Download or read book Die Ausdehnungslehre written by Hermann Grassmann and published by Cambridge University Press. This book was released on 2013-10-16 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1862 extended version of a revolutionary 1844 work in German by the mathematician Hermann Grassmann (1809-77).
Download or read book Grassmann Algebra Volume 1 Foundations written by John Browne and published by John M Browne. This book was released on 2012-10-25 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: Grassmann Algebra Volume 1: Foundations Exploring extended vector algebra with Mathematica Grassmann algebra extends vector algebra by introducing the exterior product to algebraicize the notion of linear dependence. With it, vectors may be extended to higher-grade entities: bivectors, trivectors, … multivectors. The extensive exterior product also has a regressive dual: the regressive product. The pair behaves a little like the Boolean duals of union and intersection. By interpreting one of the elements of the vector space as an origin point, points can be defined, and the exterior product can extend points into higher-grade located entities from which lines, planes and multiplanes can be defined. Theorems of Projective Geometry are simply formulae involving these entities and the dual products. By introducing the (orthogonal) complement operation, the scalar product of vectors may be extended to the interior product of multivectors, which in this more general case may no longer result in a scalar. The notion of the magnitude of vectors is extended to the magnitude of multivectors: for example, the magnitude of the exterior product of two vectors (a bivector) is the area of the parallelogram formed by them. To develop these foundational concepts, we need only consider entities which are the sums of elements of the same grade. This is the focus of this volume. But the entities of Grassmann algebra need not be of the same grade, and the possible product types need not be constricted to just the exterior, regressive and interior products. For example quaternion algebra is simply the Grassmann algebra of scalars and bivectors under a new product operation. Clifford, geometric and higher order hypercomplex algebras, for example the octonions, may be defined similarly. If to these we introduce Clifford's invention of a scalar which squares to zero, we can define entities (for example dual quaternions) with which we can perform elaborate transformations. Exploration of these entities, operations and algebras will be the focus of the volume to follow this. There is something fascinating about the beauty with which the mathematical structures that Hermann Grassmann discovered describe the physical world, and something also fascinating about how these beautiful structures have been largely lost to the mainstreams of mathematics and science. He wrote his seminal Ausdehnungslehre (Die Ausdehnungslehre. Vollständig und in strenger Form) in 1862. But it was not until the latter part of his life that he received any significant recognition for it, most notably by Gibbs and Clifford. In recent times David Hestenes' Geometric Algebra must be given the credit for much of the emerging awareness of Grassmann's innovation. In the hope that the book be accessible to scientists and engineers, students and professionals alike, the text attempts to avoid any terminology which does not make an essential contribution to an understanding of the basic concepts. Some familiarity with basic linear algebra may however be useful. The book is written using Mathematica, a powerful system for doing mathematics on a computer. This enables the theory to be cross-checked with computational explorations. However, a knowledge of Mathematica is not essential for an appreciation of Grassmann's beautiful ideas.
Download or read book Bulletin of the International Association for Promoting the Study of Quaternions and Allied Systems of Mathematics written by International Association for Promoting the Study of Quaternions and Allied Systems of Mathematics and published by . This book was released on 1900 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bibliography of Quaternions and Allied Systems of Mathematics written by Alexander Macfarlane and published by . This book was released on 1904 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Philosophical Papers 1896 99 written by Bertrand Russell and published by Psychology Press. This book was released on 1993 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 1990. Routledge is an imprint of Taylor & Francis, an informa company.
Download or read book The Quarterly Journal of Pure and Applied Mathematics written by and published by . This book was released on 1887 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Collected Papers of Bertrand Russell Volume 2 written by Nicholas Griffin and published by Taylor & Francis. This book was released on 2024-08-01 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1896-1899 papers, few of which were published in Russell's lifetime, concentrate primarily on physics, arithmetic and the concept of quantity. Several views that later became well-known in his The Principles of Mathematics actually originate in his earlier work, and though incomplete,An Analysis of Mathematical Reasoning, forms a centrepiece of the volume.
Download or read book Worlds Out of Nothing written by Jeremy Gray and published by Springer Science & Business Media. This book was released on 2011-02-01 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the latest historical research, Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Topics covered in the first part of the book are projective geometry, especially the concept of duality, and non-Euclidean geometry. The book then moves on to the study of the singular points of algebraic curves (Plücker’s equations) and their role in resolving a paradox in the theory of duality; to Riemann’s work on differential geometry; and to Beltrami’s role in successfully establishing non-Euclidean geometry as a rigorous mathematical subject. The final part of the book considers how projective geometry rose to prominence, and looks at Poincaré’s ideas about non-Euclidean geometry and their physical and philosophical significance. Three chapters are devoted to writing and assessing work in the history of mathematics, with examples of sample questions in the subject, advice on how to write essays, and comments on what instructors should be looking for.
Download or read book From Past to Future Gra mann s Work in Context written by Hans-Joachim Petsche and published by Springer Science & Business Media. This book was released on 2010-12-16 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the occasion of the 200th anniversary of the birth of Hermann Graßmann (1809-1877), an interdisciplinary conference was held in Potsdam, Germany, and in Graßmann's hometown Szczecin, Poland. The idea of the conference was to present a multi-faceted picture of Graßmann, and to uncover the complexity of the factors that were responsible for his creativity. The conference demonstrated not only the very influential reception of his work at the turn of the 20th century, but also the unexpected modernity of his ideas, and their continuing development in the 21st century. This book contains 37 papers presented at the conference. They investigate the significance of Graßmann's work for philosophical as well as for scientific and methodological questions, for comparative philology in general and for Indology in particular, for psychology, physiology, religious studies, musicology, didactics, and, last but not least, mathematics. In addition, the book contains numerous illustrations and English translations of original sources, which are published here for the first time. These include life histories of Graßmann (written by his son Justus) and of his brother Robert (written by Robert himself), as well as the paper "On the concept and extent of pure theory of number'' by Justus Graßmann (the father).
Download or read book The Collected Mathematical Papers written by Arthur Cayley and published by . This book was released on 1897 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Prehistory of Mathematical Structuralism written by Erich H. Reck and published by Oxford University Press. This book was released on 2020 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic.
Download or read book The Monist written by Paul Carus and published by . This book was released on 1896 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vols. 2 and 5 include appendices.
Download or read book Theory of Linear and Integer Programming written by Alexander Schrijver and published by John Wiley & Sons. This book was released on 1998-06-11 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Als Ergänzung zu den mehr praxisorientierten Büchern, die auf dem Gebiet der linearen und Integerprogrammierung bereits erschienen sind, beschreibt dieses Werk die zugrunde liegende Theorie und gibt einen Überblick über wichtige Algorithmen. Der Autor diskutiert auch Anwendungen auf die kombinatorische Optimierung; neben einer ausführlichen Bibliographie finden sich umfangreiche historische Anmerkungen.
Download or read book A Treatise on Universal Algebra written by Alfred North Whitehead and published by . This book was released on 1898 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Catalogue of Science and Technology No written by Henry Sotheran Ltd and published by . This book was released on 1922 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Library Bulletin written by Cornell University. Libraries and published by . This book was released on 1886 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Foundations of Logic 1903 05 written by Bertrand Russell and published by Psychology Press. This book was released on 1994 with total page 1344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers the period from the beginning of Whitehead and Russell's work on Volume 2 of the Principles of Mathematics to the critical discovery of the theory of descriptions in 1905. Contains many previously unpublished manuscripts.
