Geometrical Methods of Mathematical Physics

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Summary: Introduction to Differential Geometry for physicists
Review: A heuristic and intuitive intro. to manifolds, fiber bundles, connections etc. Some applications are briefly touched upon. This is a good book to study for those that feel they didn't learn enough geometry from their GR class. Note: no complex algebraic geometry here, so this book would be considered too elementary for those looking for a mathematics book for strings.

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Summary: a little time and no love
Review: I am very angry with paying this much money for a book which obviously dosen't live up to it's name. Think I that Schuz's writing "exposition" is no more than symbolic buffoonery. If you want a book that will knack ya sax off than get a copy of Schutz's "A First Course in General Relativity". <end transmission>

Rating:
Summary: Not as good as "a first course in general relativity"
Review: I had read first the "first course in general relativity"and was exited,so i fygured out that this book from the same author would reach the same standards,but it didnt.If Ihadnt read the first book from Schutz this book would be incomprenheceble.The greatest problem i think is the lack of exercices.Without them you cant really go anywhere.Another problem ,i believe,is the short space given to analyzeeach topic.Eventhough i understand tensor calculus very well I just cant get anywhere with the differential forms.
Eventhough its not the worst book out there its not the best either.My advise,buy a better book.

Rating:
Summary: Not as good as "a first course in general relativity"
Review: I had read first the "first course in general relativity"and was exited,so i fygured out that this book from the same author would reach the same standards,but it didnt.If Ihadnt read the first book from Schutz this book would be incomprenheceble.The greatest problem i think is the lack of exercices.Without them you cant really go anywhere.Another problem ,i believe,is the short space given to analyzeeach topic.Eventhough i understand tensor calculus very well I just cant get anywhere with the differential forms.
Eventhough its not the worst book out there its not the best either.My advise,buy a better book.

Rating:
Summary: A Great Introduction to Diff. Geometry
Review: This book presents the basic concepts of differential geometry in a clear, concise manner using modern notation. Schutz's writing style is very readable and there is a considerable breadth of coverage. In areas where one might wish for greater depth, Schutz provides excellent references. My only regret is that the physical applications chapters weren't longer. An excellent starter book and a good quick reference if you continue in differential geometry, GR or field theory.

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Summary: A Very Accessible Book ! Buy It !
Review: This is a very enjoyable and clearly written book. From a physics point of view the approach is rather abstract, so although differential geometry is developed from 'scratch', it is probably better to have studied a more elementary text on the theory of 2-surfaces in 3-space first (eg Faber's book Differential Geometry and Relativity Theory ). The first chapter sets the mathematical background expected of the reader. The rudiments of analysis, topology, calculus of many variables and basic linear algebra is reviewed.The ensuing chapters cover differential geometry from a 'modern' viewpoint but the style is quite relaxed and the links to 'co-ordinate approach' are well explained. The exercises concentrate on the abstract approach. Throughout the book the underlying structure of manifolds is concentrated upon. No extra 'structure' eg connections and 'distance' concepts are added until the final chapter on Riemannian spaces. For example the metric tensor throughout the body of the book is merely used as a map between a tangent space and its dual space. It is only used as a 'distance' operator in the final chapter.For the purposes of independent study this is a sound book, there are hints and partial solutions for many of the exercises, which is always a welcome feature for those studying entirely on their own.

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Summary: Integrability conditions discussed
Review: Written in a attractive and even seductive way, relying more on Lie algebraic language than is typical, this book is probably as stimulating an intro. to modern geometry as you can find, within certain limits. The section on noncoordinate bases might have been more clearly written, however. Frobenius's theorm is discussed, something that Fomenko et al should have covered, and the section on connections can be worked throuigh independently of the heavy machinery of exterior differential forms, which is attractive for physics students.