Geometries and Groups (Universitext)

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Product Description

This is a quite exceptional book, a lively and approachable treatment of an important field of mathematics given in a masterly style. Assuming only a school background, the authors develop locally Euclidean geometries, going as far as the modular space of structures on the torus, treated in terms of Lobachevsky's non-Euclidean geometry. Each section is carefully motivated by discussion of the physical and general scientific implications of the mathematical argument, and its place in the history of mathematics and philosophy. The book is expected to find a place alongside classics such as Hilbert and Cohn-Vossen's "Geometry and the imagination" and Weyl's "Symmetry".

Geometries and Groups (Universitext) Review

Shafarevich at his usual best writing about geometries in general. Such a fascinating subject and odd that most curricula in mathematical sciences excludes it. Bizarre but not surprising at all. Shafarevich demonstrates the vastness of Geometry on a philosophico-algebraic level; geometric intuition, how it is, when it is formed in one area is applicable in another area. And that geometric intuition is capable of creating a new geometry for each sphere of consciousness. This is how he sets it up. It will be your loss if, as many technicians, you should skim over the textual explanations at the outset.

Although the difficulty of the mathematics is only first year university level, he manages to give a vast coverage and give a deep sense of what theoretical geometry is like.

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