This is the first volume of a three-volume introduction to modern geometry which emphasizes applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory. This new edition offers substantial revisions, and the material is written in concrete language with terminology acceptable to physicists.
Modern Geometry - Methods and Applications
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Text: English (translation)
Original Language: Russian
Original Language: Russian
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13 of 15 people found the following review helpful:
5.0 out of 5 stars
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This review is from: Modern Geometry - Methods and Applications: Part I: The Geometry of Surfaces, Transformation Groups, and Fields (Graduate Texts in Mathematics) (Pt. 1) (Hardcover)
There's some great material that professor Novikov presents in this three volume set, indispensible to the mathematician and physicist. What seperates it (and elevates it) from it's numerous competitors in the differential geometry textbook line is the following:1. He presents pretty much every idea in multiple ways and from multiple viewpoints, illustrating the ubiquity and flexibility of the ideas. 2. He gives concrete examples of the concepts so you can see them in action. The examples are selected from a very wide range of physical problems. 3. He presents the ideas in a formal setting first but then gives them in a form useful for actual computation or working problems one would actually encounter. 4. He segregates the material cleanly into what I would call "algebraic" and "differential" sections. Thus, if you are interested in only a specific viewpoint or topic, you can fairly well read that section independent of the others. The book's chapters are for the most part independent. 5. There is virtually no prerequisite knowledge for this text, and yet it provides enough to not bore even the "sophisticated reader", for even they will no doubt learn something from the elegeant presentation. I only own the first volume, but I have looked at the others in libraries and I would say for the most part the above holds for them too, making this three-volume set truly a masterpiece, a pearl in the sea of mathematical literature. Anyone iterested in a readable, relevant, viable introduction to the huge world of differential gometry will not be disappointed.
9 of 14 people found the following review helpful:
4.0 out of 5 stars
Required background reading...,
By Professor Joseph L. McCauley "Joseph L. McCauley" (Austria+Texas) - See all my reviews
This review is from: Modern Geometry - Methods and Applications: Part I: The Geometry of Surfaces, Transformation Groups, and Fields (Graduate Texts in Mathematics) (Pt. 1) (Hardcover)
..if you want to understand the much of Arnol'd's book on classical mechanics. Written for physicists in language that physicists can follow, the book starts with advanced calculus (geometry of surfaces and curves in 2D and 3D) and provides a readable and informative introduction to Riemannian geometry, including connections defined by structure coefficients of a Lie algebra, all the way through gauge theories. However, the books by Schutz and by Nakahara cover interesting topics not included here, so see them as well.
6 of 17 people found the following review helpful:
5.0 out of 5 stars
Best book to begin differential geometry with ..,
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This review is from: Modern Geometry - Methods and Applications: Part I: The Geometry of Surfaces, Transformation Groups, and Fields (Graduate Texts in Mathematics) (Pt. 1) (Hardcover)
Written by prominent mathematicians it is the one of the best books on the topic .The language of the book is very simple so it is suitable for physics ...
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Inside This Book
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First Sentence:
We begin by discussing some of the concepts fundamental to geometry. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
symmetric connexion compatible, rik rlm, conformal form, full isometry group, direct isometries, metric gij, extended phase space, tensor operation, spinor representation, covariant differentiation, invariant scalar product, covector field, metric gab, underlying space, curvature form, natural parameter, curvature tensor, second fundamental form Key Phrases - Capitalized Phrases (CAPs): (learn more)
The Algebraic Theory, The Differential Calculus of Tensors, The Theory of Surfaces, Implicit Function Theorem, Examples of Lagrangians, Space-like Surfaces, The Behaviour of Tensors Under Mappings New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
We begin by discussing some of the concepts fundamental to geometry. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
symmetric connexion compatible, rik rlm, conformal form, full isometry group, direct isometries, metric gij, extended phase space, tensor operation, spinor representation, covariant differentiation, invariant scalar product, covector field, metric gab, underlying space, curvature form, natural parameter, curvature tensor, second fundamental form Key Phrases - Capitalized Phrases (CAPs): (learn more)
The Algebraic Theory, The Differential Calculus of Tensors, The Theory of Surfaces, Implicit Function Theorem, Examples of Lagrangians, Space-like Surfaces, The Behaviour of Tensors Under Mappings New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
See all 100 books this book cites
- Cyclotomic Fields (Graduate Texts in Mathematics) by S. Lang in Front Matter, Back Matter (1), and Back Matter (2)
- Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1) by John B Conway in Front Matter, and Back Matter
- Algebraic Number Theory (Graduate Texts in Mathematics) by Serge Lang in Back Matter (1), and Back Matter (2)
- Electrodynamics of Continuous Media, Second Edition: Volume 8 (Course of Theoretical Physics) by L D Landau in Back Matter
- Foundations of Hyperbolic Manifolds (Graduate Texts in Mathematics) by John G. Ratcliffe in Back Matter
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