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