Diferenças entre edições de "Garrett Birkhoff"

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{{em tradução|:en:Garrett Birkhoff}}
 
{{Info/Cientista
|nome =Garrett Birkhoff
Filho do matemático [[George David Birkhoff]], começou a estudar na [[Universidade Harvard]] em 1928, após menos de sete anos do início de sua educação formal. Após bacharelar-se em 1932 foi para a [[Universidade de Cambridge]] na [[Inglaterra]] estudar [[física matemática]], decidindo então estudar [[álgebra abstrata]] com [[Philip Hall]]. Quando em visita à [[Universidade de Munique]] encontrou-se com [[Constantin Carathéodory]], que lhe indicou dois livros textos fundamentais, [[Bartel Leendert van der Waerden]] sobre [[álgebra abstrata]] e [[Andreas Speiser]] sobre [[teoria dos grupos]].
 
==Obras==
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* 1967 (1940). ''Lattice Theory, 3rd ed''. American Mathematical Society.
Birkhoff held no Ph.D., a qualification British higher education did not emphasize at that time, and did not even bother obtaining an M.A. Nevertheless, after being a member of Harvard's [[Society of Fellows]], 1933&ndash;36, he spent the rest of his career teaching at Harvard. From these facts can be inferred the number and quality of Birkhoff's papers published by his 25th year.
* 1997 (1941) (with [[Saunders Mac Lane]]). ''A Survey of Modern Algebra''. A K Peters. ISBN 1-56881-068-7
 
* 1978 (1950). ''Hydrodynamics: A study in logic, fact, and similitude ''. Greenwood Press.
During the 1930s, Birkhoff, along with his Harvard colleagues [[Marshall Stone]] and [[Saunders Mac Lane]], substantially advanced American teaching and research in [[abstract algebra]]. In 1941 he and Mac Lane published ''A Survey of Modern Algebra'', the second undergraduate textbook in English on the subject (Cyrus Colton MacDuffee's ''An Introduction to Abstract Algebra'' was published in 1940). Mac Lane and Birkhoff's ''Algebra'' (1967) is a more advanced text on [[abstract algebra]]. A number of papers he wrote in the 1930s, culminating in his monograph, ''Lattice Theory'' (1940; the third edition remains in print), turned [[lattice theory]] into a major branch of [[abstract algebra]]. His 1935 paper, "On the Structure of Abstract Algebras" founded a new branch of mathematics, [[universal algebra]]. Birkhoff's approach to this development of universal algebra and lattice theory acknowledged prior ideas of [[Charles Sanders Peirce]], [[Ernst Schröder]], and [[Alfred North Whitehead]]; in fact, Whitehead had written a 1898 monograph entitled ''Universal Algebra''.
* 1957 (with E. Zarantello). ''Jets, Wakes, and Cavities''. Academic Press.
 
* 1989 (1962) (with [[Gian-Carlo Rota]]). ''Ordinary Differential Equations''. John Wiley.
During and after [[World War II]], Birkhoff's interests gravitated towards what he called "engineering" mathematics. During the war, he worked on radar aiming and ballistics, including the [[bazooka]]. In the development of weapons, mathematical questions arose, some of which were not addressed by the hitherto literature on fluid dynamics. Birkhoff's research was presented in his texts on fluid dynamics, ''Hydrodynamics'' (1950) and ''Jets, Wakes and Cavities'' (1957).
* 1999 (1967) (with [[Saunders Mac Lane]]). ''Algebra''. Chelsea. ISBN 0-8218-1646-2
 
* 1970 (with Thomas Bartee). ''Modern Applied Algebra''. McGraw-Hill.
Birkhoff, a friend of [[John von Neumann]], took a close interest in the rise of the electronic computer. Birkhoff supervised the Ph.D. thesis of [[David M. Young, Jr.|David M. Young]] on the numerical solution of the partial differential equation of Poisson, in which Young proposed the successive over-relaxation (SOR) method. Birkhoff then worked with [[Richard S. Varga]], a former student; Varga was employed at [[Bettis Atomic Power Laboratory]] of the [[Westinghouse Electric (1886)|Westinghouse Electronic Corporation]] in Pittsburgh and was helping to design nuclear reactors. Extending the results of Young, the Birkhoff-Varga collaboration led to many publications on [[positive operator]]s and [[iterative method]]s for ''p''-cylic matrices.
* 1973. ''Source Book in Classical Analysis''. Harvard Uni. Press.
 
Birkhoff's research and consulting work (notably for [[General Motors Corporation|General Motors]]) developed computational methods besides numerical linear algebra, notably the representation of smooth curves via [[cubic spline]]s.
 
Birkhoff published more than 200 papers and supervised more than 50 Ph.Ds. He was a member of the [[United States National Academy of Sciences|National Academy of Sciences]] and the [[American Academy of Arts and Sciences]].
 
==Selected books==
* 1967 (1940). ''Lattice Theory, 3rd ed''. American Mathematical Society.
* 1997 (1941) (with [[Saunders Mac Lane]]). ''A Survey of Modern Algebra''. A K Peters. ISBN 1-56881-068-7
* 1978 (1950). ''Hydrodynamics: A study in logic, fact, and similitude ''. Greenwood Press.
* 1957 (with E. Zarantello). ''Jets, Wakes, and Cavities''. Academic Press.
* 1989 (1962) (with [[Gian-Carlo Rota]]). ''Ordinary Differential Equations''. John Wiley.
* 1999 (1967) (with [[Saunders Mac Lane]]). ''Algebra''. Chelsea. ISBN 0-8218-1646-2
* 1970 (with Thomas Bartee). ''Modern Applied Algebra''. McGraw-Hill.
* 1973. ''Source Book in Classical Analysis''. Harvard Uni. Press.
 
==Ver também==
*[[Birkhoff polytope]]
*[[Birkhoff's representation theorem]]
*[[Birkhoff's HSP theorem]]
*[[Birkhoff's theorem]]s
*[[Pierce–Birkhoff conjecture]]
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==Ligações externas==