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Inhaltsangabe
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.
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Críticas
"The book is well laid out with no shortage of diagrams and with each chapter prefaced with its own useful introduction...Also well written, it makes pleasurable reading." Proceedings of the Edinburgh Mathematical Society
Reseña del editor
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.
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Introduction to Hyperbolic Geometry
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Paperback. Zustand: Near Fine. First printing. 23.5 x 15.5 cm. 287pp. 59 figures, Index. Yellow softcover. Spine is lightly sunned. Universitext. Bestandsnummer des Verkäufers 81577
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Introduction to Hyperbolic Geometry
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Introduction to Hyperbolic Geometry (Universitext)
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Zustand: acceptable. This copy may contain significant wear, including bending, heavy writing, tears, and or water damage. This book is a functional copy, not necessarily a beautiful copy. Copy may have loose pages. May not include access codes or CDs. May be an Ex library book with stickers and stamps. Dustjacket may be missing. Bestandsnummer des Verkäufers GBV.0387943390.A
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Introduction to Hyperbolic Geometry
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Introduction to Hyperbolic Geometry (Paperback)
Verlag:
Springer-Verlag New York Inc., New York, NY, 1995
ISBN 10: 0387943390
ISBN 13: 9780387943398
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Paperback. Zustand: new. Paperback. This text for advanced undergraduates emphasizes the logical connections of the subject. The derivations of formulas from the axioms do not make use of models of the hyperbolic plane until the axioms are shown to be categorical; the differential geometry of surfaces is developed far enough to establish its connections to the hyperbolic plane; and the axioms and proofs use the properties of the real number system to avoid the tedium of a completely synthetic approach. The development includes properties of the isometry group of the hyperbolic plane, tilings, and applications to special relativity. Elementary techniques from complex analysis, matrix theory, and group theory are used, and some mathematical sophistication on the part of students is thus required, but a formal course in these topics is not a prerequisite. 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. The book goes well beyond the standard course in later chapters, and there is enough material for an honors course, or for supplementary reading. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9780387943398
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Introduction to Hyperbolic Geometry (Universitext)
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Introduction to Hyperbolic Geometry
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Introduction to Hyperbolic Geometry (Universitext)
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Introduction to Hyperbolic Geometry
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Introduction to Hyperbolic Geometry
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