introduction to hyperbolic geometry universitext

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Introduction To Hyperbolic Geometry

Author : Arlan Ramsay
ISBN : 9781475755855
Genre : Mathematics
File Size : 37. 11 MB
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This book is an introduction to hyperbolic and differential geometry that provides material in the early chapters that can serve as a textbook for a standard upper division course on hyperbolic geometry. For that material, the students need to be familiar with calculus and linear algebra and willing to accept one advanced theorem from analysis without proof. The book goes well beyond the standard course in later chapters, and there is enough material for an honors course, or for supplementary reading. Indeed, parts of the book have been used for both kinds of courses. Even some of what is in the early chapters would surely not be nec essary for a standard course. For example, detailed proofs are given of the Jordan Curve Theorem for Polygons and of the decomposability of poly gons into triangles, These proofs are included for the sake of completeness, but the results themselves are so believable that most students should skip the proofs on a first reading. The axioms used are modern in character and more "user friendly" than the traditional ones. The familiar real number system is used as an in gredient rather than appearing as a result of the axioms. However, it should not be thought that the geometric treatment is in terms of models: this is an axiomatic approach that is just more convenient than the traditional ones.

Lectures On Hyperbolic Geometry

Author : Riccardo Benedetti
ISBN : 354055534X
Genre : Mathematics
File Size : 64. 30 MB
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The core of the book is the study of the space of the hyperbolic manifolds endowed with the Chabauty and the geometric topology, and in particular the proof of the hypberbolic surgery theorem in dimension three, based on the representation of three-mainfolds as glued ideal tetrahedra. The development of this main theme requires setting a wide background forming the body of the book: the classical geometry of the hyperbolic space, the Fenchel-Nielsen parametrization of the Teichmüller space, Mostow's rigidity theorem, Margulis' lemma. As a conclusion some features of bounded cohomology, flat fiber bundles and amenable groups are mentioned.

Non Euclidean Geometry

Author : H. S. M. Coxeter
ISBN : 0883855224
Genre : Mathematics
File Size : 83. 34 MB
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A reissue of Professor Coxeter's classic text on non-Euclidean geometry. It surveys real projective geometry, and elliptic geometry. After this the Euclidean and hyperbolic geometries are built up axiomatically as special cases. This is essential reading for anybody with an interest in geometry.

Analytic Hyperbolic Geometry In N Dimensions

Author : Abraham Albert Ungar
ISBN : 9781482236682
Genre : Mathematics
File Size : 46. 17 MB
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The concept of the Euclidean simplex is important in the study of n-dimensional Euclidean geometry. This book introduces for the first time the concept of hyperbolic simplex as an important concept in n-dimensional hyperbolic geometry. Following the emergence of his gyroalgebra in 1988, the author crafted gyrolanguage, the algebraic language that sheds natural light on hyperbolic geometry and special relativity. Several authors have successfully employed the author’s gyroalgebra in their exploration for novel results. Françoise Chatelin noted in her book, and elsewhere, that the computation language of Einstein described in this book plays a universal computational role, which extends far beyond the domain of special relativity. This book will encourage researchers to use the author’s novel techniques to formulate their own results. The book provides new mathematical tools, such as hyperbolic simplexes, for the study of hyperbolic geometry in n dimensions. It also presents a new look at Einstein’s special relativity theory.

Vorlesungen Ber Riemannsche Fl Chen

Author : Robert C. Gunning
ISBN : 3411008377
Genre : Riemann surfaces
File Size : 77. 98 MB
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Elementary Geometry In Hyperbolic Space

Author : Werner Fenchel
ISBN : 3110117347
Genre : Mathematics
File Size : 42. 80 MB
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Hyperbolic geometry is in a period of revised interest. This book contains a substantial account of the parts of the theory basic to the study of Kleinian groups, but it also contains the more broad-reaching thoughts of the author, one of the pioneers in the theory of convex bodies and a major contributor in other fields of mathematics. Annotation copyrighted by Book News, Inc., Portland, OR

Modern Geometry With Applications

Author : George Jennings
ISBN : STANFORD:36105016222056
Genre : Mathematics
File Size : 32. 92 MB
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This is an introduction to the theory and applications of modern geometry. It differs from other books in its field in its emphasis on applications and its discussion of Special Relativity as a major example of a non-Euclidean geometry. Besides Special Relativity, it covers two other important areas of non-Euclidean geometry: spherical geometry (used in navigation and astronomy) and projective geometry (used in art). In addition, it reviews many useful topics from Euclidean geometry, emphasizing transformations, and includes a chapter on conics and planetary orbits. Applications are stressed throughout the book. Every topic is motivated by an application and many additional applications are given in the exercises. The book would be an excellent introduction to higher geometry for those students, especially prospective mathematics teachers, who need to know how geometry is used in addition to its formal theory.

Quod Erat Knobelandum

Author : Clara Löh
ISBN : 9783662489567
Genre : Mathematics
File Size : 22. 51 MB
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Fünfzehn ausgewählte mathematische Themen mit Aufgaben und Lösungen laden zum Entdecken und Knobeln ein und bieten Einblicke in die faszinierende Welt der Mathematik - von A wie Aussagenlogik bis Z wie Zahlentheorie. Die Themen wecken so die Neugierde für Mathematik und fördern die Begeisterung von Schülerinnen und Schülern ab Klasse 7. Anleitungen zum mathematischen Problemlösen und Beweisen erleichtern dabei den Einstieg. Das vorliegende Buch enthält das überarbeitete und ergänzte Material des Schülerzirkels Mathematik der Fakultät für Mathematik an der Universität Regensburg aus den Schuljahren 2012/13 bis 2014/15. Stimme zum Buch: "Es ist erfreulich, dass die Aufgaben und Lösungen aus dem Schülerzirkel Mathematik der Universität Regensburg einem breiten Leserkreis zur Verfügung gestellt werden. Die Verbindung von pfiffigen Knobelaufgaben als Einstieg in ein Thema mit der Vermittlung des mathematischen Hintergrundwissens wird sicher vielen Schülerinnen und Schülern den Weg in die Welt der Mathematik ebnen." Hanns-Heinrich Langmann, Projektleiter Bundesweite Mathematik-Wettbewerbe bei Bildung & Begabung

An Invitation To Algebraic Geometry

Author : Karen Smith
ISBN : 0387989803
Genre : Mathematics
File Size : 59. 1 MB
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This is a description of the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.

Automorphe Formen

Author : Anton Deitmar
ISBN : 9783642123900
Genre : Mathematics
File Size : 82. 77 MB
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Das Buch bietet eine Einführung in die Theorie der automorphen Formen. Beginnend bei klassischen Modulformen führt der Autor seine Leser hin zur modernen, darstellungstheoretischen Beschreibung von automorphen Formen und ihren L-Funktionen. Das Hauptgewicht legt er auf den Übergang von der klassischen, elementaren Sichtweise zu der modernen, durch die Darstellungstheorie begründete Herangehensweise. Diese Art der Verbindung von klassischer und moderner Sichtweise war in der Lehrbuchliteratur bisher nicht zu finden.

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