HOME  TheInfoList.com 
William Thurston WILLIAM PAUL THURSTON (October 30, 1946 – August 21, 2012) was an American mathematician . He was a pioneer in the field of lowdimensional topology . In 1982, he was awarded the Fields Medal for his contributions to the study of 3manifolds . From 2003 until his death he was a professor of mathematics and computer science at Cornell University Cornell University . CONTENTS* 1 Mathematical contributions * 1.1 Foliations * 1.2 The geometrization conjecture * 1.3 Orbifold Orbifold theorem * 2 Education and career * 2.1 Selected works * 3 See also * 4 References * 5 Further reading * 6 External links MATHEMATICAL CONTRIBUTIONSFOLIATIONSHis early work, in the early 1970s, was mainly in foliation theory, where he had a dramatic impact [...More...]  "William Thurston" on: Wikipedia Yahoo 

John N. Mather JOHN NORMAN MATHER (June 9, 1942 – January 28, 2017) was a mathematician at Princeton University Princeton University known for his work on singularity theory and Hamiltonian dynamics . He was descended from Atherton Mather (16631734), a cousin of Cotton Mather Cotton Mather . His early work dealt with the stability of smooth mappings between smooth manifolds of dimensions n (for the source manifold N) and p (for the target manifold P). He determined the precise dimensions (n,p) for which smooth mappings are stable with respect to smooth equivalence by diffeomorphisms of the source and target (i.e. infinitely differentiable coordinate changes) [...More...]  "John N. Mather" on: Wikipedia Yahoo 

Nsphere In mathematics , the NSPHERE is the generalization of the ordinary sphere to spaces of arbitrary dimension . It is an ndimensional manifold that can be embedded in Euclidean (n + 1)space. The 0sphere is a pair of points, the 1sphere is a circle, and the 2sphere is an ordinary sphere. Generally, when embedded in an (n + 1)dimensional Euclidean space, an nsphere is the surface or boundary of an (n + 1)dimensional ball . That is, for any natural number n, an nsphere of radius r may be defined in terms of an embedding in (n + 1)dimensional Euclidean space Euclidean space as the set of points that are at distance r from a central point, where the radius r may be any positive real number . Thus, the nsphere would be defined by: S n = { x R n + 1 : x = r } [...More...]  "Nsphere" on: Wikipedia Yahoo 

Cohomology In mathematics , specifically in homology theory and algebraic topology , COHOMOLOGY is a general term for a sequence of abelian groups associated to a topological space , often defined from a cochain complex . Cohomology Cohomology can be viewed as a method of assigning richer algebraic invariants to a space than homology. Some versions of cohomology arise by dualizing the construction of homology. In other words, cochains are functions on the group of chains in homology theory. From its beginning in topology , this idea became a dominant method in the mathematics of the second half of the twentieth century. From the initial idea of homology as a method of constructing algebraic invariants of topological spaces, the range of applications of homology and cohomology theories has spread throughout geometry and algebra . The terminology tends to hide the fact that cohomology, a contravariant theory, is more natural than homology in many applications [...More...]  "Cohomology" on: Wikipedia Yahoo 

Figureeight Knot The FIGUREEIGHT KNOT or FIGUREOFEIGHT KNOT is a type of stopper knot . It is very important in both sailing and rock climbing as a method of stopping ropes from running out of retaining devices. Like the overhand knot , which will jam under strain, often requiring the rope to be cut, the figureofeight will also jam, but is usually more easily undone than the overhand knot. The figureeight or figureofeight knot is also called (in books) the Flemish knot. The name figureofeight knot appears in Lever's Sheet Anchor; or, a Key to Rigging (London, 1808). The word of nowadays is usually omitted. The knot is the sailor's common singlestrand stopper knot and is tied in the ends of tackle falls and running rigging, unless the latter is fitted with monkey's tails. It is used about ship wherever a temporary stopper knot is required [...More...]  "Figureeight Knot" on: Wikipedia Yahoo 

