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Daniel Quillen
Daniel Gray Quillen (June 22, 1940 – April 30, 2011) was an American mathematician. He is known for being the "prime architect" of higher algebraic ''K''-theory, for which he was awarded the Cole Prize in 1975 and the Fields Medal in 1978. From 1984 to 2006, he was the Waynflete Professor of Pure Mathematics at Magdalen College, Oxford. Education and career Quillen was born in Orange, New Jersey, and attended Newark Academy. He entered Harvard University, where he earned both his AB, in 1961, and his PhD in 1964; the latter completed under the supervision of Raoul Bott, with a thesis in partial differential equations. He was a Putnam Fellow in 1959. Quillen obtained a position at the Massachusetts Institute of Technology after completing his doctorate. He also spent a number of years at several other universities. He visited France twice: first as a Sloan Fellow in Paris, during the academic year 1968–69, where he was greatly influenced by Grothendieck, and then, d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orange, New Jersey
The City of Orange (known simply as Orange) is a Township (New Jersey), township in Essex County, New Jersey, Essex County, in the U.S. state of New Jersey. As of the 2020 United States census, the township's population was 34,447, an increase of 4,313 (+14.3%) from the 2010 United States census, 2010 census count of 30,134, which in turn reflected a decline of 2,734 (-8.3%) from the 32,868 counted in the 2000 United States census, 2000 census. The New Jersey Legislature originally incorporated Orange as a township (New Jersey), township on November 27, 1806, from parts of Newark, New Jersey, Newark Township. Parts of the township were taken on April 14, 1834, to form the now-defunct Clinton Township, Essex County, New Jersey (Historical), Clinton Township. On January 31, 1860, Orange was reincorporated as a town (New Jersey), town. Parts of the town were taken to form South Orange Township (April 1, 1861, now known as Maplewood, New Jersey, Maplewood), Fairmount Township, New Je ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kan–Quillen Model Structure
In higher category theory, the Kan–Quillen model structure is a special model structure on the category of simplicial sets. It consists of three classes of morphisms between simplicial sets called ''fibrations'', ''cofibrations'' and ''weak equivalences'', which fulfill the properties of a model structure. Its fibrant objects are all Kan complexes and it furthermore models the homotopy theory of CW complexes up to weak homotopy equivalence, with the correspondence between simplicial sets, Kan complexes and CW complexes being given by the geometric realization and the singular functor ( Milnor's theorem). The Kan–Quillen model structure is named after Daniel Kan and Daniel Quillen. Definition The Kan–Quillen model structure is given by: * Fibrations are Kan fibrations.Joyal 2008, Theorem 6.1. on p. 293 * Cofibrations are monomorphisms.Cisinski 2019, Theorem 3.1.8. * Weak equivalences are ''weak homotopy equivalences'', hence morphisms between simplicial sets, whose ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfred P
Alfred may refer to: Arts and entertainment *'' Alfred J. Kwak'', Dutch-German-Japanese anime television series * ''Alfred'' (Arne opera), a 1740 masque by Thomas Arne * ''Alfred'' (Dvořák), an 1870 opera by Antonín Dvořák *"Alfred (Interlude)" and "Alfred (Outro)", songs by Eminem from the 2020 album '' Music to Be Murdered By'' Business and organisations * Alfred, a radio station in Shaftesbury, England * Alfred Music, an American music publisher * Alfred University, New York, U.S. * The Alfred Hospital, a hospital in Melbourne, Australia People * Alfred (name) includes a list of people and fictional characters called Alfred * Alfred the Great (848/49 – 899), or Alfred I, a king of the West Saxons and of the Anglo-Saxons Places Antarctica * Mount Alfred (Antarctica) Australia * Alfredtown, New South Wales * County of Alfred, South Australia Canada * Alfred and Plantagenet, Ontario ** Alfred, Ontario, a community in Alfred and Plantagenet * Alfred Island, Nunavu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Massachusetts Institute Of Technology
The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of modern technology and science. In response to the increasing Technological and industrial history of the United States, industrialization of the United States, William Barton Rogers organized a school in Boston to create "useful knowledge." Initially funded by a land-grant universities, federal land grant, the institute adopted a Polytechnic, polytechnic model that stressed laboratory instruction in applied science and engineering. MIT moved from Boston to Cambridge in 1916 and grew rapidly through collaboration with private industry, military branches, and new federal basic research agencies, the formation of which was influenced by MIT faculty like Vannevar Bush. In the late twentieth century, MIT became a leading center for research in compu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equations
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to how is thought of as an unknown number solving, e.g., an algebraic equation like . However, it is usually impossible to write down explicit formulae for solutions of partial differential equations. There is correspondingly a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity and stability. Among the many open questions are the existence an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bachelor's Degree
