{"product_id":"topology-and-its-applications-9780471687559","title":"Topology and Its Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eReflecting the emerging role of topology, this book is uniquely innovative in its cross-disciplinary approach. * Includes topological applications in the scientific fields of physics, chemistry, biology, engineering, and economics. * Applets are available via a related website.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"…helpful to a beginning student, especially one who is interested in the connections between topology and the world of applications.\" (\u003ci\u003eMathematical Reviews\u003c\/i\u003e, 2007k)  \u003cp\u003e\"…a welcome addition to what is now a long list of good undergraduate topology books.\" (\u003ci\u003eCHOICE\u003c\/i\u003e, August 2007)\u003c\/p\u003e \u003cp\u003e\"..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.\" (\u003ci\u003eMAA Reviews\u003c\/i\u003e, January 12, 2007)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.  \u003cp\u003eIntroduction.\u003c\/p\u003e \u003cp\u003eI. 1 Preliminaries.\u003c\/p\u003e \u003cp\u003e1.2 Cardinality.\u003c\/p\u003e \u003cp\u003e1. Continuity.\u003c\/p\u003e \u003cp\u003e1. 1 Continuity and Open Sets in R\u003csup\u003en\u003c\/sup\u003e.\u003c\/p\u003e \u003cp\u003e1.2 Continuity and Open Sets in Topological Spaces.\u003c\/p\u003e \u003cp\u003e1.3 Metric, Product, and Quotient Topologies.\u003c\/p\u003e \u003cp\u003e1.4 Subsets of Topological Spaces.\u003c\/p\u003e \u003cp\u003e1.5 Continuous Functions and Topological Equivalence.\u003c\/p\u003e \u003cp\u003e1.6 Surfaces.\u003c\/p\u003e \u003cp\u003e1.7 Application: Chaos in Dynamical Systems.\u003c\/p\u003e \u003cp\u003e1.7.1 History of Chaos.\u003c\/p\u003e \u003cp\u003e1.7.2 A Simple Example.\u003c\/p\u003e \u003cp\u003e1.7.3 Notions of Chaos.\u003c\/p\u003e \u003cp\u003e2. Compactness and Connectedness.\u003c\/p\u003e \u003cp\u003e2.1 Closed Bounded Subsets of R.\u003c\/p\u003e \u003cp\u003e2.2 Compact Spaces.\u003c\/p\u003e \u003cp\u003e2.3 Identification Spaces and Compactness.\u003c\/p\u003e \u003cp\u003e2.4 Connectedness and path-connectedness.\u003c\/p\u003e \u003cp\u003e2.5 Cantor Sets.\u003c\/p\u003e \u003cp\u003e2.6 Application: Compact Sets in Population Dynamics and Fractals.\u003c\/p\u003e \u003cp\u003e3. Manifolds and Complexes.\u003c\/p\u003e \u003cp\u003e3.1 Manifolds.\u003c\/p\u003e \u003cp\u003e3.2 Triangulations.\u003c\/p\u003e \u003cp\u003e3.3 Classification of Surfaces.\u003c\/p\u003e \u003cp\u003e3.3.1 Gluing Disks.\u003c\/p\u003e \u003cp\u003e3.3.2 Planar Models.\u003c\/p\u003e \u003cp\u003e3.3.3 Classification of Surfaces.\u003c\/p\u003e \u003cp\u003e3.4 Euler Characteristic.\u003c\/p\u003e \u003cp\u003e3.5 Topological Groups.\u003c\/p\u003e \u003cp\u003e3.6 Group Actions and Orbit Spaces.\u003c\/p\u003e \u003cp\u003e3.6.1 Flows on Tori.\u003c\/p\u003e \u003cp\u003e3.7 Applications.\u003c\/p\u003e \u003cp\u003e3.7.1 Robotic Coordination and Configuration Spaces.\u003c\/p\u003e \u003cp\u003e3.7.2 Geometry of Manifolds.\u003c\/p\u003e \u003cp\u003e3.7.3 The Topology of the Universe.\u003c\/p\u003e \u003cp\u003e4. Homotopy and the Winding Number.