Geometry with an Introduction to Cosmic Topology
by Mike Hitchman
Number of pages: 177
This text develops non-Euclidean geometry and geometry on surfaces at a level appropriate for undergraduate students who have completed a multivariable calculus course and are ready for a course in which to practice habits of thought needed in advanced courses of the undergraduate mathematics curriculum. The text is also suited to independent study.
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by Silvio Levy - Cambridge University Press
Felix Klein discovered in 1879 that the surface that we now call the Klein quartic has many remarkable properties, including an incredible 336-fold symmetry. This volume explores the rich tangle of properties surrounding this multiform object.
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These notes are intended as a relatively quick introduction to hyperbolic geometry. They review the wonderful history of non-Euclidean geometry. They develop a number of the properties that are particularly important in topology and group theory.
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In this course the students are introduced, or re-introduced, to the method of Mathematical Proof. You will be introduced to new and interesting areas in Geometry, with most of the time spent on the study of Hyperbolic Geometry.
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Renowned for its lucid yet meticulous exposition, this text follows the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to such advanced topics as inversion and transformations.