Topology and Its Applications (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) 1st Edition by William F. Basener (PDF)

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Discover a unique and modern treatment of topology employing a cross-disciplinary approachImplemented 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 setsCompactnessHomotopySurface classificationIndex theory on surfacesManifolds and complexesTopological groupsThe fundamental group and homologySpecial “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.

User’s Reviews

Editorial Reviews: Review “…helpful to a beginning student, especially one who is interested in the connections between topology and the world of applications.” (Mathematical Reviews, 2007k) “…a welcome addition to what is now a long list of good undergraduate topology books.” (CHOICE, August 2007)”..a celebration of topology and its many applications. I enjoyed reading it and believe that it would be an interesting textbook from which to learn.” (MAA Reviews, January 12, 2007) From the Inside Flap 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 setsCompactnessHomotopySurface classificationIndex theory on surfacesManifolds and complexesTopological groupsThe fundamental group and homologySpecial “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. From the Back Cover 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 setsCompactnessHomotopySurface classificationIndex theory on surfacesManifolds and complexesTopological groupsThe fundamental group and homologySpecial “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. About the Author 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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Book arrived on time and in very good disposition.The book is very good in that it associates some very important applications to topology. However it has several typo’s and a few errors.

⭐Excellent book, very deep rigouroud and friendly.I use it for teaching

⭐The book is unique in its attempt to visualize Topology.The Schaum’s outline on Topology may be all needed to pass an exam,But this book has a lot more figures and applications than many topology books.Colored figures would improve it.

⭐The book is terrific, but it requires a level of knowledge and mathematical maturity typically not found in the repertoire of undergraduate students. If you are a graduate student seeking to learn about the various subfields of topology in a rigorous definition, proposition, theorem, proof, examples framework, then this book is for you. It is also a good reference for the professional mathematician. But, whatever you do, study a treatise on point-set topology before venturing to learn the gems of this book.The book is well-written. My only complaint is that it is too brief.

⭐On the upside, the author strives and does a good job to convey intuition and visual examples, which I think is important and not enough people do this, so kudos to the author for this.On the downside, there are many errors in the exposition and proofs. They range from innocuous (pg. 20, Lemma 6 says ‘union’ when the equation clearly and correctly shows ‘intersection’) to intermediate (pg 28, Theorem 9, he claims ‘f(f^-1(B)) = B’ when really the lhs is a subset of the rhs), to ones that threw me off (pg. 24, ‘U x V = p_1(U) intersect p_2(V)’ should be ‘U x V = p_1^-1(U) intersect p_2^-1(V)’; and pg 65, theorem 31, has incorrect / inconsistent variable references, and states without proof that open balls are path connected. That last one isn’t an error, but I had to look up, and this author, who is careful with the concepts part, seems like it would be his style to include it).All in all, I could recommend a future version if the errors are corrected. It gave me insights and had a conversational tone that made it easy to learn from, but I had to stop because the errors threw me off too much to have confidence that I’ll catch more subtle problems in more unfamiliar territory. I hope the author does an updated version with corrections.

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