\u003c\/p\u003e \u003cp\u003e4.1 Homotopy and Paths.\u003c\/p\u003e \u003cp\u003e4.2 The Winding Number.\u003c\/p\u003e \u003cp\u003e4.3 Degrees of Maps.\u003c\/p\u003e \u003cp\u003e4.4 The Brouwer Fixed Point Theorem.\u003c\/p\u003e \u003cp\u003e4.5 The Borsuk-Ulam Theorem.\u003c\/p\u003e \u003cp\u003e4.6 Vector Fields and the Poincare' Index Theorem.\u003c\/p\u003e \u003cp\u003e4.7 Applications I.\u003c\/p\u003e \u003cp\u003e4.7.1 The Fundamental Theorem of Algebra.\u003c\/p\u003e \u003cp\u003e4.7.2 Sandwiches.\u003c\/p\u003e \u003cp\u003e4.7.3 Game Theory and Nash Equilibria.\u003c\/p\u003e \u003cp\u003e4.8 Applications 1I: Calculus.\u003c\/p\u003e \u003cp\u003e4.8.1 Vector Fields, Path Integrals, and the Winding Number.\u003c\/p\u003e \u003cp\u003e4.8.2 Vector Fields on Surfaces.\u003c\/p\u003e \u003cp\u003e4.8.3 1ndex Theory for n-Symmetry Fields.\u003c\/p\u003e \u003cp\u003e4.9 Index Theory in Computer Graphics.\u003c\/p\u003e \u003cp\u003e5. Fundamental Group.\u003c\/p\u003e \u003cp\u003e5. I Definition and Basic Properties.\u003c\/p\u003e \u003cp\u003e5.2 Homotopy Equivalence and Retracts.\u003c\/p\u003e \u003cp\u003e5.3 The Fundamental Group of Spheres and Tori.\u003c\/p\u003e \u003cp\u003e5.4 The Seifert-van Kampen Theorem.\u003c\/p\u003e \u003cp\u003e5.4.1 Flowers and Surfaces.\u003c\/p\u003e \u003cp\u003e5.4.2 The Seifert-van Kampen Theorem.\u003c\/p\u003e \u003cp\u003e5.5 Covering spaces.\u003c\/p\u003e \u003cp\u003e5.6 Group Actions and Deck Transformations.\u003c\/p\u003e \u003cp\u003e5.7 Applications.\u003c\/p\u003e \u003cp\u003e5.7.1 Order and Emergent Patterns in Condensed Matter Physics.\u003c\/p\u003e \u003cp\u003e6. Homology.\u003c\/p\u003e \u003cp\u003e6.1 A-complexes.\u003c\/p\u003e \u003cp\u003e6.2 Chains and Boundaries.\u003c\/p\u003e \u003cp\u003e6.3 Examples and Computations.\u003c\/p\u003e \u003cp\u003e6.4 Singular Homology.\u003c\/p\u003e \u003cp\u003e6.5 Homotopy Invariance.\u003c\/p\u003e \u003cp\u003e6.6 Brouwer Fixed Point Theorem for D\u003csup\u003en\u003c\/sup\u003e.\u003c\/p\u003e \u003cp\u003e6.7 Homology and the Fundamental Group.\u003c\/p\u003e \u003cp\u003e6.8 Betti Numbers and the Euler Characteristic.\u003c\/p\u003e \u003cp\u003e6.9 Computational Homology.\u003c\/p\u003e \u003cp\u003e6.9.1 Computing Betti Numbers.\u003c\/p\u003e \u003cp\u003e6.9.2 Building a Filtration.\u003c\/p\u003e \u003cp\u003e6.9.3 Persistent Homology.\u003c\/p\u003e \u003cp\u003eAppendix A: Knot Theory.\u003c\/p\u003e \u003cp\u003eAppendix B: Groups.\u003c\/p\u003e \u003cp\u003eAppendix C: Perspectives in Topology.\u003c\/p\u003e \u003cp\u003eC.1 Point Set Topology.\u003c\/p\u003e \u003cp\u003eC.2 Geometric Topology.\u003c\/p\u003e \u003cp\u003eC.3 Algebraic Topology.\u003c\/p\u003e \u003cp\u003eC.4 Combinatorial Topology.\u003c\/p\u003e \u003cp\u003eC.5 Differential Topology.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003eBibliography.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":53515431575895,"sku":"9780471687559","price":107.06,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/bookcurl.com\/products\/topology-and-its-applications-9780471687559","provider":"Book Curl","version":"1.0","type":"link"}