UID:
almafu_9959328862402883
Format:
1 online resource.
Edition:
2nd edition / Saul Stahl, University of Kansas, Catherine Stenson, Juniata College.
ISBN:
1118545907
,
9781118545904
,
9781118545911
,
1118545915
,
9781118545935
,
1118545931
,
9781118546147
,
1118546148
,
1322078203
,
9781322078205
Series Statement:
Pure and applied mathematics
Content:
"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"--
Note:
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 Preliminaries.
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5.2 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.
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8.3 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 Groups.
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B.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.
Additional Edition:
Print version: Stahl, Saul. Introduction to topology and geometry. Hoboken, New Jersey : Wiley, 2013 ISBN 9781118108109
Language:
English
Keywords:
Electronic books.
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Electronic books.
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Electronic books.
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Electronic books.
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Electronic books.
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Electronic books.
URL:
https://onlinelibrary.wiley.com/doi/book/10.1002/9781118545904
URL:
https://onlinelibrary.wiley.com/doi/book/10.1002/9781118545904
URL:
https://onlinelibrary.wiley.com/doi/book/10.1002/9781118545904
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