- Tapa dura: 321 páginas
- Editor: A K Peters/CRC Press; Edición: 1 (12 de diciembre de 2014)
- Idioma: Inglés
- ISBN-10: 1466510005
- ISBN-13: 978-1466510005
- Valoración media de los clientes: Sé el primero en opinar sobre este producto
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Differential Forms and the Geometry of General Relativity (Inglés) Tapa dura – 12 dic 2014
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"In this book, the author outlines an interesting path to relativity and shows its various stages on the way … The author inserts suggestive pictures and images, which make the book more attractive and easier to read. The book addresses not only specialists and graduate students, but even advanced undergraduates, due to its interactive structure containing questions and answers."
―Zentralblatt MATH 1315
"…the presentation is very far from the ‘definition-theorem-proof-example’ style of a traditional mathematics text; rather, we meet important ideas several times, and they are developed further with each new exposure. This is a pedagogical decision which seems to me to be sound, as it allows the student’s understanding of the ideas to develop."
―Robert J. Low, Mathematical Reviews, June 2015
"This is a brilliant book. Dray has an extraordinary knack of conveying the key mathematics and concepts with an elegant economy that rivals the expositions of the legendary Paul Dirac. It is pure pleasure to see far-reaching results emerge effortlessly from easy-to-follow arguments, and for simple examples to morph into generalizations. It is so refreshing to find a book that does not obscure the basics with unnecessary technicalities, yet can develop sophisticated formalism from very modest mathematical investments."
―Paul Davies, Regents’ Professor and Director, Beyond Center for Fundamental Concepts in Science; Co-Director, Cosmology Initiative; and Principal Investigator, Center for the Convergence of Physical Science and Cancer Biology, Arizona State University
"It took Einstein eight years to create general relativity by carefully balancing his physical intuition and the rather tedious mathematical formalism at his disposal. Tevian Dray’s presentation of the geometry of general relativity in the elegant language of differential forms offers even beginners a novel and direct route to a deep understanding of the theory’s core concepts and applications, from the geometry of black holes to cosmological models."
―Jürgen Renn, Director, Max Planck Institute for the History of Science, Berlin
Reseña del editor
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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The treatment of differential forms is very terse but pedagogical. He tells you not only the formalism but (more or less) what it means. It allows a quick understanding of "what" and "what to do," although a deeper understanding of why it is this way could hardly be extracted by a beginning student. Here, Professor Dray is not entirely to blame. Very many authors of differential geometry are so caught up in the most rigid formalism that they seldom explain what it really means. They perfect the formalism while neglecting real understanding. This book would be ideal indeed for a poor overwhelmed student facing the material for the first time, a person who simply wanted to remain academically solvent. For others, who have both more time and greater needs, it would be much better to learn differential forms from Shigeyuki Morita's book or even from Bott and Tu. The "real" course in differential geometry is Barrett O'Neill's book on Semi-Riemannian Geometry. It is understandable, although not committed as much to differential forms and somewhat more formal. Real understanding of differential forms is more accessible with Morita.
For the relativity part, Professor Dray gives very good insights, and there is no reason to criticize him. For me, Oyvind Gron's books are better for the "kinder, gentler" introduction to general relativity because they give a more complete picture and include reasonably deep results. There is no replacement for Wald's book or even the telephone book of Misner, Thorne, and Wheeler, although it is almost time to update it. Professor Dray's book on General Relativity is probably the best true crash course available anywhere. For those who are not actually crashing, I think other, somewhat longer introductions will give more insight.