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Author: Edwin Curley
Publisher: Princeton University Press
ISBN: 0691214263
Category : Philosophy
Languages : en
Pages : 199
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Book Description
This book is the fruit of twenty-five years of study of Spinoza by the editor and translator of a new and widely acclaimed edition of Spinoza's collected works. Based on three lectures delivered at the Hebrew University of Jerusalem in 1984, the work provides a useful focal point for continued discussion of the relationship between Descartes and Spinoza, while also serving as a readable and relatively brief but substantial introduction to the Ethics for students. Behind the Geometrical Method is actually two books in one. The first is Edwin Curley's text, which explains Spinoza's masterwork to readers who have little background in philosophy. This text will prove a boon to those who have tried to read the Ethics, but have been baffled by the geometrical style in which it is written. Here Professor Curley undertakes to show how the central claims of the Ethics arose out of critical reflection on the philosophies of Spinoza's two great predecessors, Descartes and Hobbes. The second book, whose argument is conducted in the notes to the text, attempts to support further the often controversial interpretations offered in the text and to carry on a dialogue with recent commentators on Spinoza. The author aligns himself with those who interpret Spinoza naturalistically and materialistically.
Author: Edwin Curley
Publisher: Princeton University Press
ISBN: 0691214263
Category : Philosophy
Languages : en
Pages : 199
Get Book Here
Book Description
This book is the fruit of twenty-five years of study of Spinoza by the editor and translator of a new and widely acclaimed edition of Spinoza's collected works. Based on three lectures delivered at the Hebrew University of Jerusalem in 1984, the work provides a useful focal point for continued discussion of the relationship between Descartes and Spinoza, while also serving as a readable and relatively brief but substantial introduction to the Ethics for students. Behind the Geometrical Method is actually two books in one. The first is Edwin Curley's text, which explains Spinoza's masterwork to readers who have little background in philosophy. This text will prove a boon to those who have tried to read the Ethics, but have been baffled by the geometrical style in which it is written. Here Professor Curley undertakes to show how the central claims of the Ethics arose out of critical reflection on the philosophies of Spinoza's two great predecessors, Descartes and Hobbes. The second book, whose argument is conducted in the notes to the text, attempts to support further the often controversial interpretations offered in the text and to carry on a dialogue with recent commentators on Spinoza. The author aligns himself with those who interpret Spinoza naturalistically and materialistically.
Author: Bernard F. Schutz
Publisher: Cambridge University Press
ISBN: 1107268141
Category : Science
Languages : en
Pages : 272
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Book Description
In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.
Author: V.I. Arnold
Publisher: Springer Science & Business Media
ISBN: 1461210372
Category : Mathematics
Languages : en
Pages : 366
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Book Description
Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers. Much of this progress is represented in this revised, expanded edition, including such topics as the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems, and the Neistadt theory. In the selection of material for this book, the author explains basic ideas and methods applicable to the study of differential equations. Special efforts were made to keep the basic ideas free from excessive technicalities. Thus the most fundamental questions are considered in great detail, while of the more special and difficult parts of the theory have the character of a survey. Consequently, the reader needs only a general mathematical knowledge to easily follow this text. It is directed to mathematicians, as well as all users of the theory of differential equations.
Author: Julian Lowell Coolidge
Publisher: Courier Corporation
ISBN: 0486158535
Category : Mathematics
Languages : en
Pages : 484
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Book Description
Full and authoritative, this history of the techniques for dealing with geometric questions begins with synthetic geometry and its origins in Babylonian and Egyptian mathematics; reviews the contributions of China, Japan, India, and Greece; and discusses the non-Euclidean geometries. Subsequent sections cover algebraic geometry, starting with the precursors and advancing to the great awakening with Descartes; and differential geometry, from the early work of Huygens and Newton to projective and absolute differential geometry. The author's emphasis on proofs and notations, his comparisons between older and newer methods, and his references to over 600 primary and secondary sources make this book an invaluable reference. 1940 edition.
Author: Alexander Krasnosel'skii
Publisher: Springer
ISBN: 9783642694110
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Geometrical (in particular, topological) methods in nonlinear analysis were originally invented by Banach, Birkhoff, Kellogg, Schauder, Leray, and others in existence proofs. Since about the fifties, these methods turned out to be essentially the sole approach to a variety of new problems: the investigation of iteration processes and other procedures in numerical analysis, in bifur cation problems and branching of solutions, estimates on the number of solutions and criteria for the existence of nonzero solutions, the analysis of the structure of the solution set, etc. These methods have been widely applied to the theory of forced vibrations and auto-oscillations, to various problems in the theory of elasticity and fluid. mechanics, to control theory, theoretical physics, and various parts of mathematics. At present, nonlinear analysis along with its geometrical, topological, analytical, variational, and other methods is developing tremendously thanks to research work in many countries. Totally new ideas have been advanced, difficult problems have been solved, and new applications have been indicated. To enumerate the publications of the last few years one would need dozens of pages. On the other hand, many problems of non linear analysis are still far from a solution (problems arising from the internal development of mathematics and, in particular, problems arising in the process of interpreting new problems in the natural sciences). We hope that the English edition of our book will contribute to the further propagation of the ideas of nonlinear analysis.
