew when Pythagoras of Samos 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 of Alexandria. She succeeded her father as Librarian at the Great Library and wrote works on applied mathematics. Because of a dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked. Science and mathematics in the Islamic world during the Middle Ages followed various models and it was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences, an example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics, maths and astronomy of Ibn al-Haytham, the Renaissance brought an increased emphasis on mathematics and science to Europe. As time passed, many gravitated towards universities. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking. ”Thus, seminars, overall, science became the focus of universities in the 19th and 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. ”Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and then proceed to specialize in topics of their own choice at the graduate level. In some universities, a qualifying exam serves to test both the breadth and depth of an understanding of mathematics, the students, who pass, are permitted to work on a doctoral dissertation. Mathematicians involved with solving problems with applications in life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their knowledge and professional methodology. With professional focus on a variety of problems, theoretical systems

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Imperial College London
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Imperial College London is a public research university located in London, United Kingdom. Its founder, Prince Albert, envisioned an area comprised of the Victoria and Albert Museum, Natural History Museum, Royal Albert Hall, the Imperial Institute was opened by his wife, Queen Victoria, who laid the foundation stone in 1888. Imperial College London was granted a charter in 1907. In the same year, the joined the University of London. The curriculum was expanded to include medicine after merging with several medical schools. In 2004, Queen Elizabeth II opened the Imperial College Business School, Imperial is organized through faculties for Science, Engineering, Medicine, and Business. The main campus is located in South Kensington, the universitys emphasis is on emerging technology and its practical application. Imperials contributions to society include the discovery of penicillin, the development of fibre optics, Imperial is consistently ranked among the top universities in the world. In 2017, it ranked 8th in the Times Higher Education World University Rankings, 9th in the QS World University Rankings, in 2015, Imperial was also ranked the most innovative university in Europe, and in 2017 as the 5th most international university in the world. Staff and alumni include 15 Nobel laureates,2 Fields Medalists,70 Fellows of the Royal Society,82 Fellows of the Royal Academy of Engineering, and 78 Fellows of the Academy of Medical Sciences. The Great Exhibition in 1851 was organised by Prince Albert, Henry Cole, Francis Fuller and other members of the Royal Society for the Encouragement of Arts, Manufactures and Commerce. The Great Exhibition made a surplus of £186,000 used in creating an area in the South of Kensington encouraging culture and education for everyone. Its founder, Prince Albert, envisioned an area composed of the Victoria and Albert Museum, Natural History Museum, Royal Albert Hall. Several royal colleges and the Imperial Institute merged to form what is now Imperial College London, as a result of a movement earlier in the decade, many politicians donated funds to establish the college, including Benjamin Disraeli, William Gladstone and Robert Peel. It was also supported by Prince Albert, who persuaded August Wilhelm von Hofmann to be the first professor, William Henry Perkin studied and worked at the college under von Hofmann, but resigned his position after discovering the first synthetic dye, mauveine, in 1856. It is considered the highest honour given in the chemical industry. The Royal School of Mines was established by Sir Henry de la Beche in 1851, developing from the Museum of Economic Geology and he created a school which laid the foundations for the teaching of science in the country, and which has its legacy today at Imperial. The Royal College of Science was established in 1881, the main objective was to support the training of science teachers and to develop teaching in other science subjects alongside the Royal School of Mines earth sciences specialities