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On the Hypotheses Which Lie at the Bases of Geometry

On the Hypotheses Which Lie at the Bases of Geometry
Author: Bernhard Riemann
Publisher: Birkhäuser
Total Pages: 172
Release: 2016-04-19
Genre: Mathematics
ISBN: 3319260421

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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.


The Development of Peirce's Philosophy

The Development of Peirce's Philosophy
Author: Murray G. Murphey
Publisher: Hackett Publishing
Total Pages: 454
Release: 1993-01-01
Genre: Philosophy
ISBN: 9780872201835

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A reprint of the Harvard University Press edition of 1961. Includes a new preface and a new appendix with footnotes keyed to the manuscript classifications by Max Fisch.


Mathematical Papers

Mathematical Papers
Author: William Kingdon Clifford
Publisher:
Total Pages: 776
Release: 1882
Genre: Mathematics
ISBN:

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Beyond Geometry

Beyond Geometry
Author: Peter Pesic
Publisher: Courier Corporation
Total Pages: 226
Release: 2007-01-01
Genre: Mathematics
ISBN: 0486453502

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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.


Computational Models in Architecture

Computational Models in Architecture
Author: Nikola Marinčić
Publisher: Birkhäuser
Total Pages: 296
Release: 2019-04-18
Genre: Architecture
ISBN: 3035618623

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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.


Quantum Theory

Quantum Theory
Author: Peter Bongaarts
Publisher: Springer
Total Pages: 460
Release: 2014-12-01
Genre: Science
ISBN: 3319095617

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This book was inspired by the general observation that the great theories of modern physics are based on simple and transparent underlying mathematical structures – a fact not usually emphasized in standard physics textbooks – which makes it easy for mathematicians to understand their basic features. It is a textbook on quantum theory intended for advanced undergraduate or graduate students: mathematics students interested in modern physics, and physics students who are interested in the mathematical background of physics and are dissatisfied with the level of rigor in standard physics courses. More generally, it offers a valuable resource for all mathematicians interested in modern physics, and all physicists looking for a higher degree of mathematical precision with regard to the basic concepts in their field.


The Foundations of Geometry

The Foundations of Geometry
Author: David Hilbert
Publisher:
Total Pages: 158
Release: 1902
Genre: Geometry
ISBN:

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General Theory of Relativity

General Theory of Relativity
Author: C. W. Kilmister
Publisher: Elsevier
Total Pages: 376
Release: 2013-10-22
Genre: Science
ISBN: 1483154653

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General Theory of Relativity deals with the general theory of relativity and covers topics ranging from the principle of equivalence and the space-theory of matter to the hypotheses which lie at the bases of geometry, along with the effect of gravitation on the propagation of light. The motion of particles in general relativity theory is also discussed. This book is comprised of 14 chapters and begins with a review of the principle of equivalence, paying particular attention to the question of the existence of inertial frames in Newtonian mechanics. The beginnings and foundations of general relativity are then considered, together with modern developments in the field. Subsequent chapters explore the general notion of multiply extended magnitudes; the space-theory of matter; the effect of gravitation on light propagation; gravitational waves and the motion of particles in general relativity theory; and homogeneity and covariance. An invariant formulation of gravitational radiation theory is also presented. The last three chapters examine continued gravitational contraction, a spinor approach to general relativity, and gravitational red-shift in nuclear resonance. This monograph will be of interest to physicists and mathematicians.


Science and Hypothesis

Science and Hypothesis
Author: Henri Poincaré
Publisher: Bloomsbury Publishing
Total Pages: 208
Release: 2017-11-16
Genre: Philosophy
ISBN: 135002676X

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Science and Hypothesis is a classic text in history and philosophy of science. Widely popular since its original publication in 1902, this first new translation of the work in over a century features unpublished material missing from earlier editions. Addressing errors introduced by Greenstreet and Halsted in their early 20th-century translations, it incorporates all the changes, corrections and additions Poincaré made over the years. Taking care to update the writing for a modern audience, Poincaré's ideas and arguments on the role of hypotheses in mathematics and in science become clearer and closer to his original meaning, while David J. Stump's introduction gives fresh insights into Poincaré's philosophy of science. By approaching Science and Hypothesis from a contemporary perspective, it presents a better understanding of Poincare's hierarchy of the sciences, with arithmetic as the foundation, geometry as the science of space, then mechanics and the rest of physics. For philosophers of science and scientists working on problems of space, time and relativity, this is a much needed translation of a ground-breaking work which demonstrates why Poincaré is still relevant today.