{"product_id":"introduction-to-topology-and-geometry-isbn-9781118108109","title":"Introduction to Topology and Geometry","description":"\u003cp\u003e\u003cb\u003eAn easily accessible introduction to over three\u003c\/b\u003e \u003cb\u003ecenturies of innovations in geometry\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePraise for the First Edition\u003c\/p\u003e \u003cp\u003e“. . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained.” —CHOICE\u003c\/p\u003e \u003cp\u003eThis fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparalleled range of topics. \u003c\/p\u003e \u003cp\u003eIllustrating modern mathematical topics, \u003ci\u003eIntroduction to Topology and Geometry, Second Edition\u003c\/i\u003e discusses introductory topology, algebraic topology, knot theory, the geometry of surfaces, Riemann geometries, fundamental groups, and differential geometry, which opens the doors to a wealth of applications. With its logical, yet flexible, organization, the \u003ci\u003eSecond Edition:\u003cbr\u003e \u003cbr\u003e \u003c\/i\u003e• Explores historical notes interspersed throughout the exposition to provide readers with a feel for how the mathematical disciplines and theorems came into being\u003cbr\u003e \u003cbr\u003e • Provides exercises ranging from routine to challenging, allowing readers at varying levels of study to master the concepts and methods\u003cbr\u003e \u003cbr\u003e • Bridges seemingly disparate topics by creating thoughtful and logical connections\u003cbr\u003e \u003cbr\u003e • Contains coverage on the elements of polytope theory, which acquaints readers with an exposition of modern theory\u003cbr\u003e \u003cbr\u003e \u003ci\u003eIntroduction to Topology and Geometry, Second Edition\u003c\/i\u003e is an excellent introductory text for topology and geometry courses at the upper-undergraduate level. In addition, the book serves as an ideal reference for professionals interested in gaining a deeper understanding of the topic.\u003c\/p\u003e  \u003cp\u003ePreface ix\u003c\/p\u003e \u003cp\u003eAcknowledgments xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Informal Topology 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Graphs 13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Nodes and Arcs 13\u003c\/p\u003e \u003cp\u003e2.2 Traversability 16\u003c\/p\u003e \u003cp\u003e2.3 Colorings 21\u003c\/p\u003e \u003cp\u003e2.4 Planarity 25\u003c\/p\u003e \u003cp\u003e2.5 Graph Homeomorphisms 31\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Surfaces 41\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Polygonal Presentations 42\u003c\/p\u003e \u003cp\u003e3.2 Closed Surfaces 50\u003c\/p\u003e \u003cp\u003e3.3 Operations on Surfaces 71\u003c\/p\u003e \u003cp\u003e3.4 Bordered Surfaces 79\u003c\/p\u003e \u003cp\u003e3.5 Riemann Surfaces 94\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Graphs and Surfaces 103\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Embeddings and Their Regions 103\u003c\/p\u003e \u003cp\u003e4.2 Polygonal Embeddings 113\u003c\/p\u003e \u003cp\u003e4.3 Embedding a Fixed Graph 118\u003c\/p\u003e \u003cp\u003e4.4 Voltage Graphs and Their Coverings 128\u003c\/p\u003e \u003cp\u003eAppendix: 141\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Knots and Links 143\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Preliminaries 144\u003c\/p\u003e \u003cp\u003e5.2 Labelings 147\u003c\/p\u003e \u003cp\u003e5.3 From Graphs to Links and on to Surfaces 158\u003c\/p\u003e \u003cp\u003e5.4 The Jones Polynomial 169\u003c\/p\u003e \u003cp\u003e5.5 The Jones Polynomial and Alternating Diagrams 187\u003c\/p\u003e \u003cp\u003e5.6 Knots and surfaces 194\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 The Differential Geometry of Surfaces 205\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Surfaces, Normals, and Tangent Planes 205\u003c\/p\u003e \u003cp\u003e6.2 The Gaussian Curvature 212\u003c\/p\u003e \u003cp\u003e6.3 The First Fundamental Form 219\u003c\/p\u003e \u003cp\u003e6.4 Normal Curvatures 229\u003c\/p\u003e \u003cp\u003e6.5 The Geodesic Polar Parametrization 236\u003c\/p\u003e \u003cp\u003e6.6 Polyhedral Surfaces I 242\u003c\/p\u003e \u003cp\u003e6.7 Gauss’s Total Curvature Theorem 247\u003c\/p\u003e \u003cp\u003e6.8 Polyhedral Surfaces II 252\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Riemann Geometries 259\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Hyperbolic Geometry 275\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Neutral Geometry 275\u003c\/p\u003e \u003cp\u003e8.2 