LEADER 04558nam 2200721 450 001 9910806170003321 005 20200520144314.0 010 $a0-471-66260-7 010 $a1-118-54614-8 010 $a1-118-54590-7 010 $a1-118-54591-5 035 $a(CKB)3280000000033678 035 $a(EBL)1771574 035 $a(SSID)ssj0000877550 035 $a(PQKBManifestationID)11446571 035 $a(PQKBTitleCode)TC0000877550 035 $a(PQKBWorkID)10829063 035 $a(PQKB)10165907 035 $a(MiAaPQ)EBC1771574 035 $a(DLC) 2012051654 035 $a(Au-PeEL)EBL1771574 035 $a(CaPaEBR)ebr10915838 035 $a(CaONFJC)MIL639071 035 $a(OCoLC)889675104 035 $a(PPN)19867872X 035 $a(EXLCZ)993280000000033678 100 $a20140902h20132013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to topology and geometry /$fSaul Stahl, Catherine Stenson 205 $aSecond edition. 210 1$aHoboken, New Jersey :$cWiley,$d2013. 210 4$dİ2013 215 $a1 online resource (533 p.) 225 1 $aPure and Applied Mathematics 300 $aDescription based upon print version of record. 311 $a1-322-07820-3 311 $a1-118-10810-8 320 $aIncludes bibliographical references and index. 327 $aCover ; 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 Preliminaries 327 $a5.2 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-plane 327 $a8.3 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 Poincare? 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 Groups 327 $aB.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 330 $a"Presenting upper graduate level material in an accessible way for undergraduates, this Second Edition strikes a welcome balance between academic rigor and accessibility while covering an unparalleled range of topics, including the elements of projective geometry, conics and the applications and properties of conic selections, cross ratio points of infinity and fundamental transformations of projective geometry, the points of a homography/involution, and more. In addition, this comprehensive book includes numerous exercises and historical notes"--$cProvided by publisher. 410 0$aPure and applied mathematics. 606 $aTopology 606 $aGeometry 615 0$aTopology. 615 0$aGeometry. 676 $a514 686 $aMAT038000$2bisacsh 700 $aStahl$b Saul$0141807 702 $aStenson$b Catherine$f1972- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910806170003321 996 $aIntroduction to topology and geometry$94038329 997 $aUNINA