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Morwen Thistlethwaite
Morwen Bernard Thistlethwaite (born 5 June 1945) is a knot theorist and professor of mathematics for the University of Tennessee in Knoxville. He has made important contributions to both knot theory and Rubik's Cube group theory. Biography Morwen Thistlethwaite received his BA from the University of Cambridge in 1967, his MSc from the University of London in 1968, and his PhD from the University of Manchester in 1972 where his advisor was Michael Barratt. He studied piano with Tanya Polunin, James Gibb and Balint Vazsonyi, giving concerts in London before deciding to pursue a career in mathematics in 1975. He taught at the North London Polytechnic from 1975 to 1978 and the Polytechnic of the South Bank, London from 1978 to 1987. He served as a visiting professor at the University of California, Santa Barbara for a year before going to the University of Tennessee, where he currently is a professor. His wife, Stella Thistlethwaite, also teaches at the University of Tennessee-K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
London South Bank University
London South Bank University (LSBU) is a public university in Elephant and Castle, London. It is based in the London Borough of Southwark, near the South Bank of the River Thames, from which it takes its name. Founded in 1892 as the Borough Polytechnic Institute, it achieved university status in 1992 under the Further and Higher Education Act 1992. In September 2003, the university underwent its most recent name change to become London South Bank University (LSBU) and has since opened several new centres including the School of Health and Social Care, the Centre for Efficient and Renewable Energy in Buildings (CEREB), a new Student Centre, an Enterprise Centre, and a new media centre Elephant Studios. The university has students and 1,700 staff. In November 2016, the university was named the Entrepreneurial University of the Year at the Times Higher Education awards, Times Higher Education Awards. In the inaugural 2017 Teaching Excellence Framework, London South Bank Universi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subgroup Series
In mathematics, specifically group theory, a subgroup series of a group (mathematics), group G is a Chain (order theory), chain of subgroups: :1 = A_0 \leq A_1 \leq \cdots \leq A_n = G where 1 is the trivial group, trivial subgroup. Subgroup series can simplify the study of a group to the study of simpler subgroups and their relations, and #Functional series, several subgroup series can be invariantly defined and are important invariants of groups. A subgroup series is used in the subgroup method. Subgroup series are a special example of the use of filtration (mathematics), filtrations in abstract algebra. Definition Normal series, subnormal series A subnormal series (also normal series, normal tower, subinvariant series, or just series) of a group (mathematics), group ''G'' is a sequence of subgroups, each a normal subgroup of the next one. In a standard notation :1 = A_0\triangleleft A_1\triangleleft \cdots \triangleleft A_n = G. There is no requirement made that ''A''''i'' be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Menasco
William W. Menasco is a topologist and a professor at the University at Buffalo. He is best known for his work in knot theory. Biography Menasco received his B.A. from the University of California, Los Angeles in 1975, and his Ph.D. from the University of California, Berkeley in 1981, where his advisor was Robion Kirby. He served as assistant professor at Rutgers University from 1981 to 1984. He then taught as a visiting professor at the University at Buffalo where he became an assistant professor in 1985, an associate professor in 1991. In 1994 he became a professor at the University at Buffalo where he currently serves. Work Menasco proved that a link with an alternating diagram, such as an alternating link, will be non-split if and only if the diagram is connected. Menasco, along with Morwen Thistlethwaite Morwen Bernard Thistlethwaite (born 5 June 1945) is a knot theorist and professor of mathematics for the University of Tennessee in Knoxville. He has made important ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kunio Murasugi
Kunio (written: 邦夫, 邦男, 邦雄, 邦生, 國男, 國士, 国男, 国夫, 州男 or 久仁生) is a masculine Japanese given name. Notable people with the name include: *, Japanese businessman *, Japanese businessman *, Japanese judge *, Japanese politician *, Japanese mayor *, Japanese Go player *, Japanese field hockey player *, Japanese animator *, Japanese dramatist and writer *, Japanese footballer *, Japanese bonsai artist *, Japanese karateka *Kunio Lemari (1942–2008), Marshallese politician and President of the Marshall Islands *, Japanese architect *, Japanese businessman, adventurer, and college professor *, Japanese photographer *, Secretary General of the World Customs Organization *, Japanese actor and voice actor (not to be confused with the manga character of the same name) *, Japanese politician *, Japanese general *, Japanese businessman *, Japanese footballer *, Japanese shogi player *, Japanese writer *, Japanese mechanical designer *, Japanese cross-coun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Louis Kauffman
