Geometry with an Introduction to Cosmic Topology

Livro digital

Título:
Geometry with an Introduction to Cosmic Topology

Autor:
Michael P. Hitchman

Categoria:
Tecnologia > Geral

Doador:
Raffaello D. N.

Sinopse:
Geometry with an Introduction to Cosmic Topology approaches geometry through one of the most natural large questions in mathematics: what shape could the universe have? Its table of contents begins with an invitation to geometry, then develops the complex plane, transformations, Mobius transformations, hyperbolic geometry, elliptic geometry, geometry on surfaces, quotient spaces, and finally cosmic topology. The text builds the subject through the Erlangen Program, using spaces and transformation groups as the organizing lens. It gives special attention to inversions, the Poincare disk model, measurement in non-Euclidean geometries, curvature, the Gauss-Bonnet formula, and the connection between two-dimensional surfaces and possible three-dimensional shapes of the universe. This is an elegant undergraduate bridge between geometry, topology, and cosmology. Readers with multivariable calculus background get a coherent mathematical story rather than a loose collection of theorems, with enough essays, constructions, and exercises to support both classroom use and independent study.