|
Colin McLarty
Colin McLarty (born July 12, 1951) is an American logician whose publications have ranged widely in philosophical logic, philosophy and the foundations of mathematics, foundations of mathematical logic, mathematics, as well as in the history of science and of history of mathematics, mathematics. Research Category theory He has written papers about Saunders Mac Lane, one of the founders of category theory. McLarty's ''Elementary Categories and Elementary Toposes'' describes category theory and topos theory at an elementary level. McLarty worked on establishing that Fermat's Last Theorem can be proven in a setting with much weaker assumptions than the ones used in Wiles' proof, which makes use of involved category theoretical constructions. History of Mathematics He is a member of thGrothendieck Circle which provides on-line and open access to many writings about the mathematician Alexandre Grothendieck, who revolutionized Banach space, Banach-space theory and algebraic geome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Colin McLarty
Colin McLarty (born July 12, 1951) is an American logician whose publications have ranged widely in philosophical logic, philosophy and the foundations of mathematics, foundations of mathematical logic, mathematics, as well as in the history of science and of history of mathematics, mathematics. Research Category theory He has written papers about Saunders Mac Lane, one of the founders of category theory. McLarty's ''Elementary Categories and Elementary Toposes'' describes category theory and topos theory at an elementary level. McLarty worked on establishing that Fermat's Last Theorem can be proven in a setting with much weaker assumptions than the ones used in Wiles' proof, which makes use of involved category theoretical constructions. History of Mathematics He is a member of thGrothendieck Circle which provides on-line and open access to many writings about the mathematician Alexandre Grothendieck, who revolutionized Banach space, Banach-space theory and algebraic geome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Case Western Reserve Campus 2005
Case or CASE may refer to: Containers * Case (goods), a package of related merchandise * Cartridge case or casing, a firearm cartridge component * Bookcase, a piece of furniture used to store books * Briefcase or attaché case, a narrow box to carry paperwork * Computer case, the enclosure for a PC's main components * Keep case, DVD or CD packaging * Pencil case * Phone case, protective or vanity accessory for mobile phones ** Battery case * Road case or flight case, for fragile equipment in transit * Shipping container or packing case * Suitcase, a large luggage box * Type case, a compartmentalized wooden box for letterpress typesetting Places * Case, Laclede County, Missouri * Case, Warren County, Missouri * Case River, a Kabika tributary in Ontario, Canada * Case Township, Michigan * Case del Conte, Italy People * Case (name), people with the surname (or given name) * Case (singer), American R&B singer-songwriter and producer (Case Woodard) Arts, entertainment, and media * ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Lawvere
Francis William Lawvere (; born February 9, 1937) is a mathematician known for his work in category theory, topos theory and the philosophy of mathematics. Biography Lawvere studied continuum mechanics as an undergraduate with Clifford Truesdell. He learned of category theory while teaching a course on functional analysis for Truesdell, specifically from a problem in John L. Kelley's textbook ''General Topology''. Lawvere found it a promising framework for simple rigorous axioms for the physical ideas of Truesdell and Walter Noll. Truesdell supported Lawvere's application to study further with Samuel Eilenberg, a founder of category theory, at Columbia University in 1960. Before completing the Ph.D. Lawvere spent a year in Berkeley as an informal student of model theory and set theory, following lectures by Alfred Tarski and Dana Scott. In his first teaching position at Reed College he was instructed to devise courses in calculus and abstract algebra from a foundational persp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Johnstone (mathematician)
Peter Tennant Johnstone (born 1948) is Professor of the Foundations of Mathematics at the University of Cambridge, and a fellow of St. John's College. He invented or developed a broad range of fundamental ideas in topos theory. His thesis, completed at the University of Cambridge in 1974, was entitled "Some Aspects of Internal Category Theory in an Elementary Topos". He is a great-great nephew of the Reverend George Gilfillan who was eulogised in William McGonagall William Topaz McGonagall (March 1825 – 29 September 1902) was a Scottish poet of Irish descent. He gained notoriety as an extremely bad poet who exhibited no recognition of, or concern for, his peers' opinions of his work. He wrote about 2 ...'s first poem. Books *. :— " r too hard to read, and not for the faint-hearted"An anonymous referee, as quoted by Johnstone in his ''Sketches of an elephant'', p. ix. *. *. * (v.3 in preparation) References External linksJohnstone's web page* * {{DEFAULTS ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Hyland
(John) Martin Elliott Hyland is professor of mathematical logic at the University of Cambridge and a fellow of King's College, Cambridge. His interests include mathematical logic, category theory, and theoretical computer science. Education Hyland was educated at the University of Oxford where he was awarded a Doctor of Philosophy degree in 1975 for research supervised by Robin Gandy. Research and career Martin Hyland is best known for his work on category theory applied to logic (proof theory, recursion theory), theoretical computer science (lambda-calculus and semantics) and higher-dimensional algebra. In particular he is known for work on the effective topos (within topos theory) and on game semantics. His former doctoral students include Eugenia Cheng and Valeria de Paiva Valeria Correa Vaz de Paiva is a Brazilian mathematician, logician, and computer scientist. Her work includes research on logical approaches to computation, especially using category theory, knowledg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topos Theory
