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This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic D-modules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are well-known researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology.
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Homological Algebra (Hardcover, 1994 ed.)
S.I. Gelfand; Edited by A.I. Kostrikin; Translated by S.I. Gelfand; Yu. I. Manin; Edited by I.R. Shafarevich; Translated by …
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R3,098
Discovery Miles 30 980
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Ships in 10 - 15 working days
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This book, the first printing of which was published as volume 38
of the Encyclopaedia of Mathematical Sciences, presents a modern
approach to homological algebra, based on the systematic use of the
terminology and ideas of derived categories and derived functors.
The book contains applications of homological algebra to the theory
of sheaves on topological spaces, to Hodge theory, and to the
theory of modules over rings of algebraic differential operators
(algebraic D-modules). The authors Gelfand and Manin explain all
the main ideas of the theory of derived categories. Both authors
are well-known researchers and the second, Manin, is famous for his
work in algebraic geometry and mathematical physics. The book is an
excellent reference for graduate students and researchers in
mathematics and also for physicists who use methods from algebraic
geometry and algebraic topology.
In a departure from traditional teaching methods, this text focuses on theory more than computations, relying on independent study. Its material is geared toward aspects of high-school mathematics that promise to prove particularly useful for future studies and work. The first of three chapters deals with sequences, their definitions, and methods of mathematic induction. The next chapter addresses combinations, and the final chapter examines limits through a series of introductory problems, problems related to the definition of limit, and problems related to the computation of limits. Answers and hints to the test problems are provided, and "road signs" appear in the margins, marking passages requiring particular attention. 1969 ed.
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