Author: J.M. Selig
Publisher: Springer Science & Business Media
ISBN: 1475724845
Category : Computers
Languages : en
Pages : 273
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Book Description
The main aim of this book is to introduce Lie groups and allied algebraic and geometric concepts to a robotics audience. These topics seem to be quite fashionable at the moment, but most of the robotics books that touch on these topics tend to treat Lie groups as little more than a fancy notation. I hope to show the power and elegance of these methods as they apply to problems in robotics. A subsidiary aim of the book is to reintroduce some old ideas by describing them in modem notation, particularly Study's Quadric-a description of the group of rigid motions in three dimensions as an algebraic variety (well, actually an open subset in an algebraic variety)-as well as some of the less well known aspects of Ball's theory of screws. In the first four chapters, a careful exposition of the theory of Lie groups and their Lie algebras is given. Except for the simplest examples, all examples used to illustrate these ideas are taken from robotics. So, unlike most standard texts on Lie groups, emphasis is placed on a group that is not semi-simple-the group of proper Euclidean motions in three dimensions. In particular, the continuous subgroups of this group are found, and the elements of its Lie algebra are identified with the surfaces of the lower Reuleaux pairs. These surfaces were first identified by Reuleaux in the latter half of the 19th century.
Author: Jean Gallier
Publisher: Springer Science & Business Media
ISBN: 1461301378
Category : Mathematics
Languages : en
Pages : 584
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Book Description
As an introduction to fundamental geometric concepts and tools needed for solving problems of a geometric nature using a computer, this book fills the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, or robotics that do not cover the underlying geometric concepts in detail. Gallier offers an introduction to affine, projective, computational, and Euclidean geometry, basics of differential geometry and Lie groups, and explores many of the practical applications of geometry. Some of these include computer vision, efficient communication, error correcting codes, cryptography, motion interpolation, and robot kinematics. This comprehensive text covers most of the geometric background needed for conducting research in computer graphics, geometric modeling, computer vision, and robotics and as such will be of interest to a wide audience including computer scientists, mathematicians, and engineers.
Author: Paul B. Larson
Publisher: American Mathematical Soc.
ISBN: 1470454629
Category : Education
Languages : en
Pages : 345
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Book Description
This book introduces a new research direction in set theory: the study of models of set theory with respect to their extensional overlap or disagreement. In Part I, the method is applied to isolate new distinctions between Borel equivalence relations. Part II contains applications to independence results in Zermelo–Fraenkel set theory without Axiom of Choice. The method makes it possible to classify in great detail various paradoxical objects obtained using the Axiom of Choice; the classifying criterion is a ZF-provable implication between the existence of such objects. The book considers a broad spectrum of objects from analysis, algebra, and combinatorics: ultrafilters, Hamel bases, transcendence bases, colorings of Borel graphs, discontinuous homomorphisms between Polish groups, and many more. The topic is nearly inexhaustible in its variety, and many directions invite further investigation.
Author: Vladimir Boltyanski
Publisher: Springer Science & Business Media
ISBN: 1461553199
Category : Mathematics
Languages : en
Pages : 438
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Book Description
VII Preface In many fields of mathematics, geometry has established itself as a fruitful method and common language for describing basic phenomena and problems as well as suggesting ways of solutions. Especially in pure mathematics this is ob vious and well-known (examples are the much discussed interplay between lin ear algebra and analytical geometry and several problems in multidimensional analysis). On the other hand, many specialists from applied mathematics seem to prefer more formal analytical and numerical methods and representations. Nevertheless, very often the internal development of disciplines from applied mathematics led to geometric models, and occasionally breakthroughs were b~ed on geometric insights. An excellent example is the Klee-Minty cube, solving a problem of linear programming by transforming it into a geomet ric problem. Also the development of convex programming in recent decades demonstrated the power of methods that evolved within the field of convex geometry. The present book focuses on three applied disciplines: control theory, location science and computational geometry. It is our aim to demonstrate how methods and topics from convex geometry in a wider sense (separation theory of convex cones, Minkowski geometry, convex partitionings, etc.) can help to solve various problems from these disciplines.
Author: Joe Warren
Publisher: Morgan Kaufmann
ISBN: 9781558604469
Category : Art
Languages : en
Pages : 326
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Book Description
Subdivision Methods for Geometric Design provides computer graphics students and designers with a comprehensive guide to subdivision methods, including the background information required to grasp underlying concepts, techniques for manipulating subdivision algorithms to achieve specific effects, and a wide array of digital resources on a dynamic companion Web site. Subdivision Methods promises to be a groundbreaking book, important for both advanced students and working professionals in the field of computer graphics.
