Transformation Groups For Beginners
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Transformation Groups For Beginners
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Author : Sergeĭ Vasilʹevich Duzhin
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Transformation Groups For Beginners written by Sergeĭ Vasilʹevich Duzhin 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 2004 with Mathematics categories.
Presents a discussion of algebraic operations on the points in the plane and rigid motions in the Euclidean plane. This work introduces the notions of a transformation group and of an abstract group. It gives an elementary exposition of the basic ideas of Sophus Lie about symmetries of differential equations.
Transformation Groups For Beginners
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Author : Sergeĭ Vasilʹevich Duzhin
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Transformation Groups For Beginners written by Sergeĭ Vasilʹevich Duzhin 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 2004 with MATHEMATICS categories.
This book is intended for undergraduate students and all those interested in mathematics. Its goal is to give an easy introduction to the concept of a transformation group using examples from different areas of mathematics. The warm-up of the first two chapters includes a discussion of algebraic operations on points in the plane, and of Euclidean plane movements. Then the notions of a transformation group and of an abstract group are introduced. Group actions, orbits, and invariants constitute the subject of the next chapter. The book concludes with an elementary exposition of the basic ideas of Sophus Lie about symmetries of differential equations. The book contains plenty of figures, as well as many exercises with hints and solutions, which help the reader to master the material.
Transformation Groups And Algebraic K Theory
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Author : Wolfgang Lück
language : en
Publisher: Springer
Release Date : 2006-11-14
Transformation Groups And Algebraic K Theory written by Wolfgang Lück and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The book focuses on the relation between transformation groups and algebraic K-theory. The general pattern is to assign to a geometric problem an invariant in an algebraic K-group which determines the problem. The algebraic K-theory of modules over a category is studied extensively and appplied to the fundamental category of G-space. Basic details of the theory of transformation groups sometimes hard to find in the literature, are collected here (Chapter I) for the benefit of graduate students. Chapters II and III contain advanced new material of interest to researchers working in transformation groups, algebraic K-theory or related fields.
Transformation Groups In Differential Geometry
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Author : Shoshichi Kobayashi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Transformation Groups In Differential Geometry written by Shoshichi Kobayashi 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.
Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. The object of this book is to give a biased account of automorphism groups of differential geometric struc tures. All geometric structures are not created equal; some are creations of ~ods while others are products of lesser human minds. Amongst the former, Riemannian and complex structures stand out for their beauty and wealth. A major portion of this book is therefore devoted to these two structures. Chapter I describes a general theory of automorphisms of geometric structures with emphasis on the question of when the automorphism group can be given a Lie group structure. Basic theorems in this regard are presented in §§ 3, 4 and 5. The concept of G-structure or that of pseudo-group structure enables us to treat most of the interesting geo metric structures in a unified manner. In § 8, we sketch the relationship between the two concepts. Chapter I is so arranged that the reader who is primarily interested in Riemannian, complex, conformal and projective structures can skip §§ 5, 6, 7 and 8. This chapter is partly based on lec tures I gave in Tokyo and Berkeley in 1965.
Cohomological Methods In Transformation Groups
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Author : C. Allday
language : en
Publisher: Cambridge University Press
Release Date : 1993-07
Cohomological Methods In Transformation Groups written by C. Allday and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-07 with Mathematics categories.
This is an account of the theory of certain types of compact transformation groups, namely those that are susceptible to study using ordinary cohomology theory and rational homotopy theory, which in practice means the torus groups and elementary abelian p-groups. The efforts of many mathematicians have combined to bring a depth of understanding to this area. However to make it reasonably accessible to a wide audience, the authors have streamlined the presentation, referring the reader to the literature for purely technical results and working in a simplified setting where possible. In this way the reader with a relatively modest background in algebraic topology and homology theory can penetrate rather deeply into the subject, whilst the book at the same time makes a useful reference for the more specialised reader.
Topological Transformation Groups
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Author : Deane Montgomery
language : en
Publisher: Courier Dover Publications
Release Date : 2018-06-13
Topological Transformation Groups written by Deane Montgomery and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-13 with Mathematics categories.
Originally published: New York: Interscience Publishers, Inc., 1955. An unabridged republication of: Huntington, New York: Robert E. Krieger Publishing Company, 1974.
Transformation Groups
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Author : Tammo tom Dieck
language : en
Publisher: Walter de Gruyter
Release Date : 1987
Transformation Groups written by Tammo tom Dieck and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
Transformation Groups Applied To Mathematical Physics
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Author : Nail H. Ibragimov
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-30
Transformation Groups Applied To Mathematical Physics written by Nail H. Ibragimov 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 2001-11-30 with Science categories.
Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then It is that they can't see the problem. one day, perhaps you will find the final question. G.K. Chesterton. The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R.van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in - gional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in pack ing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Introduction To Compact Transformation Groups
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Author :
language : en
Publisher: Academic Press
Release Date : 1972-09-29
Introduction To Compact Transformation Groups written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-09-29 with Mathematics categories.
Introduction to Compact Transformation Groups
From Groups To Geometry And Back
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Author : Vaughn Climenhaga
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-04-07
From Groups To Geometry And Back written by Vaughn Climenhaga 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 2017-04-07 with Mathematics categories.
Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering spaces and deck transformations. In the other direction, Cayley graphs, planar models, and fundamental domains appear as geometric objects associated to groups. The final chapter discusses groups themselves as geometric objects, including a gentle introduction to Gromov's theorem on polynomial growth and Grigorchuk's example of intermediate growth. The book is accessible to undergraduate students (and anyone else) with a background in calculus, linear algebra, and basic real analysis, including topological notions of convergence and connectedness. This book is a result of the MASS course in algebra at Penn State University in the fall semester of 2009.