Modern Geometry Methods and Applications

Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education.

Modern Geometry    Methods and Applications

Author: B.A. Dubrovin

Publisher: Springer

ISBN: 9781461270119

Page: 432

View: 248

Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e.

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Books about Modern Geometry - Methods and Applications
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Language: en
Pages: 464
Authors: B.A. Dubrovin, A.T. Fomenko, S.P. Novikov
Categories: Mathematics
Type: BOOK - Published: 2013-03-14 - Publisher: Springer Science & Business Media

manifolds, transformation groups, and Lie algebras, as well as the basic concepts of visual topology. It was also agreed that the course should be given in as simple and concrete a language as possible, and that wherever practic able the terminology should be that used by physicists. Thus it was
Modern Geometry—Methods and Applications
Language: en
Pages: 418
Authors: B.A. Dubrovin, A.T. Fomenko, S.P. Novikov
Categories: Mathematics
Type: BOOK - Published: 2011-12-23 - Publisher: Springer

Over the past fifteen years, the geometrical and topological methods of the theory of manifolds have as- sumed a central role in the most advanced areas of pure and applied mathematics as well as theoretical physics. The three volumes of Modern Geometry - Methods and Applications contain a concrete exposition
Modern Geometry — Methods and Applications
Language: en
Pages: 470
Authors: B.A. Dubrovin, A.T. Fomenko, S.P. Novikov
Categories: Mathematics
Type: BOOK - Published: 2011-10-28 - Publisher: Springer

This is the first volume of a three-volume introduction to modern geometry which emphasizes applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory. This new edition offers substantial revisions,