Topology and Its Applications / Wiley Series in Pure and Applied Mathematics (ePub)
(Sprache: Englisch)
Discover a unique and modern treatment of topology employing a
cross-disciplinary approach
Implemented recently to understand diverse topics, such as cell
biology, superconductors, and robot motion, topology has been
transformed from a theoretical...
cross-disciplinary approach
Implemented recently to understand diverse topics, such as cell
biology, superconductors, and robot motion, topology has been
transformed from a theoretical...
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Discover a unique and modern treatment of topology employing a
cross-disciplinary approach
Implemented recently to understand diverse topics, such as cell
biology, superconductors, and robot motion, topology has been
transformed from a theoretical field that highlights mathematical
theory to a subject that plays a growing role in nearly all fields
of scientific investigation. Moving from the concrete to the
abstract, Topology and Its Applications displays both the beauty
and utility of topology, first presenting the essentials of
topology followed by its emerging role within the new frontiers in
research.
Filling a gap between the teaching of topology and its modern
uses in real-world phenomena, Topology and Its Applications is
organized around the mathematical theory of topology, a framework
of rigorous theorems, and clear, elegant proofs.
This book is the first of its kind to present applications in
computer graphics, economics, dynamical systems, condensed matter
physics, biology, robotics, chemistry, cosmology, material science,
computational topology, and population modeling, as well as other
areas of science and engineering. Many of these applications are
presented in optional sections, allowing an instructor to customize
the presentation.
The author presents a diversity of topological areas, including
point-set topology, geometric topology, differential topology, and
algebraic/combinatorial topology. Topics within these areas
include:
* 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 briefly
explain the basic intuition essential to understanding several
topics. A generous number of figures and examples, many of which
come from applications such as liquid crystals, space probe data,
and computer graphics, are all available from the publisher's Web
site.
cross-disciplinary approach
Implemented recently to understand diverse topics, such as cell
biology, superconductors, and robot motion, topology has been
transformed from a theoretical field that highlights mathematical
theory to a subject that plays a growing role in nearly all fields
of scientific investigation. Moving from the concrete to the
abstract, Topology and Its Applications displays both the beauty
and utility of topology, first presenting the essentials of
topology followed by its emerging role within the new frontiers in
research.
Filling a gap between the teaching of topology and its modern
uses in real-world phenomena, Topology and Its Applications is
organized around the mathematical theory of topology, a framework
of rigorous theorems, and clear, elegant proofs.
This book is the first of its kind to present applications in
computer graphics, economics, dynamical systems, condensed matter
physics, biology, robotics, chemistry, cosmology, material science,
computational topology, and population modeling, as well as other
areas of science and engineering. Many of these applications are
presented in optional sections, allowing an instructor to customize
the presentation.
The author presents a diversity of topological areas, including
point-set topology, geometric topology, differential topology, and
algebraic/combinatorial topology. Topics within these areas
include:
* 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 briefly
explain the basic intuition essential to understanding several
topics. A generous number of figures and examples, many of which
come from applications such as liquid crystals, space probe data,
and computer graphics, are all available from the publisher's Web
site.
Autoren-Porträt von William F. Basener
WILLIAM F. BASENER, PhD, is an Assistant Professor in the Department of Mathematics and Statistics at Rochester Institute of Technology in Rochester, New York. He received his PhD in mathematics in 2001 from Boston University. His research interests include dynamical systems, differential equations, applied topology, economics, and the topology of manifolds. Dr. Basener is the recipient of numerous teaching awards.
Bibliographische Angaben
- Autor: William F. Basener
- 2013, 1. Auflage, 384 Seiten, Englisch
- Verlag: John Wiley & Sons
- ISBN-10: 1118626222
- ISBN-13: 9781118626221
- Erscheinungsdatum: 12.06.2013
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eBook Informationen
- Dateiformat: ePub
- Grösse: 6.61 MB
- Mit Kopierschutz
Sprache:
Englisch
Kopierschutz
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