Customer Reviews

Modern Geometry - Methods and Applications: Part I: The Geometry of Surfaces, Transformation Groups, and Fields (Graduate Texts in Mathematics) (Pt. 1)

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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.

..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.

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 ...