Download or read book Continuous Geometry written by John von Neumann and published by Princeton University Press. This book was released on 1998-05-10 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled the lattice system Ln. In characterizing its properties, von Newmann founded the field of continuous geometry. For students and researchers interested in ring theory or projective geometries, von Neumann discusses his findings and their applications.
Download or read book Continuous Geometry written by John von Neumann and published by Princeton University Press. This book was released on 2016-06-02 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled the lattice system Ln. In characterizing its properties, von Neumann founded the field of continuous geometry. This book, based on von Neumann's lecture notes, begins with the development of the axioms of continuous geometry, dimension theory, and--for the irreducible case--the function D(a). The properties of regular rings are then discussed, and a variety of results are presented for lattices that are continuous geometries, for which irreducibility is not assumed. For students and researchers interested in ring theory or projective geometries, this book is required reading.
Download or read book Continuous Geometry PMS 25 written by John von Neumann and published by . This book was released on 1960-12-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled the lattice system Ln. In characterizing its properties, von Neumann founded the field of continuous geometry. This book, based on von Neumann's lecture notes, begins with the development of the axioms of continuous geometry, dimension theory, andDLfor the irreducible caseDLthe function D(a). The properties of regular rings are then discussed, and a variety of results are presented for lattices that are continuous geometries, for which irreducibility is not assumed. For students and researchers interested in ring theory or projective geometries, this book is required reading. This historic book should be in the hands of everyone interested in rings and projective geometry. DLR. J. Smith, The Australian Journal of Science Much in this book is still of great value, partly because it cannot be found elsewhere ... partly because of the very clear and comprehensible presentation. This makes the book valuable for a first study of continuous geometry as well as for research in this field. DLF. D. Veldkamp, Nieuw Archief voor Wiskunde
Download or read book Continuous Geometries with a Transition Probability written by John Von Neumann and published by American Mathematical Soc.. This book was released on 1981 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Axioms where are motivated by quantum mechanics are formulated for a probability-logic system. It is shown that these axioms characterize precisely those lattices which are lattices of all projections in a irreducible von Neumann algebra of type II1 or I[subscript]N, N [greater-than or equal to] 4 in Hilbert spaces of arbitrary dimension and real or complex scalars.
Download or read book Continuous geometry and other topics written by John Von Neumann and published by . This book was released on 1962 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Continuous Symmetry written by William H. Barker and published by American Mathematical Soc.. This book was released on 2007 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental idea of geometry is that of symmetry. With that principle as the starting point, Barker and Howe begin an insightful and rewarding study of Euclidean geometry. The primary focus of the book is on transformations of the plane. The transformational point of view provides both a path for deeper understanding of traditional synthetic geometry and tools for providing proofs that spring from a consistent point of view. As a result, proofs become more comprehensible, as techniques can be used and reused in similar settings. The approach to the material is very concrete, with complete explanations of all the important ideas, including foundational background. The discussions of the nine-point circle and wallpaper groups are particular examples of how the strength of the transformational point of view and the care of the authors' exposition combine to give a remarkable presentation of topics in geometry. This text is for a one-semester undergraduate course on geometry. It is richly illustrated and contains hundreds of exercises.
Download or read book Geometry of Quantum Theory written by V.S. Varadarajan and published by Springer Science & Business Media. This book was released on 2007-12-03 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Available for the first time in soft cover, this book is a classic on the foundations of quantum theory. It examines the subject from a point of view that goes back to Heisenberg and Dirac and whose definitive mathematical formulation is due to von Neumann. This view leads most naturally to the fundamental questions that are at the basis of all attempts to understand the world of atomic and subatomic particles.
