On the Hypotheses Which Lie at the Bases of Geometry

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Publisher : Birkhäuser
ISBN 13 : 3319260421
Total Pages : 181 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis On the Hypotheses Which Lie at the Bases of Geometry by : Bernhard Riemann

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.

Beyond Geometry

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Publisher : Courier Corporation
ISBN 13 : 0486453502
Total Pages : 226 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Beyond Geometry by : Peter Pesic

Download or read book Beyond Geometry written by Peter Pesic and published by Courier Corporation. This book was released on 2007-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eight essays trace seminal ideas about the foundations of geometry that led to the development of Einstein's general theory of relativity. This is the only English-language collection of these important papers, some of which are extremely hard to find. Contributors include Helmholtz, Klein, Clifford, Poincaré, and Cartan.

Proceedings of the Indiana Academy of Science

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Publisher :
ISBN 13 :
Total Pages : 1078 pages
Book Rating : 4.A/5 ( download)

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Book Synopsis Proceedings of the Indiana Academy of Science by : Indiana Academy of Science

Download or read book Proceedings of the Indiana Academy of Science written by Indiana Academy of Science and published by . This book was released on 1898 with total page 1078 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometry - Intuition and Concepts

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Publisher : Springer Nature
ISBN 13 : 3658386401
Total Pages : 168 pages
Book Rating : 4.6/5 (583 download)

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Book Synopsis Geometry - Intuition and Concepts by : Jost-Hinrich Eschenburg

Download or read book Geometry - Intuition and Concepts written by Jost-Hinrich Eschenburg and published by Springer Nature. This book was released on 2022-10-31 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the geometry of visual space in all its aspects. As in any branch of mathematics, the aim is to trace the hidden to the obvious; the peculiarity of geometry is that the obvious is sometimes literally before one's eyes.Starting from intuition, spatial concepts are embedded in the pre-existing mathematical framework of linear algebra and calculus. The path from visualization to mathematically exact language is itself the learning content of this book. This is intended to close an often lamented gap in understanding between descriptive preschool and school geometry and the abstract concepts of linear algebra and calculus. At the same time, descriptive geometric modes of argumentation are justified because their embedding in the strict mathematical language has been clarified. The concepts of geometry are of a very different nature; they denote, so to speak, different layers of geometric thinking: some arguments use only concepts such as point, straight line, and incidence, others require angles and distances, still others symmetry considerations. Each of these conceptual fields determines a separate subfield of geometry and a separate chapter of this book, with the exception of the last-mentioned conceptual field "symmetry", which runs through all the others: - Incidence: Projective geometry - Parallelism: Affine geometry - Angle: Conformal Geometry - Distance: Metric Geometry - Curvature: Differential Geometry - Angle as distance measure: Spherical and Hyperbolic Geometry - Symmetry: Mapping Geometry. The mathematical experience acquired in the visual space can be easily transferred to much more abstract situations with the help of the vector space notion. The generalizations beyond the visual dimension point in two directions: Extension of the number concept and transcending the three illustrative dimensions. This book is a translation of the original German 1st edition Geometrie – Anschauung und Begriffe by Jost-Hinrich Eschenburg, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.

God Created The Integers

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Publisher : Running Press Adult
ISBN 13 : 0762432721
Total Pages : 1053 pages
Book Rating : 4.7/5 (624 download)

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Book Synopsis God Created The Integers by : Stephen Hawking

Download or read book God Created The Integers written by Stephen Hawking and published by Running Press Adult. This book was released on 2007-03-29 with total page 1053 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bestselling author and physicist Stephen Hawking explores the "masterpieces" of mathematics, 25 landmarks spanning 2,500 years and representing the work of 15 mathematicians, including Augustin Cauchy, Bernard Riemann, and Alan Turing. This extensive anthology allows readers to peer into the mind of genius by providing them with excerpts from the original mathematical proofs and results. It also helps them understand the progression of mathematical thought, and the very foundations of our present-day technologies. Each chapter begins with a biography of the featured mathematician, clearly explaining the significance of the result, followed by the full proof of the work, reproduced from the original publication.

