Download or read book On the Hypotheses Which Lie at the Bases of Geometry written by Bernhard Riemann and published by Birkhäuser. This book was released on 2016-04-19 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary. The basic concepts and ideas, as well as their mathematical background, are provided, putting Riemann’s reasoning into the more general and systematic perspective achieved by later mathematicians and physicists (including Helmholtz, Ricci, Weyl, and Einstein) on the basis of his seminal ideas. Following a historical introduction that positions Riemann’s work in the context of his times, the history of the concept of space in philosophy, physics and mathematics is systematically presented. A subsequent chapter on the reception and influence of the text accompanies the reader from Riemann’s times to contemporary research. Not only mathematicians and historians of the mathematical sciences, but also readers from other disciplines or those with an interest in physics or philosophy will find this work both appealing and insightful.
Download or read book Lectures on General Relativity written by A. Papapetrou and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an elaboration of lecture notes for the graduate course on General Rela tivity given by the author at Boston University in the spring semester of 1972. It is an introduction to the subject only, as the time available for the course was limited. The author of an introduction to General Relativity is faced from the beginning with the difficult task of choosing which material to include. A general criterion as sisting in this choice is provided by the didactic character of the book: Those chapters have to be included in priority, which will be most useful to the reader in enabling him to understand the methods used in General Relativity, the results obtained so far and possibly the problems still to be solved. This criterion is not sufficient to ensure a unique choice. General Relativity has developed to such a degree, that it is impossible to include in an introductory textbook of a reasonable length even a very condensed treatment of all important problems which have been discussed until now and the author is obliged to decide, in a more or less subjective manner, which of the more recent developments to omit. The following lines indicate by means of some examples the kind of choice made in this book.
Download or read book Semi Riemannian Geometry With Applications to Relativity written by Barrett O'Neill and published by Academic Press. This book was released on 1983-07-29 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.
Download or read book General Relativity written by Hans Stephani and published by Cambridge University Press. This book was released on 1990-06-29 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an excellent introduction to the subjects of gravitation and space-time structure. It discusses the foundations of Riemann geometry; the derivation of Einstein field equations; linearised theory; far fields and gravitational waves; the invariant characterisation of exact solutions; gravitational collapse; cosmology as well as alternative gravitational theories and the problem of quantum gravity.
Download or read book Approaches to Quantum Gravity written by Daniele Oriti and published by Cambridge University Press. This book was released on 2009-03-05 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: Containing contributions from leading researchers in this field, this book provides a complete overview of this field from the frontiers of theoretical physics research for graduate students and researchers. It introduces the most current approaches to this problem, and reviews their main achievements.
Download or read book Symmetries And Curvature Structure In General Relativity written by Graham S Hall and published by World Scientific. This book was released on 2004-04-27 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a text on classical general relativity from a geometrical viewpoint. Introductory chapters are provided on algebra, topology and manifold theory, together with a chapter on the basic ideas of space-time manifolds and Einstein's theory. There is a detailed account of algebraic structures and tensor classification in general relativity and also of the relationships between the metric, connection and curvature structures on space-times. The latter includes chapters on holonomy and sectional curvature. An extensive study is presented of symmetries in general relativity, including isometries, homotheties, conformal symmetries and affine, projective and curvature collineations. Several general properties of such symmetries are studied and a preparatory section on transformation groups and on the properties of Lie algebras of vector fields on manifolds is provided.
Download or read book Solved Problems and Systematic Introduction to Special Relativity written by Michael Tsamparlis and published by Springer Nature. This book was released on with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1976 with total page 964 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Classical General Relativity written by W. B. Bonnor and published by CUP Archive. This book was released on 1984-09-13 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is made up of papers presented at the Conference on Classical General Relativity held at the City University, London, in December 1983. New tests, arising from space experimentation, pulsars and black holes have revitalised the study of Einstein's theory of gravitation (classical general relativity). Nineteen contributors survey recent progress and identify future avenues of research.
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Download or read book Weyl and the Problem of Space written by Julien Bernard and published by Springer Nature. This book was released on 2019-10-09 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates Hermann Weyl’s work on the problem of space from the early 1920s onwards. It presents new material and opens the philosophical problem of space anew, crossing the disciplines of mathematics, history of science and philosophy. With a Kantian starting point Weyl asks: among all the infinitely many conceivable metrical spaces, which one applies to the physical world? In agreement with general relativity, Weyl acknowledges that the metric can quantitatively vary with the physical situation. Despite this freedom, Weyl “deduces”, with group-theoretical technicalities, that there is only one “kind” of legitimate metric. This construction was then decisive for the development of gauge theories. Nevertheless, the question of the foundations of the metric of physical theories is only a piece of a wider epistemological problem. Contributing authors mark out the double trajectory that goes through Weyl’s texts, from natural science to philosophy and conversely, always through the mediation of mathematics. Readers may trace the philosophical tradition to which Weyl refers and by which he is inspired (Kant, Husserl, Fichte, Leibniz, Becker etc.), and explore the mathematical tradition (Riemann, Helmholtz, Lie, Klein) that permitted Weyl to elaborate and solve his mathematical problem of space. Furthermore, this volume analyzes the role of the interlocutors with whom Weyl discussed the nature of physical space (Einstein, Cartan, De Sitter, Schrödinger, Eddington). This volume features the work of top specialists and will appeal to postgraduates and scholars in philosophy, the history of science, mathematics, or physics.