Download or read book Algebraical and Topological Foundations of Geometry written by Hans Freudenthal and published by Elsevier. This book was released on 2014-05-09 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraical and Topological Foundations of Geometry contains the proceedings of the Colloquium on Algebraic and Topological Foundations of Geometry, held in Utrecht, the Netherlands in August 1959. The papers review the algebraical and topological foundations of geometry and cover topics ranging from the geometric algebra of the Möbius plane to the theory of parallels with applications to closed geodesies. Groups of homeomorphisms and topological descriptive planes are also discussed. Comprised of 26 chapters, this book introduces the reader to the theory of parallels with applications to closed geodesies; groups of homeomorphisms; complemented modular lattices; and topological descriptive planes. Subsequent chapters focus on collineation groups; exceptional algebras and exceptional groups; the connection between algebra and constructions with ruler and compasses; and the use of differential geometry and analytic group theory methods in foundations of geometry. Von Staudt projectivities of Moufang planes are also considered, and an axiomatic treatment of polar geometry is presented. This monograph will be of interest to students of mathematics.
Download or read book Computing the Continuous Discretely written by Matthias Beck and published by Springer. This book was released on 2015-11-14 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: “You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.” — MAA Reviews “The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.” — Zentralblatt MATH “This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.” — Mathematical Reviews “Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.” — CHOICE
Download or read book A Differential Approach to Geometry written by Francis Borceux and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the classical theory of curves in the plane and three-dimensional space, and the classical theory of surfaces in three-dimensional space. It pays particular attention to the historical development of the theory and the preliminary approaches that support contemporary geometrical notions. It includes a chapter that lists a very wide scope of plane curves and their properties. The book approaches the threshold of algebraic topology, providing an integrated presentation fully accessible to undergraduate-level students. At the end of the 17th century, Newton and Leibniz developed differential calculus, thus making available the very wide range of differentiable functions, not just those constructed from polynomials. During the 18th century, Euler applied these ideas to establish what is still today the classical theory of most general curves and surfaces, largely used in engineering. Enter this fascinating world through amazing theorems and a wide supply of surprising examples. Reach the doors of algebraic topology by discovering just how an integer (= the Euler-Poincaré characteristics) associated with a surface gives you a lot of interesting information on the shape of the surface. And penetrate the intriguing world of Riemannian geometry, the geometry that underlies the theory of relativity. The book is of interest to all those who teach classical differential geometry up to quite an advanced level. The chapter on Riemannian geometry is of great interest to those who have to “intuitively” introduce students to the highly technical nature of this branch of mathematics, in particular when preparing students for courses on relativity.
Download or read book Modern Projective Geometry written by Claude-Alain Faure and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops projective geometries and provides a systematic treatment of morphisms. It introduces a new fundamental theorem and its applications describing morphisms of projective geometries in homogeneous coordinates by semilinear maps. Other topics treated include three equivalent definitions of projective geometries and their correspondence with certain lattices; quotients of projective geometries and isomorphism theorems; and recent results in dimension theory.
Download or read book Arithmetic and Geometry written by Gisbert Wüstholz and published by Princeton University Press. This book was released on 2019-10-08 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Lectures by outstanding scholars on progress made in the past ten years in the most progressive areas of arithmetic and geometry - primarily arithmetic geometry"--
Download or read book The Nature of Time Geometry Physics and Perception written by R. Buccheri and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are very few concepts that fascinate equally a theoretical physicist studying black holes and a patient undergoing seriolls mental psychosis. Time, undoubtedly, can well be ranked among them. For the measure of time inside a black hole is no less bizarre than the perception of time by a schizophrenic, who may perceive it as completely "suspended," "standing still," or even "reversing its direction. " The nature of time is certainly shrouded in profound mystery. This, perhaps, since the concept entails multifarious, and occasionally incongruous, facets. No wonder the subject attracts the serious attention of scholars on the one hand, and of the lay public on the other. Our Advanced Research Workshop is an excellent il lustration of this point, as the reader will soon discover. It turned out to be a unique professional forum for an unusually lively, effective and fruitful exchange of ideas and beliefs among 48 participants from 20 countries worldwide, selected out of more than a hundred applicants. The present book is based on the select talks presented at the meeting, and aims to provide the interested layperson and specialist alike with a multidisciplinary sampling of the most up-to-date scholarly research on the nature of time. It represents a coherent, state-of-the-art volume showing that research relevant to this topic is necessarily interdisciplinary and does not ignore such delicate issues as "altered" states of consciousness, religion and metaphysics.
