Geometry

A High School Course

Author: Serge Lang,Gene Murrow

Publisher: Springer Science & Business Media

ISBN: 9783540966548

Category: Geometrie

Page: 394

View: 1711

Posted in Geometrie

Geometry I

Author: Marcel Berger

Publisher: Springer Science & Business Media

ISBN: 9783540116585

Category: Mathematics

Page: 432

View: 2101

Volume I of this 2-volume textbook provides a lively and readable presentation of large parts of classical geometry. For each topic the author presents an esthetically pleasing and easily stated theorem - although the proof may be difficult and concealed. The mathematical text is illustrated with figures, open problems and references to modern literature, providing a unified reference to geometry in the full breadth of its subfields and ramifications.
Posted in Mathematics

David Hilbert’s Lectures on the Foundations of Geometry 1891–1902

Author: Michael Hallett,Ulrich Majer

Publisher: Springer Science & Business Media

ISBN: 9783540643739

Category: Mathematics

Page: 661

View: 1867

This volume contains six sets of notes for lectures on the foundations of geometry held by Hilbert in the period 1891-1902. It also reprints the first edition of Hilbert’s celebrated Grundlagen der Geometrie of 1899, together with the important additions which appeared first in the French translation of 1900. The lectures document the emergence of a new approach to foundational study and contain many reflections and investigations which never found their way into print.
Posted in Mathematics

Geometry, Topology and Physics, Second Edition

Author: Mikio Nakahara

Publisher: CRC Press

ISBN: 9780750306065

Category: Mathematics

Page: 596

View: 3269

Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.
Posted in Mathematics

Geometry

Author: David A. Brannan,Matthew F. Esplen,Jeremy J. Gray

Publisher: Cambridge University Press

ISBN: 9780521597876

Category: Mathematics

Page: 497

View: 9236

Textbook for undergraduate courses on geometry or for self study that reveals the intricacies of geometry.
Posted in Mathematics

A Family Encyclopaedia

Or, An Explanation of Words and Things Connected with All the Arts and Sciences ...

Author: George Crabb

Publisher: N.A

ISBN: N.A

Category: Encyclopedias and dictionaries

Page: 412

View: 459

Posted in Encyclopedias and dictionaries

The Geometry of Rene Descartes

Author: René Descartes

Publisher: Cosimo, Inc.

ISBN: 1602066914

Category: Mathematics

Page: 264

View: 347

Posted in Mathematics

Analytical Geometry

Author: Izu Vaisman

Publisher: World Scientific

ISBN: 9789810231583

Category: Mathematics

Page: 284

View: 2081

This volume discusses the classical subjects of Euclidean, affine and projective geometry in two and three dimensions, including the classification of conics and quadrics, and geometric transformations. These subjects are important both for the mathematical grounding of the student and for applications to various other subjects. They may be studied in the first year or as a second course in geometry.The material is presented in a geometric way, and it aims to develop the geometric intuition and thinking of the student, as well as his ability to understand and give mathematical proofs. Linear algebra is not a prerequisite, and is kept to a bare minimum.The book includes a few methodological novelties, and a large number of exercises and problems with solutions. It also has an appendix about the use of the computer program MAPLEV in solving problems of analytical and projective geometry, with examples.
Posted in Mathematics

Modern Geometry— Methods and Applications

Part II: The Geometry and Topology of Manifolds

Author: B.A. Dubrovin,A.T. Fomenko,S.P. Novikov

Publisher: Springer Science & Business Media

ISBN: 9780387961620

Category: Mathematics

Page: 432

View: 2976

Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e.
Posted in Mathematics

Complex Geometry

Author: G. Komatsu

Publisher: CRC Press

ISBN: 9780824788186

Category: Mathematics

Page: 248

View: 6135

Presents the proceedings of an international conference on complex geometry and related topics, held in commemoration of the 50th anniversary of Osaka University, Osaka, Japan. The text focuses on the CR invariants, hyperbolic geometry, Yamabe-type problems, and harmonic maps.
Posted in Mathematics

