Modern Geometry Methods And Applications

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Modern Geometry Methods And Applications

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Author : B. A. Dubrovin
language : en
Publisher: Springer Science & Business Media
Release Date : 1984

Modern Geometry Methods And Applications written by B. A. Dubrovin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Geometry categories.

Part II. The geometry and topology of manifolds. This is the second volume of a three-volume introduction to modern geometry, with emphasis on applications to other areas of mathematics and theoretical physics. Topics covered include homotopy groups, fibre bundles, dynamical systems, and foliations. The exposition is simple and concrete, and in a terminology palatable to physicists.

Modern Geometry Methods And Applications

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Author : B.A. Dubrovin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Modern Geometry Methods And Applications written by B.A. Dubrovin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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

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Author : B.A. Dubrovin
language : en
Publisher: Springer
Release Date : 1984-03-16

Modern Geometry Methods And Applications written by B.A. Dubrovin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-03-16 with Mathematics categories.

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.

Modern Geometry Methods And Applications

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Author : B.A. Dubrovin
language : en
Publisher: Springer
Release Date : 1984-03-16

Modern Geometry Methods And Applications written by B.A. Dubrovin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-03-16 with Mathematics categories.

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.

Modern Geometry

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Author : A. T. Fomenko
language : en
Publisher:
Release Date : 1992

Modern Geometry written by A. T. Fomenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Geometry categories.

Geometric Methods And Applications

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Author : Jean Gallier
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-04

Geometric Methods And Applications written by Jean Gallier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-04 with Mathematics categories.

This book is an introduction to the fundamental concepts and tools needed for solving problems of a geometric nature using a computer. It attempts to fill the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, robotics, or machine learning. This book covers the following topics: affine geometry, projective geometry, Euclidean geometry, convex sets, SVD and principal component analysis, manifolds and Lie groups, quadratic optimization, basics of differential geometry, and a glimpse of computational geometry (Voronoi diagrams and Delaunay triangulations). Some practical applications of the concepts presented in this book include computer vision, more specifically contour grouping, motion interpolation, and robot kinematics. In this extensively updated second edition, more material on convex sets, Farkas’s lemma, quadratic optimization and the Schur complement have been added. The chapter on SVD has been greatly expanded and now includes a presentation of PCA. The book is well illustrated and has chapter summaries and a large number of exercises throughout. It will be of interest to a wide audience including computer scientists, mathematicians, and engineers. Reviews of first edition: "Gallier's book will be a useful source for anyone interested in applications of geometrical methods to solve problems that arise in various branches of engineering. It may help to develop the sophisticated concepts from the more advanced parts of geometry into useful tools for applications." (Mathematical Reviews, 2001) "...it will be useful as a reference book for postgraduates wishing to find the connection between their current problem and the underlying geometry." (The Australian Mathematical Society, 2001)

Modern Geometry With Applications

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Author : George A. Jennings
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-06-12

Modern Geometry With Applications written by George A. Jennings and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-12 with Mathematics categories.

This introduction to modern geometry differs from other books in the field due to its emphasis on applications and its discussion of special relativity as a major example of a non-Euclidean geometry. Additionally, it covers the two important areas of non-Euclidean geometry, spherical geometry and projective geometry, as well as emphasising transformations, and conics and planetary orbits. Much emphasis is placed on applications throughout the book, which motivate the topics, and many additional applications are given in the exercises. It makes an excellent introduction for those who need to know how geometry is used in addition to its formal theory.

Modern Geometry Methods And Applications

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Author : B.A. Dubrovin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Modern Geometry Methods And Applications written by B.A. Dubrovin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

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.

Modern Geometry

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Author : B. A. Dubrovin
language : en
Publisher:
Release Date : 1984

Modern Geometry written by B. A. Dubrovin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Geometry categories.

Geometry And The Imagination

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Author : D. Hilbert
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-03-17

Geometry And The Imagination written by D. Hilbert and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-17 with Education categories.

This remarkable book has endured as a true masterpiece of mathematical exposition. There are few mathematics books that are still so widely read and continue to have so much to offer—even after more than half a century has passed! The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians. “Hilbert and Cohn-Vossen” is full of interesting facts, many of which you wish you had known before. It's also likely that you have heard those facts before, but surely wondered where they could be found. The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in R 3 R3. In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: π/4=1−1/3+1/5−1/7+−… π/4=1−1/3+1/5−1/7+−…. In the section on lattices in three and more dimensions, the authors consider sphere-packing problems, including the famous Kepler problem. One of the most remarkable chapters is “Projective Configurations”. In a short introductory section, Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. Here, we see regular polyhedra again, from a different perspective. One of the high points of the chapter is the discussion of Schlafli's Double-Six, which leads to the description of the 27 lines on the general smooth cubic surface. As is true throughout the book, the magnificent drawings in this chapter immeasurably help the reader. A particularly intriguing section in the chapter on differential geometry is Eleven Properties of the Sphere. Which eleven properties of such a ubiquitous mathematical object caught their discerning eye and why? Many mathematicians are familiar with the plaster models of surfaces found in many mathematics departments. The book includes pictures of some of the models that are found in the Göttingen collection. Furthermore, the mysterious lines that mark these surfaces are finally explained! The chapter on kinematics includes a nice discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. This is another example of a simple situation that leads to a rich geometry. It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. It surely belongs in the “pantheon” of great mathematics books.