A bachelor's degree (from Medieval Latin ''baccalaureus'') or baccalaureate (from Modern Latin ''baccalaureatus'') is an undergraduate degree awarded by colleges and universities upon completion of a course of study lasting three to six years (depending on the institution and academic discipline). The two most common bachelor's degrees are the Bachelor of Arts (BA) and the Bachelor of Science (BS or BSc). In some institutions and educational systems, certain bachelor's degrees can only be taken as graduate or postgraduate educations after a first degree has been completed, although more commonly the successful completion of a bachelor's degree is a prerequisite for further courses such as a master's or a doctorate. In countries with qualifications frameworks, bachelor's degrees are normally one of the major levels in the framework (sometimes two levels where non-honours and honours bachelor's degrees are considered separately). However, some qualifications titled bachelor's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University
Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyman John Harvard (clergyman), John Harvard, it is the oldest institution of higher learning in the United States. Its influence, wealth, and rankings have made it one of the most prestigious universities in the world. Harvard was founded and authorized by the Massachusetts General Court, the governing legislature of Colonial history of the United States, colonial-era Massachusetts Bay Colony. While never formally affiliated with any Religious denomination, denomination, Harvard trained Congregationalism in the United States, Congregational clergy until its curriculum and student body were gradually secularized in the 18th century. By the 19th century, Harvard emerged as the most prominent academic and cultural institution among the Boston B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newark Academy
Newark Academy is a coeducational private day school located in Livingston, Essex County, in the U.S. state of New Jersey, serving students in sixth through twelfth grades. It was the first school in New Jersey to offer the International Baccalaureate (IB) program. The school receives about 650 applicants for 115 spots, an acceptance rate of 17%. The school has been accredited by the Middle States Association of Colleges and Schools Commission on Elementary and Secondary Schools since 1928.Newark Academy Commission on Elementary and Secondary Schools. Acces ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magdalen College, Oxford
Magdalen College ( ) is a Colleges of the University of Oxford, constituent college of the University of Oxford. It was founded in 1458 by Bishop of Winchester William of Waynflete. It is one of the wealthiest Oxford colleges, as of 2022, and one of the strongest academically, setting the record for the highest Norrington Table, Norrington Score in 2010 and topping the table twice since then. It is home to several of the university's distinguished Chair (academic), chairs, including the Serena Professor of Italian#Serena Professors at Oxford, Agnelli-Serena Professorship, the Sherardian Professor of Botany, Sherardian Professorship, and the four Waynflete Professorships. The large, square Magdalen Tower is an Oxford landmark, and it is a tradition, dating to the days of Henry VII of England, Henry VII, that the college choir sings from the top of it at 6 a.m. on May Morning. The college stands next to the River Cherwell and the University of Oxford Botanic Garden. Within i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Waynflete Professorships
The Waynflete Professorships are four professorial fellowships at the University of Oxford endowed by Magdalen College and named in honour of the college founder William of Waynflete, who had a great interest in science. These professorships are statutory professorships of the University, that is, they are professorships established in the university's regulations, and which are by those regulations attached to Magdalen College in particular. The oldest professorship is the Waynflete Professor of Metaphysical Philosophy. The three science professorships were created following the recommendation of the University Commission in 1857, in recognition of William of Waynflete's lifetime support of science. The professorships are the Waynflete Professor of Chemistry, the Waynflete Professor of Physiology, and the Waynflete Professor of Pure Mathematics. Waynflete Professors of Metaphysical Philosophy This Waynflete Professorship is one of five statutory professorships in philosophy at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic K-theory
Algebraic ''K''-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called ''K''-groups. These are groups in the sense of abstract algebra. They contain detailed information about the original object but are notoriously difficult to compute; for example, an important outstanding problem is to compute the ''K''-groups of the integers. ''K''-theory was discovered in the late 1950s by Alexander Grothendieck in his study of intersection theory on algebraic varieties. In the modern language, Grothendieck defined only ''K''0, the zeroth ''K''-group, but even this single group has plenty of applications, such as the Grothendieck–Riemann–Roch theorem. Intersection theory is still a motivating force in the development of (higher) algebraic ''K''-theory through its links with motivic cohomology and specifically Chow groups. The subject also includes classi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
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, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History 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, by deriving four corollaries to Thales's theorem. 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 math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
