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Differential Geometry


Elementary Differential Geometry, Revised 2nd Edition, Second Edition

Elementary Differential Geometry, Revised 2nd Edition, Second Edition Lowest new price: $84.79
Lowest used price: $47.00
List price: $96.95
Author: Barrett O'Neill

Written primarily for students who have completed the standard first courses in calculus and linear algebra, Elementary Differential Geometry, Revised 2nd Edition, provides an introduction to the geometry of curves and surfaces.

The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard.

This revision of the Second Edition provides a thorough update of commands for the symbolic computation programs Mathematica or Maple, as well as additional computer exercises. As with the Second Edition, this material supplements the content but no computer skill is necessary to take full advantage of this comprehensive text.

  • Over 36,000 copies sold worldwide
  • Accessible, practical yet rigorous approach to a complex topic--also suitable for self-study
  • Extensive update of appendices on Mathematica and Maple software packages
  • Thorough streamlining of second edition's numbering system
  • Fuller information on solutions to odd-numbered problems
  • Additional exercises and hints guide students in using the latest computer modeling tools

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The Geometry of Spacetime: An Introduction to Special and General Relativity (Undergraduate Texts in Mathematics)

The Geometry of Spacetime: An Introduction to Special and General Relativity (Undergraduate Texts in Mathematics) Lowest new price: $64.13
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Author: James J. Callahan
Brand: James J Callahan

Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory.

Features:

  • The Geometry of Spacetime An Introduction to Special and General Relativity

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Regular Polytopes

Regular Polytopes Lowest new price: $7.99
Lowest used price: $3.25
List price: $16.95
Author: H. S. M. Coxeter
Brand: Coxeter, H. S. M.

Polytopes are geometrical figures bounded by portions of lines, planes, or hyperplanes. In plane (two dimensional) geometry, they are known as polygons and comprise such figures as triangles, squares, pentagons, etc. In solid (three dimensional) geometry they are known as polyhedra and include such figures as tetrahedra (a type of pyramid), cubes, icosahedra, and many more; the possibilities, in fact, are infinite! H. S. M. Coxeter's book is the foremost book available on regular polyhedra, incorporating not only the ancient Greek work on the subject, but also the vast amount of information that has been accumulated on them since, especially in the last hundred years. The author, professor of Mathematics, University of Toronto, has contributed much valuable work himself on polytopes and is a well-known authority on them.
Professor Coxeter begins with the fundamental concepts of plane and solid geometry and then moves on to multi-dimensionality. Among the many subjects covered are Euler's formula, rotation groups, star-polyhedra, truncation, forms, vectors, coordinates, kaleidoscopes, Petrie polygons, sections and projections, and star-polytopes. Each chapter ends with a historical summary showing when and how the information contained therein was discovered. Numerous figures and examples and the author's lucid explanations also help to make the text readily comprehensible.
Although the study of polytopes does have some practical applications to mineralogy, architecture, linear programming, and other areas, most people enjoy contemplating these figures simply because their symmetrical shapes have an aesthetic appeal. But whatever the reasons, anyone with an elementary knowledge of geometry and trigonometry will find this one of the best source books available on this fascinating study.

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Geometry of Surfaces (Universitext)

Geometry of Surfaces (Universitext) Lowest new price: $53.25
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Author: John Stillwell
Brand: John C Stillwell

The geometry of surfaces is an ideal starting point for learning geometry, for, among other reasons, the theory of surfaces of constant curvature has maximal connectivity with the rest of mathematics. This text provides the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. It includes exercises and informal discussions.

Features:

  • Geometry of Surfaces

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Differential Forms and the Geometry of General Relativity

Differential Forms and the Geometry of General Relativity Lowest new price: $28.13
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List price: $59.95
Author: Tevian Dray

Differential Forms and the Geometry of General Relativity provides readers with a coherent path to understanding relativity. Requiring little more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics of general relativity.

The book contains two intertwined but distinct halves. Designed for advanced undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that describes some of the surprising implications of relativity without introducing more formalism than necessary. This nonstandard approach uses differential forms rather than tensor calculus and minimizes the use of "index gymnastics" as much as possible.

The second half of the book takes a more detailed look at the mathematics of differential forms. It covers the theory behind the mathematics used in the first half by emphasizing a conceptual understanding instead of formal proofs. The book provides a language to describe curvature, the key geometric idea in general relativity.

