Introduction to Hyperbolic Geometry

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9780387943398: Introduction to Hyperbolic Geometry

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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Book Description:

"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

Contenuti:

Preface; Introduction; 1. Axioms for Plane Geometry; 2. Some Neutral Theorems of Plane Geometry; 3. Qualitative Description of the Hyperbolic Plane; 4. H3 and Euclidean Approximations in H2; 5. Differential Geometry of Surface; 6. Quantitative Considerations; 7. Consistency and Categoricalness of the Hyperbolic Axioms- the Classical Models; 8. Matrix Representation of the Isometry Group; 9. Differential and Hyperbolic Geometry in More Dimensions; 10. Connections with the Lorentz Group of Special Relativity; 11. Constructions by Straightedge and Compass in the Hyperbolic Plane; Index

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Ramsay, Arlan; Richtmyer, Robert D.
Editore: Springer-Verlag New York Inc., United States (1995)
ISBN 10: 0387943390 ISBN 13: 9780387943398
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Descrizione libro Springer-Verlag New York Inc., United States, 1995. Paperback. Condizione libro: New. 1995 ed.. 234 x 155 mm. Language: English Brand New Book ***** Print on Demand *****.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. Codice libro della libreria AAV9780387943398

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Ramsay, Arlan; Richtmyer, Robert D.
Editore: Springer-Verlag New York Inc., United States (1995)
ISBN 10: 0387943390 ISBN 13: 9780387943398
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Descrizione libro Springer-Verlag New York Inc., United States, 1995. Paperback. Condizione libro: New. 1995 ed.. 234 x 155 mm. Language: English . Brand New Book ***** Print on Demand *****. 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. Codice libro della libreria AAV9780387943398

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Ramsay, Arlan; Richtmyer, Robert D.
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ISBN 10: 0387943390 ISBN 13: 9780387943398
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Descrizione libro Springer, 1995. Condizione libro: New. This item is printed on demand for shipment within 3 working days. Codice libro della libreria LP9780387943398

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Descrizione libro Springer, 1995. Paperback. Condizione libro: NEW. 9780387943398 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0275392

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Descrizione libro Springer-Verlag New York Inc., 1995. PAP. Condizione libro: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria LQ-9780387943398

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Descrizione libro Springer-Verlag New York Inc., 1995. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria IQ-9780387943398

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Descrizione libro Springer, 1995. Condizione libro: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: Preface; Introduction; 1. Axioms for Plane Geometry; 2. Some Neutral Theorems of Plane Geometry; 3. Qualitative Description of the Hyperbolic Plane; 4. H3 and Euclidean Approximations in H2; 5. Differential Geometry of Surface; 6. Quantitative Considerations; 7. Consistency and Categoricalness of the Hyperbolic Axioms- the Classical Models; 8. Matrix Representation of the Isometry Group; 9. Differential and Hyperbolic Geometry in More Dimensions; 10. Connections with the Lorentz Group of Special Relativity; 11. Constructions by Straightedge and Compass in the Hyperbolic Plane; Index. Codice libro della libreria ABE_book_new_0387943390

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Descrizione libro Springer, 1995. Paperback. Condizione libro: New. book. Codice libro della libreria 0387943390

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Ramsay, Arlan; Richtmyer, Robert D.
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Descrizione libro Springer, 2016. Paperback. Condizione libro: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Codice libro della libreria ria9780387943398_lsuk

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Ramsay, Arlan; Richtmyer, Robert D.
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Descrizione libro Springer Dez 1995, 1995. Taschenbuch. Condizione libro: Neu. 279x210x16 mm. This item is printed on demand - Print on Demand Neuware - 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. 289 pp. Englisch. Codice libro della libreria 9780387943398

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