Geometry: A Comprehensive Course

Author: Dan Pedoe

Publisher: Courier Corporation

ISBN: 0486131734

Category: Mathematics

Page: 464

View: 606

Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.
Posted in Mathematics

Geometry, Combinatorial Designs and Related Structures

Author: J. W. P. Hirschfeld,S. S. Magliveras,M. J. de Resmini

Publisher: Cambridge University Press

ISBN: 9780521595384

Category: Mathematics

Page: 258

View: 3971

This volume examines state of the art research in finite geometries and designs.
Posted in Mathematics

Non-Euclidean Geometry

Author: Roberto Bonola

Publisher: Courier Corporation

ISBN: 048615503X

Category: Mathematics

Page: 448

View: 1201

Examines various attempts to prove Euclid's parallel postulate — by the Greeks, Arabs, and Renaissance mathematicians. It considers forerunners and founders such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss, others. Includes 181 diagrams.
Posted in Mathematics

Geometry, Perspective Drawing, and Mechanisms

Author: Don Row,Talmage James Reid

Publisher: World Scientific

ISBN: 981434382X

Category: Mathematics

Page: 328

View: 9428

The aim of this book is to examine the geometry of our world and, by blending theory with a variety of every-day examples, to stimulate the imagination of the readers and develop their geometric intuition. It tries to recapture the excitement that surrounded geometry during the Renaissance as the development of perspective drawing gathered pace, or more recently as engineers sought to show that all the world was a machine. The same excitement is here still, as enquiring minds today puzzle over a random-dot stereogram or the interpretation of an image painstakingly transmitted from Jupiter. The book will give a solid foundation for a variety of undergraduate courses, to provide a basis for a geometric component of graduate teacher training, and to provide background for those who work in computer graphics and scene analysis. It begins with a self-contained development of the geometry of extended Euclidean space. This framework is then used to systematically clarify and develop the art of perspective drawing and its converse discipline of scene analysis and to analyze the behavior of bar-and-joint mechanisms and hinged-panel mechanisms. Spherical polyhedra are introduced and scene analysis is applied to drawings of these and associated objects. The book concludes by showing how a natural relaxation of the axioms developed in the early chapters leads to the concept of a matroid and briefly examines some of the attractive properties of these natural structures.
Posted in Mathematics

Lectures on Classical Differential Geometry

Author: Dirk Jan Struik

Publisher: Courier Corporation

ISBN: 9780486656090

Category: Mathematics

Page: 232

View: 9640

Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there. For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text — ideal for classroom use, but also perfectly suited for self-study. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.
Posted in Mathematics

Axiomatic Geometry

Author: John M. Lee

Publisher: American Mathematical Soc.

ISBN: 0821884786

Category: Mathematics

Page: 469

View: 5176

The story of geometry is the story of mathematics itself: Euclidean geometry was the first branch of mathematics to be systematically studied and placed on a firm logical foundation, and it is the prototype for the axiomatic method that lies at the foundation of modern mathematics. It has been taught to students for more than two millennia as a mode of logical thought. This book tells the story of how the axiomatic method has progressed from Euclid's time to ours, as a way of understanding what mathematics is, how we read and evaluate mathematical arguments, and why mathematics has achieved the level of certainty it has. It is designed primarily for advanced undergraduates who plan to teach secondary school geometry, but it should also provide something of interest to anyone who wishes to understand geometry and the axiomatic method better. It introduces a modern, rigorous, axiomatic treatment of Euclidean and (to a lesser extent) non-Euclidean geometries, offering students ample opportunities to practice reading and writing proofs while at the same time developing most of the concrete geometric relationships that secondary teachers will need to know in the classroom. -- P. [4] of cover.
Posted in Mathematics

Quasicrystals and Geometry

Author: Marjorie Senechal

Publisher: CUP Archive

ISBN: 9780521575416

Category: Mathematics

Page: 286

View: 3375

This first-ever detailed account of quasicrystal geometry will be of great value to mathematicians at all levels with an interest in quasicrystals and geometry, and will also be of interest to graduate students and researchers in solid state physics, crystallography and materials science.
Posted in Mathematics