An Aristotelian Realist Philosophy of Mathematics

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Publisher : Springer
ISBN 13 : 1137400730
Total Pages : 316 pages
Book Rating : 4.1/5 (374 download)

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Book Synopsis An Aristotelian Realist Philosophy of Mathematics by : J. Franklin

Download or read book An Aristotelian Realist Philosophy of Mathematics written by J. Franklin and published by Springer. This book was released on 2014-04-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.

Differential Geometry in the Large

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Publisher : Cambridge University Press
ISBN 13 : 1108879993
Total Pages : 402 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Differential Geometry in the Large by : Owen Dearricott

Download or read book Differential Geometry in the Large written by Owen Dearricott and published by Cambridge University Press. This book was released on 2020-10-22 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2019 'Australian-German Workshop on Differential Geometry in the Large' represented an extraordinary cross section of topics across differential geometry, geometric analysis and differential topology. The two-week programme featured talks from prominent keynote speakers from across the globe, treating geometric evolution equations, structures on manifolds, non-negative curvature and Alexandrov geometry, and topics in differential topology. A joy to the expert and novice alike, this proceedings volume touches on topics as diverse as Ricci and mean curvature flow, geometric invariant theory, Alexandrov spaces, almost formality, prescribed Ricci curvature, and Kähler and Sasaki geometry.

Lobachevsky Geometry and Modern Nonlinear Problems

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Publisher : Springer
ISBN 13 : 3319056697
Total Pages : 315 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Lobachevsky Geometry and Modern Nonlinear Problems by : Andrey Popov

Download or read book Lobachevsky Geometry and Modern Nonlinear Problems written by Andrey Popov and published by Springer. This book was released on 2014-08-06 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the basic concepts of hyperbolic Lobachevsky geometry and their possible applications to modern nonlinear applied problems in mathematics and physics, summarizing the findings of roughly the last hundred years. The central sections cover the classical building blocks of hyperbolic Lobachevsky geometry, pseudo spherical surfaces theory, net geometrical investigative techniques of nonlinear differential equations in partial derivatives, and their applications to the analysis of the physical models. As the sine-Gordon equation appears to have profound “geometrical roots” and numerous applications to modern nonlinear problems, it is treated as a universal “object” of investigation, connecting many of the problems discussed. The aim of this book is to form a general geometrical view on the different problems of modern mathematics, physics and natural science in general in the context of non-Euclidean hyperbolic geometry.

Embracing Beauty

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Publisher : Cambridge University Press
ISBN 13 : 1107124131
Total Pages : 279 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Embracing Beauty by : John Heard

Download or read book Embracing Beauty written by John Heard and published by Cambridge University Press. This book was released on 2019-04-11 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traces the development of pure mathematics during the long nineteenth century in Britain, with extensive references and primary sources.

Computational Models in Architecture

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Publisher : Birkhäuser
ISBN 13 : 3035618623
Total Pages : 296 pages
Book Rating : 4.0/5 (356 download)

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Book Synopsis Computational Models in Architecture by : Nikola Marinčić

Download or read book Computational Models in Architecture written by Nikola Marinčić and published by Birkhäuser. This book was released on 2019-04-18 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This scientific work focuses on computer-aided computational models in architecture. The author initially investigates established computational models and then expands these with newer approaches to modeling. In his research the author integrates approaches to analytical philosophy, probability theory, formal logic, quantum physics, abstract algebra, computer-aided design, computer graphics, glossematics, machine learning, architecture, and others. For researchers in the fields of information technology and architecture.

Mathematical Principles of Topological and Geometric Data Analysis

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Publisher : Springer Nature
ISBN 13 : 303133440X
Total Pages : 287 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Mathematical Principles of Topological and Geometric Data Analysis by : Parvaneh Joharinad

