Kategoria BISAC: Mathematics >> Geometry - Non-Euclidean

What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common? All are related to a type of manifold called locally mixed symmetric spaces in this book. The presentation emphasizes geometric concepts and relations and gives each reader the "roter Faden", starting from the basics and proceeding towards quite advanced topics which lie at the intersection of differential and algebraic geometry, algebra and topology.

Avoiding technicalities and assuming only a working knowledge of real Lie groups, the text...

This undergraduate textbook provides a comprehensive treatment of Euclidean and transformational geometries, supplemented by substantial discussions of topics from various non-Euclidean and less commonly taught geometries, making it ideal for both mathematics majors and pre-service teachers. Emphasis is placed on developing students' deductive reasoning skills as they are guided through proofs, constructions, and solutions to problems.  The text frequently emphasizes strategies and heuristics of problem solving including constructing proofs (Where to begin? How to proceed? Which...