In mathematics, a topos (, ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site). Topoi behave much like the category of sets and possess a notion of localization; they are a direct generalization of point-set topology. The Grothendieck topoi find applications in algebraic geometry; the more general elementary topoi are used in logic. The mathematical field that studies topoi is called topos theory. Grothendieck topos (topos in geometry) Since the introduction of sheaves into mathematics in the 1940s, a major theme has been to study a space by studying sheaves on a space. This idea was expounded by Alexander Grothendieck by introducing the notion of a "topos". The main utility of this notion is in the abundance of situations in mathematics where topological heuristics are very effective, but an honest topological space is lacking; it is sometimes possible to find a topos formaliz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Abstract Nonsense
In mathematics, abstract nonsense, general abstract nonsense, generalized abstract nonsense, and general nonsense are terms used by mathematicians to describe abstract methods related to category theory and homological algebra. More generally, "abstract nonsense" may refer to a proof that relies on category-theoretic methods, or even to the study of category theory itself. Background Roughly speaking, category theory is the study of the general form, that is, categories of mathematical theories, without regard to their content. As a result, mathematical proofs that rely on category-theoretic ideas often seem out-of-context, somewhat akin to a non sequitur. Authors sometimes dub these proofs "abstract nonsense" as a light-hearted way of alerting readers to their abstract nature. Labeling an argument "abstract nonsense" is usually ''not'' intended to be derogatory,Michael Monastyrsky, ''Some Trends in Modern Mathematics and the Fields Medal.'' Can. Math. Soc. Notes, March and April ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homological Algebra
Homological algebra is the branch of mathematics that studies homology (mathematics), homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract algebra (theory of module (mathematics), modules and Syzygy (mathematics), syzygies) at the end of the 19th century, chiefly by Henri Poincaré and David Hilbert. Homological algebra is the study of homological functors and the intricate algebraic structures that they entail; its development was closely intertwined with the emergence of category theory. A central concept is that of chain complexes, which can be studied through both their homology and cohomology. Homological algebra affords the means to extract information contained in these complexes and present it in the form of homological invariant (mathematics), invariants of ring (mathematics), rings, modules, topological spaces, and other 'tan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Nonsense
In mathematics, abstract nonsense, general abstract nonsense, generalized abstract nonsense, and general nonsense are terms used by mathematicians to describe abstract methods related to category theory and homological algebra. More generally, "abstract nonsense" may refer to a proof that relies on category-theoretic methods, or even to the study of category theory itself. Background Roughly speaking, category theory is the study of the general form, that is, categories of mathematical theories, without regard to their content. As a result, mathematical proofs that rely on category-theoretic ideas often seem out-of-context, somewhat akin to a non sequitur. Authors sometimes dub these proofs "abstract nonsense" as a light-hearted way of alerting readers to their abstract nature. Labeling an argument "abstract nonsense" is usually ''not'' intended to be derogatory,Michael Monastyrsky, ''Some Trends in Modern Mathematics and the Fields Medal.'' Can. Math. Soc. Notes, March and Apr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jeremy Gray
Jeremy John Gray (born 25 April 1947) is an English mathematician primarily interested in the history of mathematics. Biography Gray studied mathematics at Oxford University from 1966 to 1969, and then at Warwick University, obtaining his Ph.D. in 1980 under the supervision of Ian Stewart and David Fowler. He has worked at the Open University since 1974, and became a lecturer there in 1978. He also lectured at the University of Warwick from 2002 to 2017, teaching a course on the history of mathematics. Gray was a consultant on the television series, '' The Story of Maths'',''To Infinity and Beyond'' 27 October 2008 21:00 BBC Four a co-production between the Open University and the BBC. He edits Archive for History of Exact Sciences. In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. In 2012 he became a fellow of the American Mathematical Society. Books Gray has been awarded prizes for his contributions to mathematics, including t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oxford University Press
Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print books by decree in 1586, it is the second oldest university press after Cambridge University Press. It is a department of the University of Oxford and is governed by a group of 15 academics known as the Delegates of the Press, who are appointed by the vice-chancellor of the University of Oxford. The Delegates of the Press are led by the Secretary to the Delegates, who serves as OUP's chief executive and as its major representative on other university bodies. Oxford University Press has had a similar governance structure since the 17th century. The press is located on Walton Street, Oxford, opposite Somerville College, in the inner suburb of Jericho. For the last 500 years, OUP has primarily focused on the publication of pedagogical texts and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.jpg "Click for more on -> Oxford University Press")