Wolfgang Haken WOLFGANG HAKEN (born June 21, 1928 in Berlin Berlin , Germany Germany ) is a mathematician who specializes in topology , in particular 3manifolds . In 1962 he left Germany Germany to become a visiting professor at the University of Illinois at UrbanaChampaign University of Illinois at UrbanaChampaign , he became a full professor by 1965, and he is now an emeritus professor. In 1976 together with colleague Kenneth Appel also at the University of Illinois at UrbanaChampaign, Haken solved one of the most famous problems in mathematics, the fourcolor problem . They proved that any map can be filled in with four colors without any adjacent "countries" sharing the same color. Haken has introduced several important ideas, including Haken manifolds , Kneser–Haken finiteness , and an expansion of the work of Kneser into a theory of normal surfaces [...More...]  "Wolfgang Haken" on: Wikipedia Yahoo 

Euler Characteristic In mathematics , and more specifically in algebraic topology and polyhedral combinatorics , the EULER CHARACTERISTIC (or EULER NUMBER, or EULER–POINCARé CHARACTERISTIC) is a topological invariant , a number that describes a topological space 's shape or structure regardless of the way it is bent. It is commonly denoted by {displaystyle chi } (Greek lowercase letter chi ). The Euler characteristic Euler characteristic was originally defined for polyhedra and used to prove various theorems about them, including the classification of the Platonic solids . Leonhard Euler Leonhard Euler , for whom the concept is named, was responsible for much of this early work. In modern mathematics, the Euler characteristic Euler characteristic arises from homology and, more abstractly, homological algebra [...More...]  "Euler Characteristic" on: Wikipedia Yahoo 

Haefliger Structure In mathematics, a HAEFLIGER STRUCTURE on a topological space is a generalization of a foliation of a manifold, introduced by Haefliger (1970 , 1971 ). Any foliation on a manifold induces a Haefliger structure, which uniquely determines the foliation. CONTENTS * 1 Definition * 2 Haefliger structure and foliations * 3 Classifying space * 4 References DEFINITIONA Haefliger structure on a space X is determined by a HAEFLIGER COCYCLE. A codimensionq Haefliger cocycle consists of a covering of X by open sets Uα, together with continuous maps Ψαβ from Uα ∩ Uβ to the sheaf of germs of local diffeomorphisms of Rq, satisfying the 1cocycle condition ( u ) = ( u ) ( u ) {displaystyle displaystyle Psi _{gamma alpha }(u)=Psi _{gamma beta }(u)Psi _{beta alpha }(u)} for u U U U [...More...]  "Haefliger Structure" on: Wikipedia Yahoo 

National Academy Of Sciences The NATIONAL ACADEMY OF SCIENCES (NAS) is a United States United States nonprofit , nongovernmental organization . NAS is part of the National Academies of Sciences, Engineering, and Medicine Medicine , along with the National Academy of Engineering Engineering (NAE) and the National Academy of Medicine (NAM). As a national academy , new members of the organization are elected annually by current members, based on their distinguished and continuing achievements in original research. Election to the National Academies is one of the highest honors in the scientific field. Members serve pro bono as "advisers to the nation" on science , engineering , and medicine . The group holds a congressional charter under Title 36 of the United States United States Code [...More...]  "National Academy Of Sciences" on: Wikipedia Yahoo 

Washington, D.C. WASHINGTON, D.C., formally the DISTRICT OF COLUMBIA and commonly referred to as "WASHINGTON", "THE DISTRICT", or simply "D.C.", is the capital of the United States. The signing of the Residence Act on July 16, 1790, approved the creation of a capital district located along the Potomac River on the country's East Coast . The U.S. Constitution provided for a federal district under the exclusive jurisdiction of the Congress and the District is therefore not a part of any state. The states of Maryland and Virginia Virginia each donated land to form the federal district, which included the preexisting settlements of Georgetown and Alexandria . Named in honor of President George Washington George Washington , the City of Washington was founded in 1791 to serve as the new national capital [...More...]  "Washington, D.C." on: Wikipedia Yahoo 

