Author | David A. Brannan | |

ISBN-10 | 9781139503709 | |

Release | 2011-12-22 | |

Pages | 602 | |

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This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective, inversive, hyperbolic and elliptic. In each case they carefully explain the key results and discuss the relationships between the geometries. New features in this second edition include concise end-of-chapter summaries to aid student revision, a list of further reading and a list of special symbols. The authors have also revised many of the end-of-chapter exercises to make them more challenging and to include some interesting new results. Full solutions to the 200 problems are included in the text, while complete solutions to all of the end-of-chapter exercises are available in a new Instructors' Manual, which can be downloaded from www.cambridge.org/9781107647831. |

Author | Silvio Levy | |

ISBN-10 | 0521629624 | |

Release | 1997-09-28 | |

Pages | 194 | |

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Lectures on hyperbolic geometry, dynamics in several complex variables, convex geometry, and volume estimation. |

Author | Lawrence S. Leff | |

ISBN-10 | 0764139185 | |

Release | 2009 | |

Pages | 497 | |

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Explains the principles of plane geometry and includes practice exercises and model problems. |

Author | John M. Lee | |

ISBN-10 | 9780821884782 | |

Release | 2013-04-10 | |

Pages | 469 | |

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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. |

Author | René Respondek | |

ISBN-10 | 9783640864195 | |

Release | 2011 | |

Pages | 40 | |

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Studienarbeit aus dem Jahr 2005 im Fachbereich Mathematik - Geometrie, Note: 1,3, Universitat Osnabruck, Veranstaltung: Seminar: Chaos - Making a new science, 17 Quellen im Literaturverzeichnis, Sprache: Deutsch, Abstract: Es liegt in der Natur des Menschen, komplizierte Sachverhalte zu hinterfragen und zu verstehen. So beschaftigen sich Wissenschaftler seit Jahrhunderten damit, ihre Umwelt und vor allem dort auftauchende, scheinbar chaotische Systeme in eine geordnete und verstandliche Struktur zu bringen. Ein Beispiel hierfur ist die uber zweitausend Jahre gultige Euklidische Geometrie, die als Standardgeometrie ein Bestandteil der klassischen Mathematik ist und unter anderem unsere Umwelt in ein ganzzahlig dimensionales System einordnet. Sie ermoglicht z. B. Daten mittels grafischer Instrumente aufzuarbeiten, zu veranschaulichen und daraus folgend besser analysieren bzw. verstehen zu konnen. Der Wissenschaftler Benoit Mandelbrot hat seit den sechziger Jahren mit seinen wissenschaftlichen Forschungen und seiner Gabe, Muster und Formen intuitiv zu erfassen, ein neues Gebiet der Geometrie erschlossen, das sich auf Grenzen der euklidischen Dimension bezieht. Ausgangspunkt hierfur waren Uberlegungen uber eine bis dahin vollkommen neue Ansicht der geometrischen Welt. Diese zeigt sich in Gebilden mathematischer Monster wie der Koch Kurve, deren Dimensionen nach Mandelbrot den fraktalen Dimensionen" zugeordnet werden. Inwiefern Mandelbrots Erkenntnisse die bis dahin gultige Wissenschaft revolutionierte und der Wissenschaft bis zum heutigen Zeitpunkt neue, leistungsfahige Methoden bereitstellt, wird in den folgenden Kapiteln betrachtet. Zunachst wird in Kapitel 2 auf die Geschichte, die Euklidische Geometrie und ihre Grenzen eingegangen. In Kapitel 3 wird die fraktale Geometrie bzw. die gebrochenzahlige Dimension sowie die Koch Kurve dargestellt, wobei insbesondere das Wesen einer Kustenlinie naher analysiert wird. Zudem wird auf den Begriff der Selbstahnlichkeit eingega" |

Author | Takashi Sakai | |

ISBN-10 | 0821889567 | |

Release | 1996-01-01 | |

Pages | 358 | |

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This volume is an English translation of Sakai's textbook on Riemannian Geometry which was originally written in Japanese and published in 1992. The author's intent behind the original book was to provide to advanced undergraduate and graudate students an introduction to modern Riemannian geometry that could also serve as a reference. The book begins with an explanation of the fundamental notion of Riemannian geometry. Special emphasis is placed on understandability and readability, to guide students who are new to this area. The remaining chapters deal with various topics in Riemannian geometry, with the main focus on comparison methods and their applications. |

Author | Serge Lang | |

ISBN-10 | 3540966544 | |

Release | 1988 | |

Pages | 394 | |

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Geometry has been writing in one form or another for most of life. You can find so many inspiration from Geometry also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Geometry book for free. |

Author | Marcel Berger | |

ISBN-10 | 3540116583 | |

Release | 1987 | |

Pages | 432 | |

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The first part of a two-volume text providing a readable and lively presentation of large parts of geometry in the classical sense, this book appeals systematically to the reader's intuition and vision, and illustrates the mathematical text with many figures. |

