Background
He was born in Warsaw, Kingdom of Poland and died in New York City, United States of America, where he had spent much of his career as a professor at Columbia University.
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( When this book was written, methods of algebraic topolo...)
When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology (and also cohomology) theory that embodies all three; a large number of results is thus established in a general framework. Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied. The starting point is the notion of a module over a ring. The primary operations are the tensor product of two modules and the groups of all homomorphisms of one module into another. From these, "higher order" derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. This leads in a natural way to the study of "functors" and of their "derived functors." This mathematical masterpiece will appeal to all mathematicians working in algebraic topology.
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mathematician university professor topologist
He was born in Warsaw, Kingdom of Poland and died in New York City, United States of America, where he had spent much of his career as a professor at Columbia University.
Master of Arts, University Warsaw, 1934. Doctor of Philosophy, University Warsaw, 1936. Doctor of Philosophy (honorary), Brandeis University, 1980.
Doctor of Philosophy (honorary), University Pennsylvania, 1985. Doctor of Philosophy (honorary), Columbia University, 1987. University Catholique de Louvain, 1987.
Doctor (honorary), University Paris, 1989.
His thesis advisor was Karol Borsuk. His main interest was algebraic topology. He worked on the axiomatic treatment of homology theory with Norman Steenrod (whose names the Eilenberg–Steenrod axioms bear), and on homological algebra with Saunders Mac Lane.
In the process, Eilenberg and Mac Lane created category theory.
Later in life he worked mainly in pure category theory, being one of the founders of the field The Eilenberg swindle (or telescope) is a construction applying the telescoping cancellation idea to projective modules.
Eilenberg also wrote an important book on automata theory. The X-machine, a form of automaton, was introduced by Eilenberg in 1974.
Eilenberg was also a prominent collector of Asian art
His collection mainly consisted of small sculptures and other artifacts from India, Indonesia, Nepal, Thailand, Cambodia, Sri Lanka and Central Asia. In 1991-1992, the Metropolitan Museum of Art in New York staged an exhibition from more than 400 items that Eilenberg had donated to the museum, entitled The Lotus Transcendent: Indian and Southeast Asian Art From the Samuel Eilenberg Collection".
(This book was originally published prior to 1923, and rep...)
(This book was originally published prior to 1923, and rep...)
( This work has been selected by scholars as being cultur...)
( When this book was written, methods of algebraic topolo...)
(Lang- eng, Pages 344 It is the reproduction of the origin...)
(This is a reproduction of a book published before 1923. T...)
Member National Academy of Sciences, American Mathematics Society (councillor 1947-1959, vice president 1966-1967, Steele prize 1987), London Mathematics Society (honorary), Mathematics Association American, American Academy Arts and Sciences, Southeast Asian Mathematics Society (honorary), New York Academy of Sciences (honorary life), Polish Academy/ Sciences, Calcutta Mathematics Society (honorary), Polish Mathematics Society (honorary).
Married, 1960, divorced, 1969.