The Upper Half Plane 287\u003c\/p\u003e \u003cp\u003e8.3 The HalfPlane Theorem of Pythagoras 295\u003c\/p\u003e \u003cp\u003e8.4 HalfPlane Isometries 305\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 The Fundamental Group 317\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Definitions and the Punctured Plane 317\u003c\/p\u003e \u003cp\u003e9.2 Surfaces 325\u003c\/p\u003e \u003cp\u003e9.3 3Manifolds 332\u003c\/p\u003e \u003cp\u003e9.4 The Poincar´e Conjecture 357\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 General Topology 361\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Metric and Topological Spaces 361\u003c\/p\u003e \u003cp\u003e10.2 Continuity and Homeomorphisms 367\u003c\/p\u003e \u003cp\u003e10.3 Connectedness 377\u003c\/p\u003e \u003cp\u003e10.4 Compactness 379\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Polytopes 387\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction to Polytopes 387\u003c\/p\u003e \u003cp\u003e11.2 Graphs of Polytopes 401\u003c\/p\u003e \u003cp\u003e11.3 Regular Polytopes 405\u003c\/p\u003e \u003cp\u003e11.4 Enumerating Faces 415\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A Curves 429\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Parametrization of Curves and Arclength 429\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B A Brief Survey of Groups 441\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB.1 The General Background 441\u003c\/p\u003e \u003cp\u003eB.2 Abelian Groups 446\u003c\/p\u003e \u003cp\u003eB.3 Group Presentations 447\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix C Permutations 457\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix D Modular Arithmetic 461\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix E Solutions and Hints to Selected Exercises 465\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eReferences and Resources 497\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eSAUL STAHL, PhD,\u003c\/b\u003e is Professor in the Department of Mathematics at the University of Kansas and twice the winner of the Carl B. Allendoerfer Award from the Mathematical Association of America.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCATHERINE STENSON, PhD,\u003c\/b\u003e is Professor of Mathematics at Juniata College in Huntingdon, Pennsylvania.\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eAn easily accessible introduction to over three centuries of innovations in geometry\u003c\/b\u003e\u003c\/p\u003e Praise for the \u003ci\u003eFirst Edition\u003c\/i\u003e\u003cbr\u003e \". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained.\" —\u003ci\u003eCHOICE\u003c\/i\u003e  \u003cp\u003eThis fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparalleled range of topics.\u003c\/p\u003e \u003cp\u003eIllustrating modern mathematical topics, \u003ci\u003eIntroduction to Topology and Geometry, Second Edition\u003c\/i\u003e discusses introductory topology, algebraic topology, knot theory, the geometry of surfaces, Riemann geometries, fundamental groups, and differential geometry, which opens the doors to a wealth of applications. With its logical, yet flexible, organization, the \u003ci\u003eSecond Edition\u003c\/i\u003e:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eExplores historical notes interspersed throughout the exposition to provide readers with a feel for how the mathematical disciplines and theorems came into being\u003c\/li\u003e \u003cli\u003eProvides exercises ranging from routine to challenging, allowing readers at varying levels of study to master the concepts and methods\u003c\/li\u003e \u003cli\u003eBridges seemingly disparate topics by creating thoughtful and logical connections\u003c\/li\u003e \u003cli\u003eContains coverage on the elements of polytope theory, which acquaints readers with an exposition of modern theory\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eIntroduction to Topology and Geometry, Second Edition\u003c\/i\u003e is an excellent introductory text for topology and geometry courses at the upper-undergraduate level. In addition, the book serves as an ideal reference for professionals interested in gaining a deeper understanding of the topic.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989469020389,"sku":"NP9781118108109","price":142.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118108109.jpg?v=1761784223","url":"https:\/\/k12savings.com\/products\/introduction-to-topology-and-geometry-isbn-9781118108109","provider":"K12savings","version":"1.0","type":"link"}