Author | Harold Abelson | |

ISBN-10 | 0262510375 | |

Release | 1986-01-01 | |

Pages | 477 | |

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Turtle Geometry presents an innovative program of mathematical discovery that demonstrates how the effective use of personal computers can profoundly change the nature of a student's contact with mathematics. Using this book and a few simple computer programs, students can explore the properties of space by following an imaginary turtle across the screen.The concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduates. Harold Abelson is an associate professor in the Department of Electrical Engineering and Computer Science at MIT. Andrea diSessa is an associate professor in the Graduate School of Education, University of California, Berkeley. |

Author | Joe Harris | |

ISBN-10 | 0387977163 | |

Release | 1992-09-17 | |

Pages | 328 | |

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This book is intended to introduce students to algebraic geometry; to give them a sense of the basic objects considered, the questions asked about them, and the sort of answers one can expect to obtain. It thus emplasizes the classical roots of the subject. For readers interested in simply seeing what the subject is about, this avoids the more technical details better treated with the most recent methods. For readers interested in pursuing the subject further, this book will provide a basis for understanding the developments of the last half century, which have put the subject on a radically new footing. Based on lectures given at Brown and Harvard Universities, this book retains the informal style of the lectures and stresses examples throughout; the theory is developed as needed. The first part is concerned with introducing basic varieties and constructions; it describes, for example, affine and projective varieties, regular and rational maps, and particular classes of varieties such as determinantal varieties and algebraic groups. The second part discusses attributes of varieties, including dimension, smoothness, tangent spaces and cones, degree, and parameter and moduli spaces. |

Author | Daniel Pedoe | |

ISBN-10 | 0486658120 | |

Release | 1970 | |

Pages | 449 | |

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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. |

Author | David Hilbert | |

ISBN-10 | 3540643737 | |

Release | 2004-05-17 | |

Pages | 661 | |

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This volume contains notes for lectures on the foundations of geometry held by Hilbert from 1891-1902. These contain material which never found its way into print. The volume also reprints the first edition of Hilbert’s celebrated Grundlagen der Geometrie. |

Author | William P. Thurston | |

ISBN-10 | 0691083045 | |

Release | 1997-01 | |

Pages | 311 | |

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This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book was the origin of a grand scheme developed by Thurston that is now coming to fruition. In the 1920s and 1930s the mathematics of two-dimensional spaces was formalized. It was Thurston's goal to do the same for three-dimensional spaces. To do this, he had to establish the strong connection of geometry to topology--the study of qualitative questions about geometrical structures. The author created a new set of concepts, and the expression "Thurston-type geometry" has become a commonplace. Three-Dimensional Geometry and Topology had its origins in the form of notes for a graduate course the author taught at Princeton University between 1978 and 1980. Thurston shared his notes, duplicating and sending them to whoever requested them. Eventually, the mailing list grew to more than one thousand names. The book is the culmination of two decades of research and has become the most important and influential text in the field. Its content also provided the methods needed to solve one of mathematics' oldest unsolved problems--the Poincaré Conjecture. In 2005 Thurston won the first AMS Book Prize, for Three-dimensional Geometry and Topology. The prize recognizes an outstanding research book that makes a seminal contribution to the research literature. Thurston received the Fields Medal, the mathematical equivalent of the Nobel Prize, in 1982 for the depth and originality of his contributions to mathematics. In 1979 he was awarded the Alan T. Waterman Award, which recognizes an outstanding young researcher in any field of science or engineering supported by the National Science Foundation. |

Author | Glen E. Bredon | |

ISBN-10 | 9781475768480 | |

Release | 2013-03-09 | |

Pages | 131 | |

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This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS |

Author | Isaac Chavel | |

ISBN-10 | 0080874347 | |

Release | 1984-11-07 | |

Pages | 362 | |

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The basic goals of the book are: (i) to introduce the subject to those interested in discovering it, (ii) to coherently present a number of basic techniques and results, currently used in the subject, to those working in it, and (iii) to present some of the results that are attractive in their own right, and which lend themselves to a presentation not overburdened with technical machinery. |

Author | Saunders MacLane | |

ISBN-10 | 0387977104 | |

Release | 1992 | |

Pages | 627 | |

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An introduction to the theory of toposes which begins with illustrative examples and goes on to explain the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic. |

Author | Jeffrey Marc Lee | |

ISBN-10 | 9780821848159 | |

Release | 2009 | |

Pages | 671 | |

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Differential geometry began as the study of curves and surfaces using the methods of calculus. In time, the notions of curve and surface were generalized along with associated notions such as length, volume, and curvature. At the same time the topic has become closely allied with developments in topology. The basic object is a smooth manifold, to which some extra structure has been attached, such as a Riemannian metric, a symplectic form, a distinguished group of symmetries, or a connection on the tangent bundle. This book is a graduate-level introduction to the tools and structures of modern differential geometry. Included are the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, differential forms, de Rham cohomology, the Frobenius theorem and basic Lie group theory. The book also contains material on the general theory of connections on vector bundles and an in-depth chapter on semi-Riemannian geometry that covers basic material about Riemannian manifolds and Lorentz manifolds. An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hyper-surfaces in Euclidean space. There is also a section that derives the exterior calculus version of Maxwell's equations. The first chapters of the book are suitable for a one-semester course on manifolds. There is more than enough material for a year-long course on manifolds and geometry. |