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Modern Geometry-Methods and Applications - Part III: Introduction to Homology Theory (Hardcover, 1990 ed.): Robert G Burns Modern Geometry-Methods and Applications - Part III: Introduction to Homology Theory (Hardcover, 1990 ed.)
Robert G Burns; B.A. Dubrovin, A.T. Fomenko, S. P. Novikov
R2,432 Discovery Miles 24 320 Ships in 12 - 17 working days

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.

Modern Geometry - Methods and Applications - Part I: The Geometry of Surfaces, Transformation Groups, and Fields (Hardcover,... Modern Geometry - Methods and Applications - Part I: The Geometry of Surfaces, Transformation Groups, and Fields (Hardcover, 2nd ed. 1992)
R.G. Burns; B.A. Dubrovin, A.T. Fomenko, S. P. Novikov
R1,741 Discovery Miles 17 410 Ships in 12 - 17 working days

This is the first volume of a three-volume introduction to modern geometry, with emphasis on 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 material is explained in as simple and concrete a language as possible, in a terminology acceptable to physicists. The text for the second edition has been substantially revised.

Modern Geometry- Methods and Applications - Part II: The Geometry and Topology of Manifolds (Hardcover, 1985 ed.): R.G. Burns Modern Geometry- Methods and Applications - Part II: The Geometry and Topology of Manifolds (Hardcover, 1985 ed.)
R.G. Burns; B.A. Dubrovin, A.T. Fomenko, S. P. Novikov
R2,213 Discovery Miles 22 130 Ships in 12 - 17 working days

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.

Dynamical Systems IV - Symplectic Geometry and its Applications (Hardcover, 2nd expanded and rev. ed. 2001): V. I. Arnol'd Dynamical Systems IV - Symplectic Geometry and its Applications (Hardcover, 2nd expanded and rev. ed. 2001)
V. I. Arnol'd; Contributions by V. I. Arnol'd; Translated by G. Wassermann, A. Dzhamay; Contributions by B.A. Dubrovin; Edited by …
R4,654 Discovery Miles 46 540 Ships in 12 - 17 working days

From the reviews of the first edition:
..". In general the articles ... are well written in a style that enables one to grasp the ideas. The actual style is a readable mix of the important results, outlines of proofs and complete proofs when it does not take too long together with readable explanations of what is going on. Also very useful are the large lists of references which are important not only for their mathematical content but also because the references given also contain articles in the Soviet literature which may not be familiar or possibly accessible to readers."
"New Zealand Math. Soc. Newsletter 1991"
..". Here ... a wealth of material is displayed for us, too much to even indicate in a review. ... Your reviewer was very impressed by the contents of both volumes (EMS 2 and 4), recommending them without any restriction. As far as he could judge, most presentations seem fairly complete..."
"Mededelingen van het Wiskundig genootshap 1992 "

Modern Geometry- Methods and Applications - Part II: The Geometry and Topology of Manifolds (Paperback, Softcover reprint of... Modern Geometry- Methods and Applications - Part II: The Geometry and Topology of Manifolds (Paperback, Softcover reprint of the original 1st ed. 1985)
R.G. Burns; B.A. Dubrovin, A.T. Fomenko, S. P. Novikov
R2,475 Discovery Miles 24 750 Ships in 10 - 15 working days

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.

Modern Geometry-Methods and Applications - Part III: Introduction to Homology Theory (Paperback, Softcover reprint of the... Modern Geometry-Methods and Applications - Part III: Introduction to Homology Theory (Paperback, Softcover reprint of the original 1st ed. 1990)
Robert G Burns; B.A. Dubrovin, A.T. Fomenko, S. P. Novikov
R1,748 Discovery Miles 17 480 Ships in 10 - 15 working days

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.

Modern Geometry - Methods and Applications - Part I: The Geometry of Surfaces, Transformation Groups, and Fields (Paperback,... Modern Geometry - Methods and Applications - Part I: The Geometry of Surfaces, Transformation Groups, and Fields (Paperback, 2nd ed. 1992. Softcover reprint of the original 2nd ed. 1992)
R.G. Burns; B.A. Dubrovin, A.T. Fomenko, S. P. Novikov
R2,124 Discovery Miles 21 240 Ships in 10 - 15 working days

This is the first volume of a three-volume introduction to modern geometry, with emphasis on 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 material is explained in as simple and concrete a language as possible, in a terminology acceptable to physicists. The text for the second edition has been substantially revised.

Dynamical Systems IV - Symplectic Geometry and its Applications (Paperback, Softcover reprint of hardcover 2nd ed. 2001): V. I.... Dynamical Systems IV - Symplectic Geometry and its Applications (Paperback, Softcover reprint of hardcover 2nd ed. 2001)
V. I. Arnol'd; Contributions by V. I. Arnol'd; Translated by G. Wassermann, A. Dzhamay; Contributions by B.A. Dubrovin; Edited by …
R4,962 Discovery Miles 49 620 Ships in 10 - 15 working days

From the reviews of the first edition:
..". In general the articles ... are well written in a style that enables one to grasp the ideas. The actual style is a readable mix of the important results, outlines of proofs and complete proofs when it does not take too long together with readable explanations of what is going on. Also very useful are the large lists of references which are important not only for their mathematical content but also because the references given also contain articles in the Soviet literature which may not be familiar or possibly accessible to readers."
"New Zealand Math. Soc. Newsletter 1991"
..". Here ... a wealth of material is displayed for us, too much to even indicate in a review. ... Your reviewer was very impressed by the contents of both volumes (EMS 2 and 4), recommending them without any restriction. As far as he could judge, most presentations seem fairly complete..."
"Mededelingen van het Wiskundig genootshap 1992 "

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