Download or read book Mathematical Principles of Topological and Geometric Data Analysis written by Parvaneh Joharinad and published by Springer Nature. This book was released on 2023-07-29 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores and demonstrates how geometric tools can be used in data analysis. Beginning with a systematic exposition of the mathematical prerequisites, covering topics ranging from category theory to algebraic topology, Riemannian geometry, operator theory and network analysis, it goes on to describe and analyze some of the most important machine learning techniques for dimension reduction, including the different types of manifold learning and kernel methods. It also develops a new notion of curvature of generalized metric spaces, based on the notion of hyperconvexity, which can be used for the topological representation of geometric information. In recent years there has been a fascinating development: concepts and methods originally created in the context of research in pure mathematics, and in particular in geometry, have become powerful tools in machine learning for the analysis of data. The underlying reason for this is that data are typically equipped with some kind of notion of distance, quantifying the differences between data points. Of course, to be successfully applied, the geometric tools usually need to be redefined, generalized, or extended appropriately. Primarily aimed at mathematicians seeking an overview of the geometric concepts and methods that are useful for data analysis, the book will also be of interest to researchers in machine learning and data analysis who want to see a systematic mathematical foundation of the methods that they use.

Curvature of Space and Time, with an Introduction to Geometric Analysis

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Publisher : American Mathematical Soc.
ISBN 13 : 1470456281
Total Pages : 243 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Curvature of Space and Time, with an Introduction to Geometric Analysis by : Iva Stavrov

Download or read book Curvature of Space and Time, with an Introduction to Geometric Analysis written by Iva Stavrov and published by American Mathematical Soc.. This book was released on 2020-11-12 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein field equations. After addressing concepts in geometry such as metrics, covariant differentiation, tensor calculus and curvature, the book explains the mathematical framework for both special and general relativity. Relativistic concepts discussed include (initial value formulation of) the Einstein equations, stress-energy tensor, Schwarzschild space-time, ADM mass and geodesic incompleteness. The concluding chapters of the book introduce the reader to geometric analysis: original results of the author and her undergraduate student collaborators illustrate how methods of analysis and differential equations are used in addressing questions from geometry and relativity. The book is mostly self-contained and the reader is only expected to have a solid foundation in multivariable and vector calculus and linear algebra. The material in this book was first developed for the 2013 summer program in geometric analysis at the Park City Math Institute, and was recently modified and expanded to reflect the author's experience of teaching mathematical general relativity to advanced undergraduates at Lewis & Clark College.

Complex Nonlinearity

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Publisher : Springer Science & Business Media
ISBN 13 : 3540793577
Total Pages : 855 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Complex Nonlinearity by : Vladimir G. Ivancevic

Download or read book Complex Nonlinearity written by Vladimir G. Ivancevic and published by Springer Science & Business Media. This book was released on 2008-05-31 with total page 855 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to the topology change of this curved geometrical stage, usually called configuration manifold. Chapter 3 elaborates on geometry and topology change in relation with complex nonlinearity and chaos. Chapter 4 develops general nonlinear dynamics, continuous and discrete, deterministic and stochastic, in the unique form of path integrals and their action-amplitude formalism. This most natural framework for representing both phase transitions and topology change starts with Feynman’s sum over histories, to be quickly generalized into the sum over geometries and topologies. The last Chapter puts all the previously developed techniques together and presents the unified form of complex nonlinearity. Here we have chaos, phase transitions, geometrical dynamics and topology change, all working together in the form of path integrals. The objective of this book is to provide a serious reader with a serious scientific tool that will enable them to actually perform a competitive research in modern complex nonlinearity. It includes a comprehensive bibliography on the subject and a detailed index. Target readership includes all researchers and students of complex nonlinear systems (in physics, mathematics, engineering, chemistry, biology, psychology, sociology, economics, medicine, etc.), working both in industry/clinics and academia.

Probabilistic Models of Cosmic Backgrounds

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Publisher : CRC Press
ISBN 13 : 1040021271
Total Pages : 705 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Probabilistic Models of Cosmic Backgrounds by : Anatoliy Malyarenko

Download or read book Probabilistic Models of Cosmic Backgrounds written by Anatoliy Malyarenko and published by CRC Press. This book was released on 2024-06-30 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining research methods from various areas of mathematics and physics, Probabilistic Models of Cosmic Backgrounds describes the isotropic random sections of certain fibre bundles and their applications to creating rigorous mathematical models of both discovered and hypothetical cosmic backgrounds. Previously scattered and hard-to-find mathematical and physical theories have been assembled from numerous textbooks, monographs, and research papers, and explained from different or even unexpected points of view. This consists of both classical and newly discovered results necessary for understanding a sophisticated problem of modelling cosmic backgrounds. The book contains a comprehensive description of mathematical and physical aspects of cosmic backgrounds with a clear focus on examples and explicit calculations. Its reader will bridge the gap of misunderstanding between the specialists in various theoretical and applied areas who speak different scientific languages. The audience of the book consists of scholars, students, and professional researchers. A scholar will find basic material for starting their own research. A student will use the book as supplementary material for various courses and modules. A professional mathematician will find a description of several physical phenomena at the rigorous mathematical level. A professional physicist will discover mathematical foundations for well-known physical theories.