Louis Hirsch Kauffman (born February 3, 1945) is an American mathematician, mathematical physicist, and professor of mathematics in the Department of Mathematics, Statistics, and Computer Science at the University of Illinois at Chicago. He does research in topology, knot theory, topological quantum field theory, quantum information theory, and diagrammatic and categorical mathematics. He is best known for the introduction and development of the bracket polynomial and the Kauffman polynomial. Biography Kauffman was valedictorian of his graduating class at Norwood Norfolk Central High School in 1962. He received his B.S. at the Massachusetts Institute of Technology in 1966 and his Ph.D. in mathematics from Princeton University in 1972, with thesis ''Cyclic Branched-Covers, O(n)-Actions and Hypersurface Singularities'' written under the supervision of William Browder. Kauffman has worked at many places as a visiting professor and researcher, including the University of Za ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tait Flyping Conjecture
The Tait conjectures are three conjectures made by 19th-century mathematician Peter Guthrie Tait in his study of knots.. The Tait conjectures involve concepts in knot theory such as alternating knots, chirality, and writhe. All of the Tait conjectures have been solved, the most recent being the Flyping conjecture. Background Tait came up with his conjectures after his attempt to tabulate all knots in the late 19th century. As a founder of the field of knot theory, his work lacks a mathematically rigorous framework, and it is unclear whether he intended the conjectures to apply to all knots, or just to alternating knots. It turns out that most of them are only true for alternating knots. In the Tait conjectures, a knot diagram is called "reduced" if all the "isthmi", or "nugatory crossings" have been removed. Crossing number of alternating knots Tait conjectured that in certain circumstances, crossing number was a knot invariant, specifically: Any reduced diagram of an alternatin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flype
In the mathematical theory of knots, a flype is a kind of manipulation of knot and link diagrams used in the Tait flyping conjecture. It consists of twisting a part of a knot, a tangle T, by 180 degrees. Flype comes from a Scots word meaning ''to fold'' or ''to turn back'' ("as with a sock").. Tait used the term to mean, "a change of infinite complementary region"). Two reduced alternating diagrams of an alternating link can be transformed to each other using flypes. This is the Tait flyping conjecture, proven in 1991 by Morwen Thistlethwaite and William Menasco. See also * Reidemeister move In the mathematical area of knot theory, a Reidemeister move is any of three local moves on a link diagram. and, independently, , demonstrated that two knot diagrams belonging to the same knot, up to planar isotopy, can be related by a seque ...s are another commonly studied kind of manipulation to knot diagrams. References Knot operations {{knottheory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Writhe
In knot theory, there are several competing notions of the quantity writhe, or \operatorname. In one sense, it is purely a property of an oriented link (knot theory), link diagram and assumes integer values. In another sense, it is a quantity that describes the amount of "coiling" of a knot (mathematics), mathematical knot (or any curve, closed simple curve) in three-dimensional space and assumes real numbers as values. In both cases, writhe is a geometric quantity, meaning that while deforming a curve (or diagram) in such a way that does not change its topology, one may still change its writhe. Writhe of link diagrams In knot theory, the writhe is a property of an oriented link (knot theory), link diagram. The writhe is the total number of positive crossings minus the total number of negative crossings. A direction is assigned to the link at a point in each component and this direction is followed all the way around each component. For each crossing one comes across while travel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knot (mathematics)
In mathematics, a knot is an embedding of the circle () into three-dimensional Euclidean space, (also known as ). Often two knots are considered equivalent if they are ambient isotopic, that is, if there exists a continuous deformation of which takes one knot to the other. A crucial difference between the standard mathematical and conventional notions of a knot is that mathematical knots are closed — there are no ends to tie or untie on a mathematical knot. Physical properties such as friction and thickness also do not apply, although there are mathematical definitions of a knot that take such properties into account. The term ''knot'' is also applied to embeddings of in , especially in the case . The branch of mathematics that studies knots is known as knot theory and has many relations to graph theory. Formal definition A knot is an embedding of the circle () into three-dimensional Euclidean space (), or the 3-sphere (), since the 3-sphere is compact. Two knots ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crossing Number (knot Theory)
In the mathematics, mathematical area of knot theory, the crossing number of a knot (mathematics), knot is the smallest number of crossings of any diagram of the knot. It is a knot invariant. Examples By way of example, the unknot has crossing number 0 (number), zero, the trefoil knot three and the figure-eight knot (mathematics), figure-eight knot four. There are no other knots with a crossing number this low, and just two knots have crossing number five, but the number of knots with a particular crossing number increases rapidly as the crossing number increases. Tabulation Tables of prime knots are traditionally indexed by crossing number, with a subscript to indicate which particular knot out of those with this many crossings is meant (this sub-ordering is not based on anything in particular, except that torus knots then twist knots are listed first). The listing goes 31 (the trefoil knot), 41 (the figure-eight knot), 51, 52, 61, etc. This order has not changed significa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
