04558nam 2200721 450 991080617000332120200520144314.00-471-66260-71-118-54614-81-118-54590-71-118-54591-5(CKB)3280000000033678(EBL)1771574(SSID)ssj0000877550(PQKBManifestationID)11446571(PQKBTitleCode)TC0000877550(PQKBWorkID)10829063(PQKB)10165907(MiAaPQ)EBC1771574(DLC) 2012051654(Au-PeEL)EBL1771574(CaPaEBR)ebr10915838(CaONFJC)MIL639071(OCoLC)889675104(PPN)19867872X(EXLCZ)99328000000003367820140902h20132013 uy 0engur|n|---|||||txtccrIntroduction to topology and geometry /Saul Stahl, Catherine StensonSecond edition.Hoboken, New Jersey :Wiley,2013.©20131 online resource (533 p.)Pure and Applied MathematicsDescription based upon print version of record.1-322-07820-3 1-118-10810-8 Includes bibliographical references and index.Cover ; Title Page ; Copyright ; Contents ; Preface ; Acknowledgments ; Chapter 1: Informal Topology ; Chapter 2: Graphs ; 2.1 Nodes and Arcs ; 2.2 Traversability ; 2.3 Colorings ; 2.4 Planarity ; 2.5 Graph Homeomorphisms ; Chapter 3: Surfaces ; 3.1 Polygonal Presentations ; 3.2 Closed Surfaces ; 3.3 Operations on Surfaces ; 3.4 Bordered Surfaces ; 3.5 Riemann Surfaces ; Chapter 4: Graphs and Surfaces ; 4.1 Embeddings and Their Regions ; 4.2 Polygonal Embeddings ; 4.3 Embedding a Fixed Graph ; 4.4 Voltage Graphs and Their Coverings ; Chapter 5: Knots and Links ; 5.1 Preliminaries5.2 Labelings 5.3 From Graphs to Links and on to Surfaces ; 5.4 The Jones Polynomial ; 5.5 The Jones Polynomial and Alternating Diagrams ; 5.6 Knots and Surfaces ; Chapter 6: The Differential Geometry of Surfaces ; 6.1 Surfaces, Normals, and Tangent Planes ; 6.2 The Gaussian Curvature ; 6.3 The First Fundamental Form ; 6.4 Normal Curvatures ; 6.5 The Geodesic Polar Parametrization ; 6.6 Polyhedral Surfaces I ; 6.7 Gauss''s Total Curvature Theorem ; 6.8 Polyhedral Surfaces II ; Chapter 7: Riemann Geometries ; Chapter 8: Hyperbolic Geometry ; 8.1 Neutral Geometry ; 8.2 The Upper Half-plane8.3 The Half-plane Theorem of Pythagoras 8.4 Half-plane Isometries ; Chapter 9: The Fundamental Group ; 9.1 Definitions and the Punctured Plane ; 9.2 Surfaces ; 9.3 3-manifolds ; 9.4 The Poincaré Conjecture ; Chapter 10: General Topology ; 10.1 Metric and Topological Spaces ; 10.2 Continuity and Homeomorphisms ; 10.3 Connectedness ; 10.4 Compactness ; Chapter 11: Polytopes ; 11.1 Introduction to Polytopes ; 11.2 Graphs of Polytopes ; 11.3 Regular Polytopes ; 11.4 Enumerating Faces ; Appendix A: Curves ; A.1 Parametrization of Curves and Arclength ; Appendix B: a Brief Survey of GroupsB.1 The General Background B.2 Abelian Groups ; B.3 Group Presentations ; Appendix C: Permutations ; Appendix D: Modular Arithmetic ; Appendix E: Solutions and Hints to Selected Exercises ; References and Resources ; Index ; Pure and Applied Mathematics"Presenting upper graduate level material in an accessible way for undergraduates, this Second Edition strikes a welcome balance between academic rigor and accessibility while covering an unparalleled range of topics, including the elements of projective geometry, conics and the applications and properties of conic selections, cross ratio points of infinity and fundamental transformations of projective geometry, the points of a homography/involution, and more. In addition, this comprehensive book includes numerous exercises and historical notes"--Provided by publisher.Pure and applied mathematics.TopologyGeometryTopology.Geometry.514MAT038000bisacshStahl Saul141807Stenson Catherine1972-MiAaPQMiAaPQMiAaPQBOOK9910806170003321Introduction to topology and geometry4038329UNINA