Structure of Space and the Submicroscopic Deterministic Concept of Physics

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Publisher : CRC Press
ISBN 13 : 1771885319
Total Pages : 472 pages
Book Rating : 4.7/5 (718 download)

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Book Synopsis Structure of Space and the Submicroscopic Deterministic Concept of Physics by : Volodymyr Krasnoholovets

Download or read book Structure of Space and the Submicroscopic Deterministic Concept of Physics written by Volodymyr Krasnoholovets and published by CRC Press. This book was released on 2017-07-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, Structure of Space and the Submicroscopic Deterministic Concept of Physics, completely formalizes fundamental physics by showing that all space, which consists of objects and distances, arises from the same origin: manifold of sets. A continuously organized mathematical lattice of topological balls represents the primary substrate named the tessellattice. All fundamental particles arise as local fractal deformations of the tessellattice. The motion of such particulate balls through the tessellattice causes it to deform neighboring cells, which generates a cloud of a new kind of spatial excitations named ‘inertons’. Thus, so-called "hidden variables" introduced in the past by de Broglie, Bohm and Vigier have acquired a sense of real quasiparticles of space.This theory of space unambiguously answers such challenging issues as: what is mass, what is charge, what is a photon, what is the wave psi-function, what is a neutrino, what are the nuclear forces, and so on. The submicroscopic concept uncovers new peculiar properties of quantum systems, especially the dynamics of particles within a section equal to the particle’s de Broglie wavelength, which are fundamentally impossible for quantum mechanics. This concept, thoroughly discussed in the book, allows one to study complex problems in quantum optics and quantum electrodynamics in detail, to disclose an inner world of particle physics by exposing the structure of quarks and nucleons in real space, and to derive gravity as the transfer of local deformations of space by inertons which in turn completely solves the problems of dark matter and dark energy. Inertons have revealed themselves in a number of experiments carried out in condensed media, plasma, nuclear physics and astrophysics, which are described in this book together with prospects for future studies in both fundamental and applied physics.

Space

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Publisher : Routledge
ISBN 13 : 1000528561
Total Pages : 344 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Space by : Peter Merriman

Download or read book Space written by Peter Merriman and published by Routledge. This book was released on 2022-02-09 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Space is the first accessible text which provides a comprehensive examination of approaches that have crossed between such diverse fields as philosophy, physics, architecture, sociology, anthropology, and geography. The text examines the influence of geometry, arithmetic, natural philosophy, empiricism, and positivism to the development of spatial thinking, as well as focusing on the contributions of phenomenologists, existentialists, psychologists, Marxists, and post-structuralists to how we occupy, live, structure, and perform spaces and practices of spacing. The book emphasises the multiple and partial construction of spaces through the embodied practices of diverse subjects, highlighting the contributions of feminists, queer theorists, anthropologists, sociologists, and post-colonial scholars to academic debates. In contrast to contemporary studies which draw a clear line between scientific and particularly quantitative approaches to space and spatiality and more ‘lived’ human enactments and performances, this book highlights the continual influence of different mathematical and philosophical understandings of space and spatiality on everyday western spatial imaginations and registers in the twenty-first century. Space is possibly the key concept underpinning research in geography, as well as being of central importance to scholars and practitioners working across the arts, humanities, social sciences, and physical sciences.

The Foundations of Einstein's Theory of Gravitation

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Publisher :
ISBN 13 :
Total Pages : 86 pages
Book Rating : 4.X/5 (1 download)

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Book Synopsis The Foundations of Einstein's Theory of Gravitation by : Erwin Freundlich

Download or read book The Foundations of Einstein's Theory of Gravitation written by Erwin Freundlich and published by . This book was released on 1922 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: