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Other titles in the Undergraduate Texts in Mathematics series:
The Geometry of Spacetime (Undergraduate Texts in Mathematics)by James Callahan
Synopses & Reviews
In 1905, Albert Einstein offered a revolutionary theory--special relativity--to explain some of the most troubling problems in current physics concerning electromagnetism and motion. Soon afterwards, Hermann Minkowski recast special relativity essentially as a new geometric structure for spacetime. These ideas are the subject of the first part of the book. The second part develops the main implications of Einstein's general relativity as a theory of gravity rooted in the differential geometry of surfaces. The author explores the way an individual observer views the world and how a pair of observers collaborate to gain objective knowledge of the world. To encompass both the general and special theory, he uses the geometry of spacetime as the unifying theme of the book. To read it, one needs only a first course in linear algebra and multivariable calculus and familiarity with the physical applications of calculus.
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.
Includes bibliographical references (p. 435-437) and index.
Table of Contents
* Relativity before 1905 * Special relativity--kinematics * Special relativity--kinetics * Arbitrary frames * Surfaces and curvatures * Intrinsic geometry * General relativity * Consequences
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