Tevian Dray's Books

The Geometry of Special Relativity

By: Tevian Dray

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The Geometry of Special Relativity

By: Tevian Dray

This unique book presents a particularly beautiful way of looking at special relativity. The author encourages students to see beyond the formulas to the deeper structure. The unification of space and time introduced by Einstein’s special theory of relativity is one of the cornerstones of the modern scientific description of the universe. Yet the unification is counterintuitive because we perceive time very differently from space. Even in relativity, time is not just another dimension, it is one with different properties The book treats the geometry of hyperbolas as the key to understanding special relativity. The author simplifies the formulas and emphasizes their geometric content. Many important relations, including the famous relativistic addition formula for velocities, then follow directly from the appropriate (hyperbolic) trigonometric addition formulas. Prior mastery of (ordinary) trigonometry is sufficient for most of the material presented, although occasional use is made of elementary differential calculus, and the chapter on electromagnetism assumes some more advanced knowledge. Changes to the Second Edition The treatment of Minkowski space and spacetime diagrams has been expanded. Several new topics have been added, including a geometric derivation of Lorentz transformations, a discussion of three-dimensional spacetime diagrams, and a brief geometric description of "area" and how it can be used to measure time and distance. Minor notational changes were made to avoid conflict with existing usage in the literature. Table of Contents Preface 1. Introduction. 2. The Physics of Special Relativity. 3. Circle Geometry. 4. Hyperbola Geometry. 5. The Geometry of Special Relativity. 6. Applications. 7. Problems III. 8. Paradoxes. 9. Relativistic Mechanics. 10. Problems II. 11. Relativistic Electromagnetism. 12. Problems III. 13. Beyond Special Relativity. 14. Three-Dimensional Spacetime Diagrams. 15. Minkowski Area via Light Boxes. 16. Hyperbolic Geometry. 17. Calculus. Bibliography. Author Biography Tevian Dray is a Professor of Mathematics at Oregon State University. His research lies at the interface between mathematics and physics, involving differential geometry and general relativity, as well as nonassociative algebra and particle physics; he also studies student understanding of "middle-division" mathematics and physics content. Educated at MIT and Berkeley, he held postdoctoral positions in both mathematics and physics in several countries prior to coming to OSU in 1988. Professor Dray is a Fellow of the American Physical Society for his work in relativity, and an award-winning teacher.

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Page Count

197

Publisher

CRC Press

Published Date

ISBN 10

1315160706

ISBN 13

9781315160702

Differential Forms and the Geometry of General Relativity

By: Tevian Dray

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Differential Forms and the Geometry of General Relativity

By: 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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Page Count

324

Publisher

CRC Press

Published Date

ISBN 10

1466510005

ISBN 13

9781466510005

The Geometry of the Octonions

By: Tevian Dray,Corinne A. Manogue

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The Geometry of the Octonions

By: Tevian Dray,Corinne A. Manogue

There are precisely two further generalizations of the real and complex numbers, namely, the quaternions and the octonions. The quaternions naturally describe rotations in three dimensions. In fact, all (continuous) symmetry groups are based on one of these four number systems. This book provides an elementary introduction to the properties of the octonions, with emphasis on their geometric structure. Elementary applications covered include the rotation groups and their spacetime generalization, the Lorentz group, as well as the eigenvalue problem for Hermitian matrices. In addition, more sophisticated applications include the exceptional Lie groups, octonionic projective spaces, and applications to particle physics including the remarkable fact that classical supersymmetry only exists in particular spacetime dimensions.Contents: Introduction"Number Systems: "The Geometry of the Complex NumbersThe Geometry of the QuaternionsThe Geometry of the OctonionsOther Number Systems"Symmetry Groups: "Some Orthogonal GroupsSome Unitary GroupsSome Symplectic GroupsSymmetry Groups over Other Division AlgebrasLie Groups and Lie AlgebrasThe Exceptional Groups"Applications: "Division Algebras in MathematicsOctonionic Eigenvalue ProblemsThe Physics of the OctonionsMagic Squares Readership: Advanced ubdergraduate and graduate students and faculty in mathematics and physics; non-experts with moderately sophisticated mathematics background. Key Features: This book is easily digestible by a large audience wanting to know the elementary introduction to octanionsSuitable for any reader with a grasp of the complex numbers, although familiarity with non-octonionic versions of some of the other topics would be helpfulMany open problems are very accessibleAdvanced topics covered are quite sophisticated, leading up to a clear discussion of (one representation of) the exceptional Lie algebras and their associated root diagrams, and of the octonionic projective spaces on which they act

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229

Publisher

World Scientific

Published Date

ISBN 10

981440182X

ISBN 13

9789814401821

The Geometry of Special Relativity

By: Tevian Dray

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The Geometry of Special Relativity

By: Tevian Dray

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Page Count

167

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CRC Press

Published Date

ISBN 10

1351663208

ISBN 13

9781351663205

Differential Forms and the Geometry of General Relativity

By: Tevian Dray

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Differential Forms and the Geometry of General Relativity

By: Tevian Dray

Requiring little more than calculus and some linear algebra, this book provides readers with a coherent path to understanding relativity. It helps readers learn just enough differential geometry to grasp the basics of general relativity. The first half of the book describes some of the surprising implications of relativity without introducing more formalism than necessary. The second half takes a more detailed look at the mathematics of differential forms, showing how they are used to describe key geometric ideas in general relativity.

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Page Count

315

Publisher

CRC Press

Published Date

ISBN 10

1466510323

ISBN 13

9781466510326

The Geometry Of The Octonions

By: Tevian Dray,Corinne A Manogue

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The Geometry Of The Octonions

By: Tevian Dray,Corinne A Manogue

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Solve jigsaw puzzle

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Page Count

229

Publisher

World Scientific

Published Date

ISBN 10

9814401838

ISBN 13

9789814401838

Book's by Tevian Dray

The Geometry of Special Relativity

The Geometry of Special Relativity

Differential Forms and the Geometry of General Relativity

Differential Forms and the Geometry of General Relativity

The Geometry of the Octonions

The Geometry of the Octonions

The Geometry of Special Relativity

The Geometry of Special Relativity

Differential Forms and the Geometry of General Relativity

Differential Forms and the Geometry of General Relativity

The Geometry Of The Octonions

The Geometry Of The Octonions

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