Modern Geometry Methods and Applications

Modern Geometry   Methods and Applications

To S. P. Novikov are due the original conception and the overall plan of the book. The work of organizing the material contained in the duplicated lecture notes in accordance with this plan was carried out by B. A. Dubrovin.

Author: B.A. Dubrovin

Publisher: Springer Science & Business Media

ISBN: 9781468499469

Category: Mathematics

Page: 464

View: 325

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 along these lines that the archetypal course was taught. It was given more permanent form as duplicated lecture notes published under the auspices of Moscow State University as: Differential Geometry, Parts I and II, by S. P. Novikov, Division of Mechanics, Moscow State University, 1972. Subsequently various parts of the course were altered, and new topics added. This supplementary material was published (also in duplicated form) as Differential Geometry, Part III, by S. P. Novikov and A. T. Fomenko, Division of Mechanics, Moscow State University, 1974. The present book is the outcome of a reworking, re-ordering, and ex tensive elaboration of the above-mentioned lecture notes. It is the authors' view that it will serve as a basic text from which the essentials for a course in modern geometry may be easily extracted. To S. P. Novikov are due the original conception and the overall plan of the book. The work of organizing the material contained in the duplicated lecture notes in accordance with this plan was carried out by B. A. Dubrovin.
Categories: Mathematics

Modern Geometry Methods and Applications

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.

Author: B.A. Dubrovin

Publisher: Springer Science & Business Media

ISBN: 9780387961620

Category: Mathematics

Page: 432

View: 395

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.
Categories: Mathematics

Modern Geometry Methods and Applications

Modern Geometry   Methods and Applications

Both scientists and students of mathematics as well as theoretical physics will find this book to be a valuable reference and text.

Author: B.A. Dubrovin

Publisher: Springer

ISBN: 146128791X

Category: Mathematics

Page: 418

View: 410

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 of these methods together with their main applications in mathematics and physics. This third volume, presented in highly accessible languages, concentrates in homology theory. It contains introductions to the contemporary methods for the calculation of homology groups and the classification of manifesto. Both scientists and students of mathematics as well as theoretical physics will find this book to be a valuable reference and text.
Categories: Mathematics

Modern Geometry

Modern Geometry

Author: B. A. Dubrovin

Publisher:

ISBN: LCCN:83016851

Category: Geometry

Page:

View: 503

Categories: Geometry

Modern Geometry

Modern Geometry

Author: Boris A. Dubrovin

Publisher:

ISBN: 3540908722

Category: Geometry

Page: 416

View: 641

Categories: Geometry

Modern Geometry

Modern Geometry

Author: B. A. Dubrovin

Publisher:

ISBN: OCLC:605916126

Category: Geometry

Page:

View: 209

Categories: Geometry