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Introduction to Topology and Geometry.
An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition ". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contain...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken :
Wiley,
2014.
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| Edición: | 2nd ed. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- 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.
- 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.
- 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.