Troels Jørgensen TROELS JøRGENSEN is a Danish mathematician at Columbia University working on hyperbolic geometry and complex analysis , who proved Jørgensen\'s inequality . He wrote his thesis in 1970 at the University of Copenhagen under the joint supervision of Werner Fenchel and Bent Fuglede [...More...]  "Troels Jørgensen" on: Wikipedia Yahoo 

Computer Science COMPUTER SCIENCE is the study of the theory, experimentation, and engineering that form the basis for the design and use of computers. It is the scientific and practical approach to computation and its applications and the systematic study of the feasibility, structure, expression, and mechanization of the methodical procedures (or algorithms ) that underlie the acquisition, representation, processing, storage, communication of, and access to, information. An alternate, more succinct definition of computer science is the study of automating algorithmic processes that scale. A computer scientist specializes in the theory of computation and the design of computational systems. Its fields can be divided into a variety of theoretical and practical disciplines [...More...]  "Computer Science" on: Wikipedia Yahoo 

Mathematician A MATHEMATICIAN is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems . Mathematics Mathematics is concerned with numbers , data , quantity , structure , space , models , and change . CONTENTS * 1 History * 2 Required education * 3 Activities * 3.1 Applied mathematics Applied mathematics * 3.2 Abstract mathematics * 3.3 Mathematics Mathematics teaching * 3.4 Consulting * 4 Occupations * 5 Quotations about mathematicians * 6 Prizes in mathematics * 7 Mathematical autobiographies * 8 See also * 9 Notes * 10 References * 11 Further reading * 12 External links HISTORY This section is on the history of mathematicians [...More...]  "Mathematician" on: Wikipedia Yahoo 

Normal Surface In mathematics , a NORMAL SURFACE is a surface inside a triangulated 3manifold that intersects each tetrahedron so that each component of intersection is a triangle or a quad (see figure). A triangle cuts off a vertex of the tetrahedron while a quad separates pairs of vertices. A normal surface may have many components of intersection, called NORMAL DISKS, with one tetrahedron, but no two normal disks can be quads that separate different pairs of vertices since that would lead to the surface selfintersecting. A normal surface intersects a tetrahedron in (possibly many) triangles (see above left) and quads (see above right) Dually, a normal surface can be considered to be a surface that intersects each handle of a given handle structure on the 3manifold in a prescribed manner similar to the above. The concept of normal surface can be generalized to arbitrary polyhedra. There are also related notions of ALMOST NORMAL SURFACE and SPUN NORMAL SURFACE [...More...]  "Normal Surface" on: Wikipedia Yahoo 

University Of California, Davis The UNIVERSITY OF CALIFORNIA, DAVIS (also referred to as UCD, UC DAVIS, or DAVIS), is a public research university and landgrant university as well as one of the 10 campuses of the University of California California (UC) system. It is located in Davis, California , just west of Sacramento Sacramento , and has the thirdlargest enrollment in the UC System after UCLA UCLA and UC Berkeley . The university has been labeled one of the "Public Ivies ," a publicly funded university considered to provide a quality of education comparable to those of the Ivy League Ivy League . The Carnegie Foundation classifies UC Davis as a comprehensive doctoral research university with a medical program, and very high research activity [...More...]  "University Of California, Davis" on: Wikipedia Yahoo 

Cornell University CORNELL UNIVERSITY (/kɔːrˈnɛl/ korNEL ) is an American private Ivy League Ivy League and public landgrant doctoral university located in Ithaca, New York Ithaca, New York . Founded in 1865 by Ezra Cornell Ezra Cornell and Andrew Dickson White , the university was intended to teach and make contributions in all fields of knowledge—from the classics to the sciences , and from the theoretical to the applied. These ideals, unconventional for the time, are captured in Cornell's motto, a popular 1865 Ezra Cornell quotation: "I would found an institution where any person can find instruction in any study." The university is broadly organized into seven undergraduate colleges and seven graduate divisions at its main Ithaca campus, with each college and division defining its own admission standards and academic programs in near autonomy [...More...]  "Cornell University" on: Wikipedia Yahoo 