Hassler whitney biography of william hill

Married Barbara Floyd Osterman, February 8, Back to Profile. Photos Works. Main Photo Add photo. School period Add photo. Career Add photo. Achievements Add photo. Membership Add photo. To submit students of this mathematician, please use the new data formnoting this mathematician's MGP ID of for the advisor ID. The Mathematics Genealogy Project is in need of funds to help pay for student help and other associated costs.

If you would like to contribute, please donate online using credit card or bank transfer or mail your tax-deductible contribution to:. His main work, however, was in topology, particularly in the theory of manifolds. Continuing work started by Veblen and Henry WhiteheadWhitney produced fundamental work in differential topology in In particular he proved theorems about the embedding of an n n n -dimensional differentiable manifold in Euclidean space and he discovered characteristic classes at the same time as Stiefel.

The term Stiefel-Whitney characteristic classes is often used today. He wrote a survey paper Topological properties of differentiable manifolds in which includes the many of the recent contributions he had made. In he gave his famous duality and product theorems: the term Whitney duality is now used. Other work on algebraic varieties and integration theory was important.

He published the book Geometric integration theory In which describes his work on the interactions between algebraic topology and the theory of integration. After an introduction, the chapters of the book are:- Grassmann algebra; Differential forms; Riemann integration theory; Smooth manifolds; Abstract integration theory; Some relations between chains and functions; General properties of chains and cochains; Chains and cochains in open sets; Flat cochains and differential forms; Lipschitz mappings; Chains and additive set functions.

Hassler whitney biography of william hill: Another difference between the press release

This topic had been the subject of the lecture which Whitney gave to the International Congress of Mathematicians, held in Cambridge, Massachusetts in His second book Complex analytic varieties was published in In addition to research at the frontiers of mathematical research, Whitney was also interested in mathematics teachings in schools. Zund writes [ 8 ] :- Whitney became actively involved in mathematical education at the elementary school level.

He gave a number of lectures on this topic, conducted summer courses for teachers, and on one occasion spent four months teaching pre-algebra mathematics to a seventh grade class of students. In he was elected honorary member of the London Mathematical Society. Whitney's earliest work, from towas on graph theory. Many of his contributions were to the graph-coloring, and the ultimate computer-assisted solution to the four-color problem relied on some of his results.

His work in graph theory culminated in a paper, [ 15 ] where he laid the foundations for matroidsa fundamental notion in modern combinatorics and representation theory independently introduced by him and Bartel Leendert van der Waerden in the mid s. Whitney's lifelong interest in geometric properties of functions also began around this time.

A complete solution to this problem was found only in by Charles Fefferman. This basic result shows that manifolds may be treated intrinsically or extrinsically, as we wish. The intrinsic definition had been published only a few years earlier in the work of Oswald Veblen and J. These theorems opened the way for much more refined studies of embedding, immersion and also of smoothing—that is, the possibility of having various smooth structures on a given topological manifold.

He was one of the major developers of cohomology theoryand characteristic classesas these concepts emerged in the late s, and his work on algebraic topology continued into the 40s. He also returned to the study of functions in the s, continuing his work on the extension problems formulated a decade earlier, and answering a question of Laurent Schwartz in a paper On Ideals of Differentiable Functions.

Whitney had, throughout the s, an almost unique interest in the topology of singular spaces and in singularities of smooth maps. An old idea, implicit even in the notion of a simplicial complex, was to study a singular space by decomposing it into smooth pieces nowadays called "strata". Whitney was the first to see any subtlety in this definition, and pointed out that a good "stratification" should satisfy conditions he termed "A" and "B", now referred to as Whitney conditions.

In his book Geometric Integration Theory he gives a theoretical basis for Stokes' theorem applied with singularities on the boundary:. These aspects of Whitney's work have looked more unified, in retrospect and with the general development of singularity theory. Whitney's purely topological work Stiefel—Whitney classbasic results on vector bundles entered the mainstream more quickly.

Inhe became involved full-time in educational problems, especially at the elementary school level. He spent many years in classrooms, both teaching mathematics and observing how it is taught. He traveled widely to lecture on the subject in the United States and abroad. He worked toward removing mathematical anxietywhich he felt leads young pupils to avoid mathematics.

Whitney spread the ideas of teaching mathematics to students in ways that relate the content to their own lives as opposed to teaching them rote memorization. Hassler Whitney published 82 works: [ 21 ] all his published articles, included the ones listed in this section and the preface of the book Whitneyare collected in the two volumes Whitney app.

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Download as PDF Printable version. In other projects. Wikimedia Commons Wikidata item. American mathematician. Princeton, New JerseyU. Algebraic topology Differential topology Graph theory Geometric measure theory Cohomology Matroid theory Singularity theory. Steele Prize Biography [ edit ]. Life [ edit ]. Death [ edit ]. Academic career [ edit ].

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Hassler whitney biography of william hill: Let me first express my

Research [ edit ]. Teaching [ edit ]. Selected publications [ edit ]. See also [ edit ]. Notes [ edit ]. Kendig also writes that him apparently being in good health, the physicians attributed the cause of the stroke to the treatments for prostate cancer he was undergoing. Retrieved Retrieved 5 February Recall that two graphs G and G' are 2-isomorphic if one can be transformed into the other by applying operations of the following types: Vertex identification Vertex cleaving Twisting.

In contrast, our viewpoint is akin to that taken by Hassler Whitney. The New York Times. Retrieved 12 November References [ edit ]. Biographical and general references [ edit ]. Scientific references [ edit ]. External links [ edit ]. Laureates of the Wolf Prize in Mathematics. Stein Mumford Simon K. Mathematics portal. United States National Medal of Science laureates.

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