A History of Geometrical Methods

A History of Geometrical Methods

Author: Julian Lowell Coolidge

Publisher: Courier Corporation

Published: 2013-02-27

Total Pages: 484

ISBN-13: 0486158535

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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.


Geometry Civilized

Geometry Civilized

Author: J. L. Heilbron

Publisher: Oxford University Press

Published: 2000

Total Pages: 344

ISBN-13: 9780198506904

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This lavishly illustrated book provides an unusually accessible approach to geometry by placing it in historical context. With concise discussions and carefully chosen illustrations the author brings the material to life by showing what problems motivated early geometers throughout the world. Geometry Civilized covers classical plane geometry, emphasizing the methods of Euclid but also drawing on advances made in China and India. It includes a wide range of problems, solutions, and illustrations, as well as a chapter on trigonometry, and prepares its readers for the study of solid geometry and conic sections.


Geometrical Methods in the Theory of Ordinary Differential Equations

Geometrical Methods in the Theory of Ordinary Differential Equations

Author: V.I. Arnold

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 366

ISBN-13: 1461210372

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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.


Geometrical Methods of Mathematical Physics

Geometrical Methods of Mathematical Physics

Author: Bernard F. Schutz

Publisher: Cambridge University Press

Published: 1980-01-28

Total Pages: 272

ISBN-13: 1107268141

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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.


Behind the Geometrical Method

Behind the Geometrical Method

Author: Edwin M. Curley

Publisher: Princeton University Press

Published: 1988-05-21

Total Pages: 204

ISBN-13: 9780691020372

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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.


Digital Geometry

Digital Geometry

Author: Reinhard Klette

Publisher: Morgan Kaufmann

Published: 2004-08-06

Total Pages: 676

ISBN-13: 1558608613

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The first book on digital geometry by the leaders in the field.


Algebraic and Geometric Methods in Statistics

Algebraic and Geometric Methods in Statistics

Author: Paolo Gibilisco

Publisher: Cambridge University Press

Published: 2010

Total Pages: 447

ISBN-13: 0521896193

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An up-to-date account of algebraic statistics and information geometry, which also explores the emerging connections between these two disciplines.


A Treatise on Some New Geometrical Methods

A Treatise on Some New Geometrical Methods

Author: Senior Lecturer of English James Booth

Publisher: Andesite Press

Published: 2015-08-11

Total Pages: 420

ISBN-13: 9781298690838

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