Download or read book Handbook of Mathematics written by Vialar Thierry and published by BoD - Books on Demand. This book was released on 2023-08-22 with total page 1134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book, revised, consists of XI Parts and 28 Chapters covering all areas of mathematics. It is a tool for students, scientists, engineers, students of many disciplines, teachers, professionals, writers and also for a general reader with an interest in mathematics and in science. It provides a wide range of mathematical concepts, definitions, propositions, theorems, proofs, examples, and numerous illustrations. The difficulty level can vary depending on chapters, and sustained attention will be required for some. The structure and list of Parts are quite classical: I. Foundations of Mathematics, II. Algebra, III. Number Theory, IV. Geometry, V. Analytic Geometry, VI. Topology, VII. Algebraic Topology, VIII. Analysis, IX. Category Theory, X. Probability and Statistics, XI. Applied Mathematics. Appendices provide useful lists of symbols and tables for ready reference. Extensive cross-references allow readers to find related terms, concepts and items (by page number, heading, and objet such as theorem, definition, example, etc.). The publisher’s hope is that this book, slightly revised and in a convenient format, will serve the needs of readers, be it for study, teaching, exploration, work, or research.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1969 with total page 1508 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Sixth Canadian Conference on General Relativity and Relativistic Astrophysics written by Stephen Paul Braham and published by American Mathematical Soc.. This book was released on 1997 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the refereed proceedings of the Sixth Canadian Conference on General Relativity and Relativistic Astrophysics held in May 1995 at the University of New Brunswick. The book includes invited talks and contributed talks and posters including state-of-the-art reviews of many of the most recent important developments in gravitational physics. This book would serve as a good supplement to standard texts on the topic. It features: review articles in key areas - black holes, numerical relativity, etc.; contributions covering most of gravitational physics; useful articles for students who wish to begin exploring the issues discussed; and, invited talks given by researchers known for their ability to communicate their expertise.
Download or read book The Riemann Legacy written by Krzysztof Maurin and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: very small domain (environment) affects through analytic continuation the whole of Riemann surface, or analytic manifold . Riemann was a master at applying this principle and also the first who noticed and emphasized that a meromorphic function is determined by its 'singularities'. Therefore he is rightly regarded as the father of the huge 'theory of singularities' which is developing so quickly and whose importance (also for physics) can hardly be overe~timated. Amazing and mysterious for our cognition is the role of Euclidean space. Even today many philosophers believe (following Kant) that 'real space' is Euclidean and other spaces being 'abstract constructs of mathematicians, should not be called spaces'. The thesis is no longer tenable - the whole of physics testifies to that. Nevertheless, there is a grain of truth in the 3 'prejudice': E (three-dimensional Euclidean space) is special in a particular way pleasantly familiar to us - in it we (also we mathematicians!) feel particularly 'confident' and move with a sense of greater 'safety' than in non-Euclidean spaces. For this reason perhaps, Riemann space M stands out among the multitude of 'interesting geometries'. For it is: 1. Locally Euclidean, i. e. , M is a differentiable manifold whose tangent spaces TxM are equipped with Euclidean metric Uxi 2. Every submanifold M of Euclidean space E is equipped with Riemann natural metric (inherited from the metric of E) and it is well known how often such submanifolds are used in mechanics (e. g. , the spherical pendulum).
Download or read book Modern Geometry Methods and Applications written by B.A. Dubrovin and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Methodological Unity of Science written by M. Bunge and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume collects some of the talks given at the Bertrand Russell Colloquium on Exact Philosophy, attached to the McGill University Foundations and Philosophy of Science Unit. It also includes a paper, on Bertrand Russell's method of philosophizing, read at the memorial symposium held at Sir Gorge Williams University shortly after the philosopher's death. All the papers appear here for the first time. Unlike many a philosophy of science anthology, this one is not center ed on the philosophy of physics. In fact the papers deal with conceptual and, in particular, philosophical problems that pop up in almost every one of the provinces of the vast territory constituted by the foundations, meth odology and philosophy of science. A couple of border territories which are in the process of being infiltrated have been added for good measure. The inclusion of papers in the philosophy of formal science and in the philosophies of physics and of biology, in a volume belonging to a series devoted to the philosophy and methodology of the social and behavioral sciences, should raise no eyebrows. Because the sciences of man make use of logic and mathematics, they are interested in questions such as whether the formal sciences have anything to do with reality (rather than with our theories about reality) and whether or not logic has kept up with the practice of mathematicians. These two problems are tackled in Part II, on the philosophy of formal science.
