Introduction to Topology and Geometry, Second Edition

Description

An easily accessible introduction to over three centuries of innovations in geometryPraise for the First Edition“. . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained.” ?CHOICEThis fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparalleled range of topics. Illustrating modern mathematical topics, Introduction to Topology and Geometry, Second Edition discusses introductory topology, algebraic topology, knot theory, the geometry of surfaces, Riemann geometries, fundamental groups, and differential geometry, which opens the doors to a wealth of applications. With its logical, yet flexible, organization, the Second Edition:• Explores historical notes interspersed throughout the exposition to provide readers with a feel for how the mathematical disciplines and theorems came into being• Provides exercises ranging from routine to challenging, allowing readers at varying levels of study to master the concepts and methods• Bridges seemingly disparate topics by creating thoughtful and logical connections• Contains coverage on the elements of polytope theory, which acquaints readers with an exposition of modern theoryIntroduction to Topology and Geometry, Second Edition is an excellent introductory text for topology and geometry courses at the upper-undergraduate level. In addition, the book serves as an ideal reference for professionals interested in gaining a deeper understanding of the topic.Content: Chapter 1 Informal Topology (pages 1–12): Chapter 2 Graphs (pages 13–40): Chapter 3 Surfaces (pages 41–102): Chapter 4 Graphs and Surfaces (pages 103–142): Chapter 5 Knots and Links (pages 143–203): Chapter 6 The Differential Geometry of Surfaces (pages 205–257): Chapter 7 Riemann Geometries (pages 259–274): Chapter 8 Hyperbolic Geometry (pages 275–315): Chapter 9 The Fundamental Group (pages 317–359): Chapter 10 General Topology (pages 361–386): Chapter 11 Polytopes (pages 387–427):