Modern Geometry with Applications

Author: George A. Jennings

Publisher: Springer Science & Business Media

ISBN: 1461208556

Category: Mathematics

Page: 204

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This introduction to modern geometry differs from other books in the field due to its emphasis on applications and its discussion of special relativity as a major example of a non-Euclidean geometry. Additionally, it covers the two important areas of non-Euclidean geometry, spherical geometry and projective geometry, as well as emphasising transformations, and conics and planetary orbits. Much emphasis is placed on applications throughout the book, which motivate the topics, and many additional applications are given in the exercises. It makes an excellent introduction for those who need to know how geometry is used in addition to its formal theory.
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Modern Geometry with Applications

Author: George Jennings

Publisher: N.A

ISBN: N.A

Category: Geometry, Modern

Page: 187

View: 4053

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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 and teachers, who need to know how geometry is used in addition to its formal theory.
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Geometry: from Isometries to Special Relativity

Author: Nam-Hoon Lee

Publisher: Springer Nature

ISBN: 3030421015

Category: Mathematics

Page: 258

View: 4843

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This textbook offers a geometric perspective on special relativity, bridging Euclidean space, hyperbolic space, and Einstein’s spacetime in one accessible, self-contained volume. Using tools tailored to undergraduates, the author explores Euclidean and non-Euclidean geometries, gradually building from intuitive to abstract spaces. By the end, readers will have encountered a range of topics, from isometries to the Lorentz–Minkowski plane, building an understanding of how geometry can be used to model special relativity. Beginning with intuitive spaces, such as the Euclidean plane and the sphere, a structure theorem for isometries is introduced that serves as a foundation for increasingly sophisticated topics, such as the hyperbolic plane and the Lorentz–Minkowski plane. By gradually introducing tools throughout, the author offers readers an accessible pathway to visualizing increasingly abstract geometric concepts. Numerous exercises are also included with selected solutions provided. Geometry: from Isometries to Special Relativity offers a unique approach to non-Euclidean geometries, culminating in a mathematical model for special relativity. The focus on isometries offers undergraduates an accessible progression from the intuitive to abstract; instructors will appreciate the complete instructor solutions manual available online. A background in elementary calculus is assumed.
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Riemannian Geometry and Geometric Analysis

Author: Jürgen Jost

Publisher: Springer Science & Business Media

ISBN: 3662223856

Category: Mathematics

Page: 458

View: 4597

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FROM REVIEWS OF THE FIRST EDITION "a very readable introduction to Riemannian geometry...it is most welcome...The book is made more interesting by the perspectives in various sections, where the author mentions the history and development of the material and provides the reader with references."-MATHEMATICAL REVIEWS
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Logic and Structure

Author: Dirk van Dalen

Publisher: Springer Science & Business Media

ISBN: 3662029626

Category: Mathematics

Page: 220

View: 9285

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New corrected printing of a well-established text on logic at the introductory level.
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Euclidean and Non-Euclidean Geometry

An Analytic Approach

Author: Patrick J. Ryan

Publisher: Cambridge University Press

ISBN: 9780521276351

Category: Mathematics

Page: 215

View: 7022

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This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic. The primary purpose is to acquaint the reader with the classical results of plane Euclidean and nonEuclidean geometry, congruence theorems, concurrence theorems, classification of isometries, angle addition and trigonometrical formulae. However, the book not only provides students with facts about and an understanding of the structure of the classical geometries, but also with an arsenal of computational techniques for geometrical investigations. The aim is to link classical and modern geometry to prepare students for further study and research in group theory, Lie groups, differential geometry, topology, and mathematical physics. The book is intended primarily for undergraduate mathematics students who have acquired the ability to formulate mathematical propositions precisely and to construct and understand mathematical arguments. Some familiarity with linear algebra and basic mathematical functions is assumed, though all the necessary background material is included in the appendices.
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Lie Sphere Geometry

With Applications to Submanifolds

Author: Thomas E. Cecil

Publisher: Springer Science & Business Media

ISBN: 1475740964

Category: Mathematics

Page: 209

View: 835

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Lie Sphere Geometry provides a modern treatment of Lie's geometry of spheres, its recent applications and the study of Euclidean space. This book begins with Lie's construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres and Lie sphere transformation. The link with Euclidean submanifold theory is established via the Legendre map. This provides a powerful framework for the study of submanifolds, especially those characterized by restrictions on their curvature spheres. Of particular interest are isoparametric, Dupin and taut submanifolds. These have recently been classified up to Lie sphere transformation in certain special cases through the introduction of natural Lie invariants. The author provides complete proofs of these classifications and indicates directions for further research and wider application of these methods.
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Great Moments in Mathematics (before 1650)

Author: Howard Whitley Eves

Publisher: MAA

ISBN: 9780883853108

Category: Mathematics

Page: 270

View: 7950

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Presents a series of lectures on the history of mathematics covering such topics as the Pythagorean Theorem, Archimedes, and Fibonacci.
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