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Structure of Dynamical Systems: A Symplectic View of Physics (Progress in Mathematics) (Volume 149)

Structure of Dynamical Systems: A Symplectic View of Physics (Progress in Mathematics) (Volume 149) Lowest new price: $171.45
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Author: J.M. Souriau
Brand: Brand: Birkhäuser

The aim of the book is to treat all three basic theories of physics, namely, classical mechanics, statistical mechanics, and quantum mechanics from the same perspective, that of symplectic geometry, thus showing the unifying power of the symplectic geometric approach. Reading this book will give the reader a deep understanding of the interrelationships between the three basic theories of physics. This book is addressed to graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics, and (geometric) quantization.

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  • Used Book in Good Condition


Lectures on Differential Geometry (2010 re-issue)

Lectures on Differential Geometry (2010 re-issue) Lowest new price: $35.00
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Author: Richard Schoen

This volume presents lectures given by Richard Schoen and Shing-Tung Yau at the Institute for Advanced Studies at Princeton University in 1984 and 1985. The lectures describe the major advances in differential geometry, which progressed rapidly in the twentieth century.

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Differential Geometry of Curves and Surfaces

Differential Geometry of Curves and Surfaces Lowest new price: $40.49
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Author: Masaaki Umehara
Brand: Ingramcontent

This engrossing volume on curve and surface theories is the result of many years of experience the authors have had with teaching the most essential aspects of this subject. The first half of the text is suitable for a university-level course, without the need for referencing other texts, as it is completely self-contained. More advanced material in the second half of the book, including appendices, also serves more experienced students well. Furthermore, this text is also suitable for a seminar for graduate students, and for self-study. It is written in a robust style that gives the student the opportunity to continue his study at a higher level beyond what a course would usually offer. Further material is included, for example, closed curves, enveloping curves, curves of constant width, the fundamental theorem of surface theory, constant mean curvature surfaces, and existence of curvature line coordinates. Surface theory from the viewpoint of manifolds theory is explained, and encompasses higher level material that is useful for the more advanced student. This includes, but is not limited to, indices of umbilics, properties of cycloids, existence of conformal coordinates, and characterizing conditions for singularities. In summary, this textbook succeeds in elucidating detailed explanations of fundamental material, where the most essential basic notions stand out clearly, but does not shy away from the more advanced topics needed for research in this field. It provides a large collection of mathematically rich supporting topics. Thus, it is an ideal first textbook in this field.

Features:

  • Differential Geometry of Curves and Surfaces

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Modern Geometry―Methods and Applications: Part III: Introduction to Homology Theory (Graduate Texts in Mathematics)

Modern Geometry―Methods and Applications: Part III: Introduction to Homology Theory (Graduate Texts in Mathematics) Lowest new price: $45.00
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Author: B.A. Dubrovin
Brand: B A Dubrovin

Focuses on homology theory This volume contains introductions to the contemporary methods for the calculation of homology groups and the classification of manifesto It is suitable for both scientists and students of mathematics as well as theoretical physics Over the past fifteen years the geometrical and topological methods of the theory of manifolds have as sumed a central role in the most advanced areas of pure and applied mathematics as well as theoretical physics The three volumes of Modern Geometry Methods and Applicationscontain a concrete exposition of these methods together with their main applications in mathematics and physics This third volume presented in highly accessible languages concentrates in homology theory It contains introductions to the contemporary methods for the calculation of homology groups and the classification of manifesto Both scientists and students of mathematics as well as theoretical physics will find this book to be a valuable reference and text

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  • Modern Geometry Methods and Applications Part 3 Introduction to Homology Theory

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Comparison Theorems in Riemannian Geometry (Ams Chelsea Publishing)

Comparison Theorems in Riemannian Geometry (Ams Chelsea Publishing) Lowest new price: $34.97
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Author: Jeff Cheeger and David G. Ebin
Brand: Brand: American Mathematical Society

The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem--the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most relevant contributions to the subject in the years 1959 to 1974. These include the pinching (or sphere) theorem, Berger's theorem for symmetric spaces, the differentiable sphere theorem, the structure of complete manifolds of non-negative curvature, and finally, results about the structure of complete manifolds of non-positive curvature. Emphasis is given to the phenomenon of rigidity, namely, the fact that although the conclusions which hold under the assumption of some strict inequality on curvature can fail when the strict inequality on curvature can fail when the strict inequality is relaxed to a weak one, the failure can happen only in a restricted way, which can usually be classified up to isometry. Much of the material, particularly the last four chapters, was essentially state-of-the-art when the book first appeared in 1975. Since then, the subject has exploded, but the material covered in the book still represents an essential prerequisite for anyone who wants to work in the field.

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  • Used Book in Good Condition

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