Introduction to Topology and Modern Geometry

A sweeping yet uniquely accessible introduction to a variety of central geometrical topics Covering over two centuries of innovations in many of the central geometrical disciplines, Introduction to Topology and Geometry is the most comprehensive introductory--level presentation of modern geometry currently available. Unique in both style and scope, the book covers an unparalleled range of topics, yet strikes a welcome balance between academic rigor and accessibility. By including subject matter previously relegated to higher--level graduate courses in mathematics and making it both interesting and accessible, the author presents a complete and cohesive picture of the science for students just entering the field. Historical notes throughout provide readers with a feel for how mathematical disciplines and theorems come into being.
Students and teachers will benefit from a uniquely unified treatment of such topics as:* Homeomorphism* Graph theory* Surface topology* Knot theory* Differential geometry* Riemannian geometry* Hyperbolic geometry* Algebraic topology* General topology Using a variety of theorems to tie these seemingly disparate topics together, the author demonstrates the essential unity of mathematics. A logical yet flexible organization makes the text useful for courses in basic geometry as well as those with a more topological focus, while exercises ranging from the routine to the challenging make the material accessible at varying levels of study.