Discover a unique and modern treatment of topology employing across-disciplinary approach
Implemented recently to understand diverse topics, such as cellbiology, superconductors, and robot motion, topology has beentransformed from a theoretical field that highlights mathematicaltheory to a subject that plays a growing role in nearly all fieldsof scientific investigation. Moving from the concrete to theabstract, Topology and Its Applications displays both the beautyand utility of topology, first presenting the essentials oftopology followed by its emerging role within the new frontiers inresearch.
Filling a gap between the teaching of topology and its modernuses in real-world phenomena, Topology and Its Applications isorganized around the mathematical theory of topology, a frameworkof rigorous theorems, and clear, elegant proofs.
This book is the first of its kind to present applications incomputer graphics, economics, dynamical systems, condensed matterphysics, biology, robotics, chemistry, cosmology, material science,computational topology, and population modeling, as well as otherareas of science and engineering. Many of these applications arepresented in optional sections, allowing an instructor to customizethe presentation.
The author presents a diversity of topological areas, includingpoint-set topology, geometric topology, differential topology, andalgebraic/combinatorial topology. Topics within these areasinclude:
* Open sets
* Compactness
* Homotopy
* Surface classification
* Index theory on surfaces
* Manifolds and complexes
* Topological groups
* The fundamental group and homology
Special "core intuition" segments throughout the book brieflyexplain the basic intuition essential to understanding severaltopics. A generous number of figures and examples, many of whichcome from applications such as liquid crystals, space probe data,and computer graphics, are all available from the publisher's Website.