Download or read book Riemannian Geometry and Geometric Analysis written by Jürgen Jost and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present textbook is a somewhat expanded version of the material of a three-semester course I gave in Bochum. It attempts a synthesis of geometric and analytic methods in the study of Riemannian manifolds. In the first chapter, we introduce the basic geometric concepts, like dif ferentiable manifolds, tangent spaces, vector bundles, vector fields and one parameter groups of diffeomorphisms, Lie algebras and groups and in par ticular Riemannian metrics. We also derive some elementary results about geodesics. The second chapter introduces de Rham cohomology groups and the es sential tools from elliptic PDE for treating these groups. In later chapters, we shall encounter nonlinear versions of the methods presented here. The third chapter treats the general theory of connections and curvature. In the fourth chapter, we introduce Jacobi fields, prove the Rauch com parison theorems for Jacobi fields and apply these results to geodesics. These first four chapters treat the more elementary and basic aspects of the subject. Their results will be used in the remaining, more advanced chapters that are essentially independent of each other. In the fifth chapter, we develop Morse theory and apply it to the study of geodesics. The sixth chapter treats symmetric spaces as important examples of Rie mannian manifolds in detail.
Download or read book Tensor Geometry written by Christopher T. J. Dodson and published by Springer Science & Business Media. This book was released on 2009-11-23 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This treatment of differential geometry and the mathematics required for general relativity makes the subject accessible, for the first time, to anyone familiar with elementary calculus in one variable and with some knowledge of vector algebra. The emphasis throughout is on the geometry of the mathematics, which is greatly enhanced by the many illustrations presenting figures of three and more dimensions as closely as the book form will allow.
Download or read book Arakelov Geometry written by Atsushi Moriwaki and published by American Mathematical Soc.. This book was released on 2014-11-05 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this book is to present the so-called birational Arakelov geometry, which can be viewed as an arithmetic analog of the classical birational geometry, i.e., the study of big linear series on algebraic varieties. After explaining classical results about the geometry of numbers, the author starts with Arakelov geometry for arithmetic curves, and continues with Arakelov geometry of arithmetic surfaces and higher-dimensional varieties. The book includes such fundamental results as arithmetic Hilbert-Samuel formula, arithmetic Nakai-Moishezon criterion, arithmetic Bogomolov inequality, the existence of small sections, the continuity of arithmetic volume function, the Lang-Bogomolov conjecture and so on. In addition, the author presents, with full details, the proof of Faltings' Riemann-Roch theorem. Prerequisites for reading this book are the basic results of algebraic geometry and the language of schemes.
Download or read book Coarse Geometry of Topological Groups written by Christian Rosendal and published by Cambridge University Press. This book was released on 2021-12-16 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a general framework for doing geometric group theory for many non-locally-compact topological transformation groups that arise in mathematical practice, including homeomorphism and diffeomorphism groups of manifolds, isometry groups of separable metric spaces and automorphism groups of countable structures. Using Roe's framework of coarse structures and spaces, the author defines a natural coarse geometric structure on all topological groups. This structure is accessible to investigation, especially in the case of Polish groups, and often has an explicit description, generalising well-known structures in familiar cases including finitely generated discrete groups, compactly generated locally compact groups and Banach spaces. In most cases, the coarse geometric structure is metrisable and may even be refined to a canonical quasimetric structure on the group. The book contains many worked examples and sufficient introductory material to be accessible to beginning graduate students. An appendix outlines several open problems in this young and rich theory.