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.
